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7.5 AVL 树 *
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0.1 关于本书
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0.2 如何使用本书
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0.3 小结
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第 1 章 初识算法
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第 1 章 初识算法
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1.1 算法无处不在
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1.2 算法是什么
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1.3 小结
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<span class="md-ellipsis">
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第 2 章 复杂度分析
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第 2 章 复杂度分析
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2.1 算法效率评估
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</span>
|
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|
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|
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</a>
|
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</li>
|
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2.2 迭代与递归
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|
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|
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|
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</a>
|
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</li>
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2.3 时间复杂度
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|
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|
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|
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</a>
|
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</li>
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2.4 空间复杂度
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|
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|
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</a>
|
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</li>
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2.5 小结
|
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</span>
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|
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|
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第 3 章 数据结构
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3.1 数据结构分类
|
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</a>
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3.3 数字编码 *
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</a>
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3.4 字符编码 *
|
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|
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</a>
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3.5 小结
|
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|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
|
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|
||
<span class="md-ellipsis">
|
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第 4 章 数组与链表
|
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|
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<label class="md-nav__link " for="__nav_5">
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第 4 章 数组与链表
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
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4.1 数组
|
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</span>
|
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|
||
|
||
</a>
|
||
</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
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<span class="md-ellipsis">
|
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4.2 链表
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
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4.3 列表
|
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</span>
|
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|
||
|
||
</a>
|
||
</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
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4.4 内存与缓存 *
|
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</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近添加">
|
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</span>
|
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|
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|
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|
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</a>
|
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
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4.5 小结
|
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|
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|
||
|
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</ul>
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</nav>
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|
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|
||
|
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|
||
|
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<li class="md-nav__item md-nav__item--nested">
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|
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|
||
<span class="md-ellipsis">
|
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第 5 章 栈与队列
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第 5 章 栈与队列
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5.1 栈
|
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</span>
|
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|
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|
||
</a>
|
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</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
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5.2 队列
|
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</span>
|
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|
||
|
||
</a>
|
||
</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
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|
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5.3 双向队列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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5.4 小结
|
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</span>
|
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|
||
|
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|
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|
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||
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||
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<li class="md-nav__item md-nav__item--nested">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
|
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|
||
<span class="md-ellipsis">
|
||
第 6 章 哈希表
|
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|
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|
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|
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</a>
|
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|
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<label class="md-nav__link " for="__nav_7">
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
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第 6 章 哈希表
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
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|
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<span class="md-ellipsis">
|
||
6.1 哈希表
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
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|
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<span class="md-ellipsis">
|
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6.2 哈希冲突
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
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6.3 哈希算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
||
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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6.4 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
||
|
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|
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|
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</ul>
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</nav>
|
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|
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|
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|
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|
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|
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--active md-nav__item--nested">
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<span class="md-ellipsis">
|
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第 7 章 树
|
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|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="true">
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第 7 章 树
|
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<ul class="md-nav__list" data-md-scrollfix>
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|
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<li class="md-nav__item">
|
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<a href="../binary_tree/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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7.1 二叉树
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../binary_tree_traversal/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
7.2 二叉树遍历
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../array_representation_of_tree/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
7.3 二叉树数组表示
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../binary_search_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.4 二叉搜索树
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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|
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|
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<label class="md-nav__link md-nav__link--active" for="__toc">
|
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|
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|
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<span class="md-ellipsis">
|
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7.5 AVL 树 *
|
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</span>
|
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|
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|
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<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
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<a href="./" class="md-nav__link md-nav__link--active">
|
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|
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|
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<span class="md-ellipsis">
|
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7.5 AVL 树 *
|
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</span>
|
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|
||
|
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</a>
|
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|
||
|
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|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
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目录
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|
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<li class="md-nav__item">
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<a href="#751-avl" class="md-nav__link">
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7.5.1 AVL 树常见术语
|
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</a>
|
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|
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<nav class="md-nav" aria-label="7.5.1 AVL 树常见术语">
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<a href="#1" class="md-nav__link">
|
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1. 节点高度
|
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</a>
|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#2" class="md-nav__link">
|
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2. 节点平衡因子
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|
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|
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|
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</ul>
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|
||
<a href="#752-avl" class="md-nav__link">
|
||
7.5.2 AVL 树旋转
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="7.5.2 AVL 树旋转">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1_1" class="md-nav__link">
|
||
1. 右旋
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2_1" class="md-nav__link">
|
||
2. 左旋
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#3" class="md-nav__link">
|
||
3. 先左旋后右旋
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#4" class="md-nav__link">
|
||
4. 先右旋后左旋
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#5" class="md-nav__link">
|
||
5. 旋转的选择
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#753-avl" class="md-nav__link">
|
||
7.5.3 AVL 树常用操作
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="7.5.3 AVL 树常用操作">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1_2" class="md-nav__link">
|
||
1. 插入节点
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2_2" class="md-nav__link">
|
||
2. 删除节点
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#3_1" class="md-nav__link">
|
||
3. 查找节点
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#754-avl" class="md-nav__link">
|
||
7.5.4 AVL 树典型应用
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.6 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_heap/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 8 章 堆
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<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>
|
||
第 8 章 堆
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.1 堆
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.2 建堆操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/top_k/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.3 Top-K 问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.4 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_graph/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 9 章 图
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 9 章 图
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.1 图
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.2 图基础操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.3 图的遍历
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.4 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_searching/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 10 章 搜索
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 10 章 搜索
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.1 二分查找
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.2 二分查找插入点
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.3 二分查找边界
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.4 哈希优化策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.5 重识搜索算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.6 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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|
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|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
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|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_sorting/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 11 章 排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 11 章 排序
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.1 排序算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.2 选择排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.3 冒泡排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.4 插入排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.5 快速排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.6 归并排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.7 堆排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.8 桶排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.9 计数排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.10 基数排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.11 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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|
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|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
|
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|
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|
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|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
|
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|
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|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 12 章 分治
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_13">
|
||
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
||
</div>
|
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|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_13">
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<span class="md-nav__icon md-icon"></span>
|
||
第 12 章 分治
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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|
||
|
||
|
||
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.1 分治算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.2 分治搜索策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.3 构建树问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.4 汉诺塔问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.5 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
|
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|
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|
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|
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<div class="md-nav__link md-nav__container">
|
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<a href="../../chapter_backtracking/" class="md-nav__link ">
|
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|
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|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 13 章 回溯
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_14">
|
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<span class="md-nav__icon md-icon"></span>
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</label>
|
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|
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</div>
|
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|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_14">
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<span class="md-nav__icon md-icon"></span>
|
||
第 13 章 回溯
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
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|
||
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.1 回溯算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
13.2 全排列问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.3 子集和问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.4 N 皇后问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
13.5 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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|
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|
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|
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|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
|
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|
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|
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|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_dynamic_programming/" class="md-nav__link ">
|
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|
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|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 14 章 动态规划
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
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<label class="md-nav__link " for="__nav_15">
|
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
|
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第 14 章 动态规划
|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
14.1 初探动态规划
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
14.2 DP 问题特性
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
14.3 DP 解题思路
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
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14.4 0-1 背包问题
|
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</a>
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14.5 完全背包问题
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</a>
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14.6 编辑距离问题
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14.7 小结
|
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第 15 章 贪心
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|
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15.4 最大切分乘积问题
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|
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|
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15.5 小结
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|
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|
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第 16 章 附录
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16.1 编程环境安装
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|
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|
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|
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|
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16.2 一起参与创作
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<h1 id="75-avl">7.5 AVL 树 *<a class="headerlink" href="#75-avl" title="Permanent link">¶</a></h1>
|
||
<p>在“二叉搜索树”章节中，我们提到，在多次插入和删除操作后，二叉搜索树可能退化为链表。在这种情况下，所有操作的时间复杂度将从 <span class="arithmatex">\(O(\log n)\)</span> 恶化为 <span class="arithmatex">\(O(n)\)</span> 。</p>
|
||
<p>如图 7-24 所示，经过两次删除节点操作，这棵二叉搜索树便会退化为链表。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_degradation_from_removing_node.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="AVL 树在删除节点后发生退化" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_removing_node.png" /></a></p>
|
||
<p align="center"> 图 7-24 AVL 树在删除节点后发生退化 </p>
|
||
|
||
<p>再例如，在图 7-25 所示的完美二叉树中插入两个节点后，树将严重向左倾斜，查找操作的时间复杂度也随之恶化。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_degradation_from_inserting_node.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="AVL 树在插入节点后发生退化" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_inserting_node.png" /></a></p>
|
||
<p align="center"> 图 7-25 AVL 树在插入节点后发生退化 </p>
|
||
|
||
<p>1962 年 G. M. Adelson-Velsky 和 E. M. Landis 在论文 "An algorithm for the organization of information" 中提出了「AVL 树」。论文中详细描述了一系列操作，确保在持续添加和删除节点后，AVL 树不会退化，从而使得各种操作的时间复杂度保持在 <span class="arithmatex">\(O(\log n)\)</span> 级别。换句话说，在需要频繁进行增删查改操作的场景中，AVL 树能始终保持高效的数据操作性能，具有很好的应用价值。</p>
|
||
<h2 id="751-avl">7.5.1 AVL 树常见术语<a class="headerlink" href="#751-avl" title="Permanent link">¶</a></h2>
|
||
<p>AVL 树既是二叉搜索树也是平衡二叉树，同时满足这两类二叉树的所有性质，因此也被称为「平衡二叉搜索树 balanced binary search tree」。</p>
|
||
<h3 id="1">1. 节点高度<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
||
<p>由于 AVL 树的相关操作需要获取节点高度，因此我们需要为节点类添加 <code>height</code> 变量：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">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="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""AVL 树节点类"""</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></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="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 节点高度</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 左子节点引用</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右子节点引用</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 树节点类 */</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">// 节点值</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">// 节点高度</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">// 左子节点</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">// 右子节点</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="cm">/* AVL 树节点类 */</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></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">// 节点值</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></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">// 节点高度</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></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">// 左子节点</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></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">// 右子节点</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></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-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="p">}</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 树节点类 */</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</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>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></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="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="c1">// 节点值</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></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">// 节点高度</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></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">// 左子节点引用</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></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">// 右子节点引用</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="cm">/* AVL 树节点结构体 */</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></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-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></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">// 节点值</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></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">// 节点高度</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></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">// 左子节点引用</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></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">// 右子节点引用</span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></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="cm">/* AVL 树节点类 */</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a> <span class="kd">var</span> <span class="nv">val</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 节点值</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="kd">var</span> <span class="nv">height</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 节点高度</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></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">// 左子节点</span>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></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">// 右子节点</span>
|
||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></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-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a> <span class="n">val</span> <span class="p">=</span> <span class="n">x</span>
|
||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a> <span class="n">height</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a> <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><span class="cm">/* AVL 树节点类 */</span>
|
||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></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-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 节点值</span>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="nx">height</span><span class="p">;</span><span class="w"> </span><span class="c1">//节点高度</span>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子节点指针</span>
|
||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子节点指针</span>
|
||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></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-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></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-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></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-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></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-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></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-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="p">}</span>
|
||
</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 树节点类 */</span>
|
||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></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-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></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">// 节点值</span>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></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">// 节点高度</span>
|
||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></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">// 左子节点指针</span>
|
||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></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">// 右子节点指针</span>
|
||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></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-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></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-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></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-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></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-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></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-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></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 树节点类 */</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></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">// 节点值</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><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">// 节点高度</span>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><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">// 左子节点</span>
|
||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><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">// 右子节点</span>
|
||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">right</span><span class="p">]);</span>
|
||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<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><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">rc</span>::<span class="n">Rc</span><span class="p">;</span>
|
||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">cell</span>::<span class="n">RefCell</span><span class="p">;</span>
|
||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
|
||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* AVL 树节点结构体 */</span>
|
||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 节点值</span>
|
||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="n">height</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 节点高度</span>
|
||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="n">left</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="c1">// 左子节点</span>
|
||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="n">right</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="c1">// 右子节点</span>
|
||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a>
|
||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="k">impl</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="cm">/* 构造方法 */</span>
|
||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">new</span><span class="p">(</span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="bp">Self</span><span class="o">>></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="n">Rc</span>::<span class="n">new</span><span class="p">(</span><span class="n">RefCell</span>::<span class="n">new</span><span class="p">(</span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="n">val</span><span class="p">,</span>
|
||
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="n">height</span>: <span class="mi">0</span><span class="p">,</span>
|
||
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="n">left</span>: <span class="nb">None</span><span class="p">,</span>
|
||
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="n">right</span>: <span class="nb">None</span>
|
||
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a> <span class="p">}))</span>
|
||
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* AVL 树节点结构体 */</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><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-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">}</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">;</span>
|
||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
|
||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="cm">/* 构造函数 */</span>
|
||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newTreeNode</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-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a>
|
||
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">));</span>
|
||
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></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">val</span><span class="p">;</span>
|
||
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></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="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></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="nb">NULL</span><span class="p">;</span>
|
||
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></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="nb">NULL</span><span class="p">;</span>
|
||
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></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-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>“节点高度”是指从该节点到其最远叶节点的距离，即所经过的“边”的数量。需要特别注意的是，叶节点的高度为 <span class="arithmatex">\(0\)</span> ，而空节点的高度为 <span class="arithmatex">\(-1\)</span> 。我们将创建两个工具函数，分别用于获取和更新节点的高度：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">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">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w"> </span><span class="sd">"""获取节点高度"""</span>
|
||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a> <span class="c1"># 空节点高度为 -1 ，叶节点高度为 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="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">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
|
||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="sd">"""更新节点高度"""</span>
|
||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a> <span class="c1"># 节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.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w"> </span><span class="k">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-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>
|
||
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></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="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></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-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">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-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 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="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-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">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></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-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="c1">// 节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="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-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.cs</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">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-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 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="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-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">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></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><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">// 节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="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-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><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-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">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>
|
||
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></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-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></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-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></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-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a>
|
||
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></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-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></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-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></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>
|
||
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></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-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></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-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></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-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></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-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></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-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></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-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a> <span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></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-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>
|
||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></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-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a> <span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></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-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></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-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></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-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></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-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">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="err">#</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="p">{</span>
|
||
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w"> </span><span class="c1">// 节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="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span>
|
||
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><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-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></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-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></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-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></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-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a>
|
||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></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-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></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>
|
||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><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-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">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-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></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="m">1</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">height</span><span class="p">;</span>
|
||
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a>
|
||
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="kt">void</span><span class="w"> </span><span class="n">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-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="w"> </span><span class="n">node</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">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-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="k">fn</span> <span class="nf">height</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</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">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </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="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</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">borrow</span><span class="p">().</span><span class="n">height</span><span class="p">,</span>
|
||
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w"> </span><span class="nb">None</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>
|
||
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a>
|
||
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="k">fn</span> <span class="nf">update_height</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</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="n">cmp</span>::<span class="n">max</span><span class="p">(</span><span class="bp">Self</span>::<span class="n">height</span><span class="p">(</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">height</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-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></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="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w"> </span><span class="k">return</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-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
|
||
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a>
|
||
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></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="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">lh</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">left</span><span class="p">);</span>
|
||
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">rh</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-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">lh</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rh</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></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">lh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></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-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></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">rh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// 获取节点高度</span>
|
||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">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-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></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-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</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="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-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="p">}</span>
|
||
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a>
|
||
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></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-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></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="nb">@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-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2">2. 节点平衡因子<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||
<p>节点的「平衡因子 balance factor」定义为节点左子树的高度减去右子树的高度，同时规定空节点的平衡因子为 <span class="arithmatex">\(0\)</span> 。我们同样将获取节点平衡因子的功能封装成函数，方便后续使用：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="3:12"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="k">def</span> <span class="nf">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">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="w"> </span><span class="sd">"""获取平衡因子"""</span>
|
||
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a> <span class="c1"># 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></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-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a> <span class="c1"># 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></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.cpp</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="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="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 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="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</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="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></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-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">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-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></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>
|
||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><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-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></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-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="p">}</span>
|
||
</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>
|
||
<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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></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">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-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></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-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><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-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="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>
|
||
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></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-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></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>
|
||
<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></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-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></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-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a> <span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></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-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a> <span class="c1">// 节点平衡因子 = 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="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-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></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-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></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-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></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-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></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-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></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-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></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-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></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-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></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-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">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-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></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="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></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="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-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="k">fn</span> <span class="nf">balance_factor</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
|
||
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span>
|
||
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w"> </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="p">}</span>
|
||
<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">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="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></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="nb">NULL</span><span class="p">)</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w"> </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="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></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-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="c1">// 获取平衡因子</span>
|
||
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">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-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></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-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></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-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="p">}</span>
|
||
</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 树的任意节点的平衡因子皆满足 <span class="arithmatex">\(-1 \le f \le 1\)</span> 。</p>
|
||
</div>
|
||
<h2 id="752-avl">7.5.2 AVL 树旋转<a class="headerlink" href="#752-avl" title="Permanent link">¶</a></h2>
|
||
<p>AVL 树的特点在于“旋转”操作，它能够在不影响二叉树的中序遍历序列的前提下，使失衡节点重新恢复平衡。换句话说，<strong>旋转操作既能保持“二叉搜索树”的性质，也能使树重新变为“平衡二叉树”</strong>。</p>
|
||
<p>我们将平衡因子绝对值 <span class="arithmatex">\(> 1\)</span> 的节点称为“失衡节点”。根据节点失衡情况的不同，旋转操作分为四种：右旋、左旋、先右旋后左旋、先左旋后右旋。下面详细介绍这些旋转操作。</p>
|
||
<h3 id="1_1">1. 右旋<a class="headerlink" href="#1_1" title="Permanent link">¶</a></h3>
|
||
<p>如图 7-26 所示，节点下方为平衡因子。从底至顶看，二叉树中首个失衡节点是“节点 3”。我们关注以该失衡节点为根节点的子树，将该节点记为 <code>node</code> ，其左子节点记为 <code>child</code> ，执行“右旋”操作。完成右旋后，子树恢复平衡，并且仍然保持二叉搜索树的性质。</p>
|
||
<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>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="右旋操作步骤" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step2" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step3" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step4" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step4.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 图 7-26 右旋操作步骤 </p>
|
||
|
||
<p>如图 7-27 所示，当节点 <code>child</code> 有右子节点（记为 <code>grandChild</code> ）时，需要在右旋中添加一步：将 <code>grandChild</code> 作为 <code>node</code> 的左子节点。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="有 grandChild 的右旋操作" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" /></a></p>
|
||
<p align="center"> 图 7-27 有 grandChild 的右旋操作 </p>
|
||
|
||
<p>“向右旋转”是一种形象化的说法，实际上需要通过修改节点指针来实现，代码如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="5:12"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="k">def</span> <span class="nf">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">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-></span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w"> </span><span class="sd">"""右旋操作"""</span>
|
||
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></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-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></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-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a> <span class="c1"># 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></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-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></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-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a> <span class="c1"># 更新节点高度</span>
|
||
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></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-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></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-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a> <span class="c1"># 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></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.cpp</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="w"> </span><span class="o">*</span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></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-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></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-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></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-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">child</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="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></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-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</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="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-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></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-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></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-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w"> </span><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="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-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></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-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></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-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></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-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></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-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="p">}</span>
|
||
</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-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></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><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="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-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></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-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="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="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">// 更新节点高度</span>
|
||
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="w"> </span><span class="n">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">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节点</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>
|
||
</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-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">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>
|
||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></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-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></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-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 向右旋转</span>
|
||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></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-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></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-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></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-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></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>
|
||
<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节点</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="nx">child</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.swift</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></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-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></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-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></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-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a> <span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></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-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></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-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a> <span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></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-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></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-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a> <span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a> <span class="k">return</span> <span class="n">child</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.js</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="err">#</span><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-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></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-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></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-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></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-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></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-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
|
||
<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></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-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></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-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></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-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></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-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></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-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 向右旋转</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">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-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">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-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></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-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></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-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节点</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><span class="p">;</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.dart</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></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><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="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="p">.</span><span class="n">left</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="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="p">.</span><span class="n">right</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 向右旋转</span>
|
||
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></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-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></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-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></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-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></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-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节点</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="n">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.rs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="k">fn</span> <span class="nf">right_rotate</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</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="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </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="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="kd">let</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">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</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">grand_child</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="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">));</span>
|
||
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span>
|
||
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
|
||
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
|
||
<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<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="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><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-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><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-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></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-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></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-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></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-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></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-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></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-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="c1">// 右旋操作</span>
|
||
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">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-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></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-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></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-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></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-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></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-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></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-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></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-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></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-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2_1">2. 左旋<a class="headerlink" href="#2_1" title="Permanent link">¶</a></h3>
|
||
<p>相应地，如果考虑上述失衡二叉树的“镜像”，则需要执行图 7-28 所示的“左旋”操作。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_left_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="左旋操作" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate.png" /></a></p>
|
||
<p align="center"> 图 7-28 左旋操作 </p>
|
||
|
||
<p>同理，如图 7-29 所示，当节点 <code>child</code> 有左子节点（记为 <code>grandChild</code> ）时，需要在左旋中添加一步：将 <code>grandChild</code> 作为 <code>node</code> 的右子节点。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="有 grandChild 的左旋操作" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" /></a></p>
|
||
<p align="center"> 图 7-29 有 grandChild 的左旋操作 </p>
|
||
|
||
<p>可以观察到，<strong>右旋和左旋操作在逻辑上是镜像对称的，它们分别解决的两种失衡情况也是对称的</strong>。基于对称性，我们只需将右旋的实现代码中的所有的 <code>left</code> 替换为 <code>right</code> ，将所有的 <code>right</code> 替换为 <code>left</code> ，即可得到左旋的实现代码：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="6:12"><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" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="k">def</span> <span class="nf">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">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-></span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="w"> </span><span class="sd">"""左旋操作"""</span>
|
||
<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></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-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></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-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="o">.</span><span class="n">left</span> <span class="o">=</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="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">grand_child</span>
|
||
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a> <span class="c1"># 更新节点高度</span>
|
||
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></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-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></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-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a> <span class="c1"># 返回旋转后子树的根节点</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>
|
||
</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-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</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="n">TreeNode</span><span class="w"> </span><span class="o">*</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-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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-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="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-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></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-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w"> </span><span class="n">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">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节点</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>
|
||
</code></pre></div>
|
||
</div>
|
||
<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">/* 左旋操作 */</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">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-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></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-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></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-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></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-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></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-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></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-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></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-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></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-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="p">}</span>
|
||
</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-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 左旋操作 */</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="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><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="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-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></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-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></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-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></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-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></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-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></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-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></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-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><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-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">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>
|
||
<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></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-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></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-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></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-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></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-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></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-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></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>
|
||
<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span>
|
||
<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></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-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></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-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></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-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></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-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a> <span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></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-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></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-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a> <span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></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-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></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-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a> <span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a> <span class="k">return</span> <span class="n">child</span>
|
||
<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></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-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="err">#</span><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-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></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-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">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-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></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-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></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-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">updateHeight</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="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
|
||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
|
||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></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-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></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-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></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-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">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-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></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-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></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-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></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-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
|
||
<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
|
||
<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w"> </span><span class="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="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></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="p">.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></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-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></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-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></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-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></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-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="k">fn</span> <span class="nf">left_rotate</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w"> </span><span class="kd">let</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">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</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="kd">let</span><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</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="n">node</span><span class="p">.</span><span class="n">borrow_mut</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">grand_child</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="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">));</span>
|
||
<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span>
|
||
<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</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="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
|
||
<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><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-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><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-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></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-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></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-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></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-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></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-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></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-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<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">// 左旋操作</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">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-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></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-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">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-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></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-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></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-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></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-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></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-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="3">3. 先左旋后右旋<a class="headerlink" href="#3" title="Permanent link">¶</a></h3>
|
||
<p>对于图 7-30 中的失衡节点 3 ，仅使用左旋或右旋都无法使子树恢复平衡。此时需要先对 <code>child</code> 执行“左旋”，再对 <code>node</code> 执行“右旋”。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_left_right_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="先左旋后右旋" class="animation-figure" src="../avl_tree.assets/avltree_left_right_rotate.png" /></a></p>
|
||
<p align="center"> 图 7-30 先左旋后右旋 </p>
|
||
|
||
<h3 id="4">4. 先右旋后左旋<a class="headerlink" href="#4" title="Permanent link">¶</a></h3>
|
||
<p>如图 7-31 所示，对于上述失衡二叉树的镜像情况，需要先对 <code>child</code> 执行“右旋”，再对 <code>node</code> 执行“左旋”。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_left_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="先右旋后左旋" class="animation-figure" src="../avl_tree.assets/avltree_right_left_rotate.png" /></a></p>
|
||
<p align="center"> 图 7-31 先右旋后左旋 </p>
|
||
|
||
<h3 id="5">5. 旋转的选择<a class="headerlink" href="#5" title="Permanent link">¶</a></h3>
|
||
<p>图 7-32 展示的四种失衡情况与上述案例逐个对应，分别需要采用右旋、先左旋后右旋、先右旋后左旋、左旋的操作。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_rotation_cases.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="AVL 树的四种旋转情况" class="animation-figure" src="../avl_tree.assets/avltree_rotation_cases.png" /></a></p>
|
||
<p align="center"> 图 7-32 AVL 树的四种旋转情况 </p>
|
||
|
||
<p>如下表所示，我们通过判断失衡节点的平衡因子以及较高一侧子节点的平衡因子的正负号，来确定失衡节点属于图 7-32 中的哪种情况。</p>
|
||
<p align="center"> 表 7-3 四种旋转情况的选择条件 </p>
|
||
|
||
<div class="center-table">
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>失衡节点的平衡因子</th>
|
||
<th>子节点的平衡因子</th>
|
||
<th>应采用的旋转方法</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td><span class="arithmatex">\(> 1\)</span> （左偏树）</td>
|
||
<td><span class="arithmatex">\(\geq 0\)</span></td>
|
||
<td>右旋</td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(> 1\)</span> （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">\(< -1\)</span> （右偏树）</td>
|
||
<td><span class="arithmatex">\(\leq 0\)</span></td>
|
||
<td>左旋</td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(< -1\)</span> （右偏树）</td>
|
||
<td><span class="arithmatex">\(>0\)</span></td>
|
||
<td>先右旋后左旋</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<p>为了便于使用，我们将旋转操作封装成一个函数。<strong>有了这个函数，我们就能对各种失衡情况进行旋转，使失衡节点重新恢复平衡</strong>。代码如下所示：</p>
|
||
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<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></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">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-></span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="w"> </span><span class="sd">"""执行旋转操作，使该子树重新恢复平衡"""</span>
|
||
<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a> <span class="c1"># 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></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-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a> <span class="c1"># 左偏树</span>
|
||
<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></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-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></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-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a> <span class="c1"># 右旋</span>
|
||
<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></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-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a> <span class="c1"># 先左旋后右旋</span>
|
||
<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></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-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></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-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a> <span class="c1"># 右偏树</span>
|
||
<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></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-60-16" name="__codelineno-60-16" href="#__codelineno-60-16"></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-60-17" name="__codelineno-60-17" href="#__codelineno-60-17"></a> <span class="c1"># 左旋</span>
|
||
<a id="__codelineno-60-18" name="__codelineno-60-18" href="#__codelineno-60-18"></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-60-19" name="__codelineno-60-19" href="#__codelineno-60-19"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-60-20" name="__codelineno-60-20" href="#__codelineno-60-20"></a> <span class="c1"># 先右旋后左旋</span>
|
||
<a id="__codelineno-60-21" name="__codelineno-60-21" href="#__codelineno-60-21"></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-60-22" name="__codelineno-60-22" href="#__codelineno-60-22"></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-60-23" name="__codelineno-60-23" href="#__codelineno-60-23"></a> <span class="c1"># 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-60-24" name="__codelineno-60-24" href="#__codelineno-60-24"></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.cpp</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</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="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></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-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></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-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></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-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></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-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></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-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</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">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-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></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-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="w"> </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="p">}</span>
|
||
<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></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-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></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-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></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-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></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-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-61-23" name="__codelineno-61-23" href="#__codelineno-61-23"></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-61-24" name="__codelineno-61-24" href="#__codelineno-61-24"></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-61-25" name="__codelineno-61-25" href="#__codelineno-61-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-61-26" name="__codelineno-61-26" href="#__codelineno-61-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-61-27" name="__codelineno-61-27" href="#__codelineno-61-27"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-61-28" name="__codelineno-61-28" href="#__codelineno-61-28"></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-61-29" name="__codelineno-61-29" href="#__codelineno-61-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></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-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></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-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></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-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></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-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></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-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></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-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></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-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></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-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-62-16" name="__codelineno-62-16" href="#__codelineno-62-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-62-17" name="__codelineno-62-17" href="#__codelineno-62-17"></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-62-18" name="__codelineno-62-18" href="#__codelineno-62-18"></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-62-19" name="__codelineno-62-19" href="#__codelineno-62-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-62-20" name="__codelineno-62-20" href="#__codelineno-62-20"></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-62-21" name="__codelineno-62-21" href="#__codelineno-62-21"></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-62-22" name="__codelineno-62-22" href="#__codelineno-62-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-62-23" name="__codelineno-62-23" href="#__codelineno-62-23"></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-62-24" name="__codelineno-62-24" href="#__codelineno-62-24"></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-62-25" name="__codelineno-62-25" href="#__codelineno-62-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-62-26" name="__codelineno-62-26" href="#__codelineno-62-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-62-27" name="__codelineno-62-27" href="#__codelineno-62-27"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-62-28" name="__codelineno-62-28" href="#__codelineno-62-28"></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-62-29" name="__codelineno-62-29" href="#__codelineno-62-29"></a><span class="p">}</span>
|
||
</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-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></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><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="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></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-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></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="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></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-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></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-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="w"> </span><span class="n">node</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">LeftRotate</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></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-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a><span class="w"> </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>
|
||
<a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></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><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="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="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></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-63-21" name="__codelineno-63-21" href="#__codelineno-63-21"></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-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-63-23" name="__codelineno-63-23" href="#__codelineno-63-23"></a><span class="w"> </span><span class="n">node</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">RightRotate</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-63-24" name="__codelineno-63-24" href="#__codelineno-63-24"></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-63-25" name="__codelineno-63-25" href="#__codelineno-63-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-63-26" name="__codelineno-63-26" href="#__codelineno-63-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-63-27" name="__codelineno-63-27" href="#__codelineno-63-27"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-63-28" name="__codelineno-63-28" href="#__codelineno-63-28"></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-63-29" name="__codelineno-63-29" href="#__codelineno-63-29"></a><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-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></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>
|
||
<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></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-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></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>
|
||
<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></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>
|
||
<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></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>
|
||
<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></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>
|
||
<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></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-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></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-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></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>
|
||
<a id="__codelineno-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-64-16" name="__codelineno-64-16" href="#__codelineno-64-16"></a><span class="w"> </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">// 右偏树</span>
|
||
<a id="__codelineno-64-18" name="__codelineno-64-18" href="#__codelineno-64-18"></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>
|
||
<a id="__codelineno-64-19" name="__codelineno-64-19" href="#__codelineno-64-19"></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>
|
||
<a id="__codelineno-64-20" name="__codelineno-64-20" href="#__codelineno-64-20"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-64-21" name="__codelineno-64-21" href="#__codelineno-64-21"></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>
|
||
<a id="__codelineno-64-22" name="__codelineno-64-22" href="#__codelineno-64-22"></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-64-23" name="__codelineno-64-23" href="#__codelineno-64-23"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-64-24" name="__codelineno-64-24" href="#__codelineno-64-24"></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-64-25" name="__codelineno-64-25" href="#__codelineno-64-25"></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>
|
||
<a id="__codelineno-64-26" name="__codelineno-64-26" href="#__codelineno-64-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-64-27" name="__codelineno-64-27" href="#__codelineno-64-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-64-28" name="__codelineno-64-28" href="#__codelineno-64-28"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-64-29" name="__codelineno-64-29" href="#__codelineno-64-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-64-30" name="__codelineno-64-30" href="#__codelineno-64-30"></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-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></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-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a> <span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></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-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a> <span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></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-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></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-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a> <span class="c1">// 右旋</span>
|
||
<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></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-65-10" name="__codelineno-65-10" href="#__codelineno-65-10"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a> <span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></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-65-13" name="__codelineno-65-13" href="#__codelineno-65-13"></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-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a> <span class="p">}</span>
|
||
<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a> <span class="p">}</span>
|
||
<a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a> <span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-65-17" name="__codelineno-65-17" href="#__codelineno-65-17"></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-65-18" name="__codelineno-65-18" href="#__codelineno-65-18"></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-65-19" name="__codelineno-65-19" href="#__codelineno-65-19"></a> <span class="c1">// 左旋</span>
|
||
<a id="__codelineno-65-20" name="__codelineno-65-20" href="#__codelineno-65-20"></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-65-21" name="__codelineno-65-21" href="#__codelineno-65-21"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-65-22" name="__codelineno-65-22" href="#__codelineno-65-22"></a> <span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-65-23" name="__codelineno-65-23" href="#__codelineno-65-23"></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-65-24" name="__codelineno-65-24" href="#__codelineno-65-24"></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-65-25" name="__codelineno-65-25" href="#__codelineno-65-25"></a> <span class="p">}</span>
|
||
<a id="__codelineno-65-26" name="__codelineno-65-26" href="#__codelineno-65-26"></a> <span class="p">}</span>
|
||
<a id="__codelineno-65-27" name="__codelineno-65-27" href="#__codelineno-65-27"></a> <span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-65-28" name="__codelineno-65-28" href="#__codelineno-65-28"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-65-29" name="__codelineno-65-29" href="#__codelineno-65-29"></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-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="err">#</span><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-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></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-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></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-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></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-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-66-9" name="__codelineno-66-9" href="#__codelineno-66-9"></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="err">#</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-66-10" name="__codelineno-66-10" href="#__codelineno-66-10"></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-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-66-12" name="__codelineno-66-12" href="#__codelineno-66-12"></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="err">#</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-66-13" name="__codelineno-66-13" href="#__codelineno-66-13"></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="err">#</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-66-14" name="__codelineno-66-14" href="#__codelineno-66-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-66-15" name="__codelineno-66-15" href="#__codelineno-66-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-66-16" name="__codelineno-66-16" href="#__codelineno-66-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-66-17" name="__codelineno-66-17" href="#__codelineno-66-17"></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-66-18" name="__codelineno-66-18" href="#__codelineno-66-18"></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-66-19" name="__codelineno-66-19" href="#__codelineno-66-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-66-20" name="__codelineno-66-20" href="#__codelineno-66-20"></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="err">#</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-66-21" name="__codelineno-66-21" href="#__codelineno-66-21"></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-66-22" name="__codelineno-66-22" href="#__codelineno-66-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-66-23" name="__codelineno-66-23" href="#__codelineno-66-23"></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="err">#</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-66-24" name="__codelineno-66-24" href="#__codelineno-66-24"></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="err">#</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-66-25" name="__codelineno-66-25" href="#__codelineno-66-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-66-26" name="__codelineno-66-26" href="#__codelineno-66-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-66-27" name="__codelineno-66-27" href="#__codelineno-66-27"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-66-28" name="__codelineno-66-28" href="#__codelineno-66-28"></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-66-29" name="__codelineno-66-29" href="#__codelineno-66-29"></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-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></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-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></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-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></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-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></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-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></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-67-10" name="__codelineno-67-10" href="#__codelineno-67-10"></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-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-67-12" name="__codelineno-67-12" href="#__codelineno-67-12"></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-67-13" name="__codelineno-67-13" href="#__codelineno-67-13"></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-67-14" name="__codelineno-67-14" href="#__codelineno-67-14"></a><span class="w"> </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="p">}</span>
|
||
<a id="__codelineno-67-16" name="__codelineno-67-16" href="#__codelineno-67-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-67-17" name="__codelineno-67-17" href="#__codelineno-67-17"></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-67-18" name="__codelineno-67-18" href="#__codelineno-67-18"></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-67-19" name="__codelineno-67-19" href="#__codelineno-67-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-67-20" name="__codelineno-67-20" href="#__codelineno-67-20"></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-67-21" name="__codelineno-67-21" href="#__codelineno-67-21"></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-67-22" name="__codelineno-67-22" href="#__codelineno-67-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-67-23" name="__codelineno-67-23" href="#__codelineno-67-23"></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-67-24" name="__codelineno-67-24" href="#__codelineno-67-24"></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-67-25" name="__codelineno-67-25" href="#__codelineno-67-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-67-26" name="__codelineno-67-26" href="#__codelineno-67-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-67-27" name="__codelineno-67-27" href="#__codelineno-67-27"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-67-28" name="__codelineno-67-28" href="#__codelineno-67-28"></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-67-29" name="__codelineno-67-29" href="#__codelineno-67-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">factor</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-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">factor</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></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="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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></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-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></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-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></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="p">.</span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></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-68-14" name="__codelineno-68-14" href="#__codelineno-68-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-68-15" name="__codelineno-68-15" href="#__codelineno-68-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-68-16" name="__codelineno-68-16" href="#__codelineno-68-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-68-17" name="__codelineno-68-17" href="#__codelineno-68-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">factor</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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-68-18" name="__codelineno-68-18" href="#__codelineno-68-18"></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="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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-68-19" name="__codelineno-68-19" href="#__codelineno-68-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-68-20" name="__codelineno-68-20" href="#__codelineno-68-20"></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-68-21" name="__codelineno-68-21" href="#__codelineno-68-21"></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-68-22" name="__codelineno-68-22" href="#__codelineno-68-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-68-23" name="__codelineno-68-23" href="#__codelineno-68-23"></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="p">.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-68-24" name="__codelineno-68-24" href="#__codelineno-68-24"></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-68-25" name="__codelineno-68-25" href="#__codelineno-68-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-68-26" name="__codelineno-68-26" href="#__codelineno-68-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-68-27" name="__codelineno-68-27" href="#__codelineno-68-27"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-68-28" name="__codelineno-68-28" href="#__codelineno-68-28"></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-68-29" name="__codelineno-68-29" href="#__codelineno-68-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="k">fn</span> <span class="nf">rotate</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</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="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w"> </span><span class="kd">let</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="bp">Self</span>::<span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||
<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w"> </span><span class="k">if</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="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w"> </span><span class="kd">let</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><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</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>
|
||
<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">right_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</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="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </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="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-69-13" name="__codelineno-69-13" href="#__codelineno-69-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</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="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">left_rotate</span><span class="p">(</span><span class="n">left</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="bp">Self</span>::<span class="n">right_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
|
||
<a id="__codelineno-69-16" name="__codelineno-69-16" href="#__codelineno-69-16"></a><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="p">}</span>
|
||
<a id="__codelineno-69-18" name="__codelineno-69-18" href="#__codelineno-69-18"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-69-19" name="__codelineno-69-19" href="#__codelineno-69-19"></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="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="w"> </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="kd">let</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><span class="n">unwrap</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">if</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</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>
|
||
<a id="__codelineno-69-22" name="__codelineno-69-22" href="#__codelineno-69-22"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-69-23" name="__codelineno-69-23" href="#__codelineno-69-23"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">left_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
|
||
<a id="__codelineno-69-24" name="__codelineno-69-24" href="#__codelineno-69-24"></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-69-25" name="__codelineno-69-25" href="#__codelineno-69-25"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-69-26" name="__codelineno-69-26" href="#__codelineno-69-26"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-69-27" name="__codelineno-69-27" href="#__codelineno-69-27"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">right_rotate</span><span class="p">(</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-69-28" name="__codelineno-69-28" href="#__codelineno-69-28"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">left_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
|
||
<a id="__codelineno-69-29" name="__codelineno-69-29" href="#__codelineno-69-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-69-30" name="__codelineno-69-30" href="#__codelineno-69-30"></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-69-31" name="__codelineno-69-31" href="#__codelineno-69-31"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-69-32" name="__codelineno-69-32" href="#__codelineno-69-32"></a><span class="w"> </span><span class="n">node</span>
|
||
<a id="__codelineno-69-33" name="__codelineno-69-33" href="#__codelineno-69-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-69-34" name="__codelineno-69-34" href="#__codelineno-69-34"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</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="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">bf</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-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bf</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-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></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-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></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-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></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-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</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="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-70-13" name="__codelineno-70-13" href="#__codelineno-70-13"></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-70-14" name="__codelineno-70-14" href="#__codelineno-70-14"></a><span class="w"> </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="p">}</span>
|
||
<a id="__codelineno-70-16" name="__codelineno-70-16" href="#__codelineno-70-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-70-17" name="__codelineno-70-17" href="#__codelineno-70-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bf</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-70-18" name="__codelineno-70-18" href="#__codelineno-70-18"></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-70-19" name="__codelineno-70-19" href="#__codelineno-70-19"></a><span class="w"> </span><span class="c1">// 左旋</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="n">leftRotate</span><span class="p">(</span><span class="n">node</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="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-70-22" name="__codelineno-70-22" href="#__codelineno-70-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</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="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-70-24" name="__codelineno-70-24" href="#__codelineno-70-24"></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-70-25" name="__codelineno-70-25" href="#__codelineno-70-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-70-26" name="__codelineno-70-26" href="#__codelineno-70-26"></a><span class="w"> </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="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-70-28" name="__codelineno-70-28" href="#__codelineno-70-28"></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-70-29" name="__codelineno-70-29" href="#__codelineno-70-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="c1">// 执行旋转操作，使该子树重新恢复平衡</span>
|
||
<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></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-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></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-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></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-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></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-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-71-9" name="__codelineno-71-9" href="#__codelineno-71-9"></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-71-10" name="__codelineno-71-10" href="#__codelineno-71-10"></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-71-11" name="__codelineno-71-11" href="#__codelineno-71-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</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="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-71-13" name="__codelineno-71-13" href="#__codelineno-71-13"></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-71-14" name="__codelineno-71-14" href="#__codelineno-71-14"></a><span class="w"> </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="p">}</span>
|
||
<a id="__codelineno-71-16" name="__codelineno-71-16" href="#__codelineno-71-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-71-17" name="__codelineno-71-17" href="#__codelineno-71-17"></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-71-18" name="__codelineno-71-18" href="#__codelineno-71-18"></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-71-19" name="__codelineno-71-19" href="#__codelineno-71-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-71-20" name="__codelineno-71-20" href="#__codelineno-71-20"></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-71-21" name="__codelineno-71-21" href="#__codelineno-71-21"></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-71-22" name="__codelineno-71-22" href="#__codelineno-71-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-71-23" name="__codelineno-71-23" href="#__codelineno-71-23"></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-71-24" name="__codelineno-71-24" href="#__codelineno-71-24"></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-71-25" name="__codelineno-71-25" href="#__codelineno-71-25"></a><span class="w"> </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="p">}</span>
|
||
<a id="__codelineno-71-27" name="__codelineno-71-27" href="#__codelineno-71-27"></a><span class="w"> </span><span class="c1">// 平衡树，无须旋转，直接返回</span>
|
||
<a id="__codelineno-71-28" name="__codelineno-71-28" href="#__codelineno-71-28"></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-71-29" name="__codelineno-71-29" href="#__codelineno-71-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h2 id="753-avl">7.5.3 AVL 树常用操作<a class="headerlink" href="#753-avl" title="Permanent link">¶</a></h2>
|
||
<h3 id="1_2">1. 插入节点<a class="headerlink" href="#1_2" title="Permanent link">¶</a></h3>
|
||
<p>AVL 树的节点插入操作与二叉搜索树在主体上类似。唯一的区别在于，在 AVL 树中插入节点后，从该节点到根节点的路径上可能会出现一系列失衡节点。因此，<strong>我们需要从这个节点开始，自底向上执行旋转操作，使所有失衡节点恢复平衡</strong>。代码如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="8:12"><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" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<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="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>
|
||
<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="w"> </span><span class="sd">"""插入节点"""</span>
|
||
<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></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-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a>
|
||
<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></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">TreeNode</span> <span class="o">|</span> <span class="kc">None</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-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w"> </span><span class="sd">"""递归插入节点（辅助方法）"""</span>
|
||
<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></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-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></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-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a> <span class="c1"># 1. 查找插入位置，并插入节点</span>
|
||
<a id="__codelineno-72-10" name="__codelineno-72-10" href="#__codelineno-72-10"></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-72-11" name="__codelineno-72-11" href="#__codelineno-72-11"></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-72-12" name="__codelineno-72-12" href="#__codelineno-72-12"></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-72-13" name="__codelineno-72-13" href="#__codelineno-72-13"></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-72-14" name="__codelineno-72-14" href="#__codelineno-72-14"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-72-15" name="__codelineno-72-15" href="#__codelineno-72-15"></a> <span class="c1"># 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-72-16" name="__codelineno-72-16" href="#__codelineno-72-16"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-72-17" name="__codelineno-72-17" href="#__codelineno-72-17"></a> <span class="c1"># 更新节点高度</span>
|
||
<a id="__codelineno-72-18" name="__codelineno-72-18" href="#__codelineno-72-18"></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-72-19" name="__codelineno-72-19" href="#__codelineno-72-19"></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-72-20" name="__codelineno-72-20" href="#__codelineno-72-20"></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.cpp</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">void</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-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></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-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a>
|
||
<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></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>
|
||
<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><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-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-73-11" name="__codelineno-73-11" href="#__codelineno-73-11"></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-73-12" name="__codelineno-73-12" href="#__codelineno-73-12"></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-73-13" name="__codelineno-73-13" href="#__codelineno-73-13"></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-73-14" name="__codelineno-73-14" href="#__codelineno-73-14"></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-73-15" name="__codelineno-73-15" href="#__codelineno-73-15"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-73-16" name="__codelineno-73-16" href="#__codelineno-73-16"></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">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-73-17" name="__codelineno-73-17" href="#__codelineno-73-17"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-73-18" name="__codelineno-73-18" href="#__codelineno-73-18"></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-73-19" name="__codelineno-73-19" href="#__codelineno-73-19"></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-73-20" name="__codelineno-73-20" href="#__codelineno-73-20"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-73-21" name="__codelineno-73-21" href="#__codelineno-73-21"></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-73-22" name="__codelineno-73-22" href="#__codelineno-73-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="kt">void</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-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></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-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a>
|
||
<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></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-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></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>
|
||
<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><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-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</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="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-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></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-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="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-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></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-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-74-16" name="__codelineno-74-16" href="#__codelineno-74-16"></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">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-74-17" name="__codelineno-74-17" href="#__codelineno-74-17"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-74-18" name="__codelineno-74-18" href="#__codelineno-74-18"></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-74-19" name="__codelineno-74-19" href="#__codelineno-74-19"></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-74-20" name="__codelineno-74-20" href="#__codelineno-74-20"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-74-21" name="__codelineno-74-21" href="#__codelineno-74-21"></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-74-22" name="__codelineno-74-22" href="#__codelineno-74-22"></a><span class="p">}</span>
|
||
</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-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="k">void</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-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></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-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a>
|
||
<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></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-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-75-10" name="__codelineno-75-10" href="#__codelineno-75-10"></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-75-11" name="__codelineno-75-11" href="#__codelineno-75-11"></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-75-12" name="__codelineno-75-12" href="#__codelineno-75-12"></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-75-13" name="__codelineno-75-13" href="#__codelineno-75-13"></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-75-14" name="__codelineno-75-14" href="#__codelineno-75-14"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-75-15" name="__codelineno-75-15" href="#__codelineno-75-15"></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">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-75-16" name="__codelineno-75-16" href="#__codelineno-75-16"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-75-17" name="__codelineno-75-17" href="#__codelineno-75-17"></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-75-18" name="__codelineno-75-18" href="#__codelineno-75-18"></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-75-19" name="__codelineno-75-19" href="#__codelineno-75-19"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</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="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-75-21" name="__codelineno-75-21" href="#__codelineno-75-21"></a><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-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></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="p">{</span>
|
||
<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></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>
|
||
<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a>
|
||
<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="cm">/* 递归插入节点（辅助函数） */</span>
|
||
<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></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-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></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-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></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-76-10" name="__codelineno-76-10" href="#__codelineno-76-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-76-11" name="__codelineno-76-11" href="#__codelineno-76-11"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-76-12" name="__codelineno-76-12" href="#__codelineno-76-12"></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="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-76-13" name="__codelineno-76-13" href="#__codelineno-76-13"></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">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-76-14" name="__codelineno-76-14" href="#__codelineno-76-14"></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="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="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-76-15" name="__codelineno-76-15" href="#__codelineno-76-15"></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-76-16" name="__codelineno-76-16" href="#__codelineno-76-16"></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-76-17" name="__codelineno-76-17" href="#__codelineno-76-17"></a><span class="w"> </span><span class="c1">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-76-18" name="__codelineno-76-18" href="#__codelineno-76-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-76-19" name="__codelineno-76-19" href="#__codelineno-76-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-76-20" name="__codelineno-76-20" href="#__codelineno-76-20"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-76-21" name="__codelineno-76-21" href="#__codelineno-76-21"></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-76-22" name="__codelineno-76-22" href="#__codelineno-76-22"></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-76-23" name="__codelineno-76-23" href="#__codelineno-76-23"></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-76-24" name="__codelineno-76-24" href="#__codelineno-76-24"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-76-25" name="__codelineno-76-25" href="#__codelineno-76-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-76-26" name="__codelineno-76-26" href="#__codelineno-76-26"></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-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></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>
|
||
<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></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-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a>
|
||
<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></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-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></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-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></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-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a> <span class="p">}</span>
|
||
<a id="__codelineno-77-12" name="__codelineno-77-12" href="#__codelineno-77-12"></a> <span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-77-13" name="__codelineno-77-13" href="#__codelineno-77-13"></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-77-14" name="__codelineno-77-14" href="#__codelineno-77-14"></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-77-15" name="__codelineno-77-15" href="#__codelineno-77-15"></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-77-16" name="__codelineno-77-16" href="#__codelineno-77-16"></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-77-17" name="__codelineno-77-17" href="#__codelineno-77-17"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-77-18" name="__codelineno-77-18" href="#__codelineno-77-18"></a> <span class="k">return</span> <span class="n">node</span> <span class="c1">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-77-19" name="__codelineno-77-19" href="#__codelineno-77-19"></a> <span class="p">}</span>
|
||
<a id="__codelineno-77-20" name="__codelineno-77-20" href="#__codelineno-77-20"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-77-21" name="__codelineno-77-21" href="#__codelineno-77-21"></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-77-22" name="__codelineno-77-22" href="#__codelineno-77-22"></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-77-23" name="__codelineno-77-23" href="#__codelineno-77-23"></a> <span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-77-24" name="__codelineno-77-24" href="#__codelineno-77-24"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-77-25" name="__codelineno-77-25" href="#__codelineno-77-25"></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-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></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-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></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="err">#</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-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a>
|
||
<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a><span class="err">#</span><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-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></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-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-78-10" name="__codelineno-78-10" href="#__codelineno-78-10"></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="err">#</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-78-11" name="__codelineno-78-11" href="#__codelineno-78-11"></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>
|
||
<a id="__codelineno-78-12" name="__codelineno-78-12" href="#__codelineno-78-12"></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="err">#</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-78-13" name="__codelineno-78-13" href="#__codelineno-78-13"></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">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-78-14" name="__codelineno-78-14" href="#__codelineno-78-14"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</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">// 更新节点高度</span>
|
||
<a id="__codelineno-78-15" name="__codelineno-78-15" href="#__codelineno-78-15"></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-78-16" name="__codelineno-78-16" href="#__codelineno-78-16"></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="err">#</span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-78-17" name="__codelineno-78-17" href="#__codelineno-78-17"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-78-18" name="__codelineno-78-18" href="#__codelineno-78-18"></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-78-19" name="__codelineno-78-19" href="#__codelineno-78-19"></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-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></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="ow">void</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="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-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a>
|
||
<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></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-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></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-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</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="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-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></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-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></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-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></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-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="p">{</span>
|
||
<a id="__codelineno-79-15" name="__codelineno-79-15" href="#__codelineno-79-15"></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">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-79-16" name="__codelineno-79-16" href="#__codelineno-79-16"></a><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">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">// 更新节点高度</span>
|
||
<a id="__codelineno-79-18" name="__codelineno-79-18" href="#__codelineno-79-18"></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-79-19" name="__codelineno-79-19" href="#__codelineno-79-19"></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-79-20" name="__codelineno-79-20" href="#__codelineno-79-20"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</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="nx">node</span><span class="p">;</span>
|
||
<a id="__codelineno-79-22" name="__codelineno-79-22" href="#__codelineno-79-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kt">void</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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></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-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a>
|
||
<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></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">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></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-80-11" name="__codelineno-80-11" href="#__codelineno-80-11"></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-80-12" name="__codelineno-80-12" href="#__codelineno-80-12"></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="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-80-13" name="__codelineno-80-13" href="#__codelineno-80-13"></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-80-14" name="__codelineno-80-14" href="#__codelineno-80-14"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-80-15" name="__codelineno-80-15" href="#__codelineno-80-15"></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">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-80-16" name="__codelineno-80-16" href="#__codelineno-80-16"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-80-17" name="__codelineno-80-17" href="#__codelineno-80-17"></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-80-18" name="__codelineno-80-18" href="#__codelineno-80-18"></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-80-19" name="__codelineno-80-19" href="#__codelineno-80-19"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-80-20" name="__codelineno-80-20" href="#__codelineno-80-20"></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-80-21" name="__codelineno-80-21" href="#__codelineno-80-21"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="k">fn</span> <span class="nf">insert</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w"> </span><span class="bp">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="bp">Self</span>::<span class="n">insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a>
|
||
<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="k">fn</span> <span class="nf">insert_helper</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-10" name="__codelineno-81-10" href="#__codelineno-81-10"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-81-11" name="__codelineno-81-11" href="#__codelineno-81-11"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-12" name="__codelineno-81-12" href="#__codelineno-81-12"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">node_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">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-81-13" name="__codelineno-81-13" href="#__codelineno-81-13"></a><span class="w"> </span><span class="n">node_val</span>
|
||
<a id="__codelineno-81-14" name="__codelineno-81-14" href="#__codelineno-81-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-15" name="__codelineno-81-15" href="#__codelineno-81-15"></a><span class="w"> </span><span class="p">.</span><span class="n">cmp</span><span class="p">(</span><span class="o">&</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-81-16" name="__codelineno-81-16" href="#__codelineno-81-16"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-17" name="__codelineno-81-17" href="#__codelineno-81-17"></a><span class="w"> </span><span class="n">Ordering</span>::<span class="n">Greater</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-18" name="__codelineno-81-18" href="#__codelineno-81-18"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-81-19" name="__codelineno-81-19" href="#__codelineno-81-19"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">insert_helper</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-81-20" name="__codelineno-81-20" href="#__codelineno-81-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-21" name="__codelineno-81-21" href="#__codelineno-81-21"></a><span class="w"> </span><span class="n">Ordering</span>::<span class="n">Less</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-22" name="__codelineno-81-22" href="#__codelineno-81-22"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-81-23" name="__codelineno-81-23" href="#__codelineno-81-23"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">insert_helper</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-81-24" name="__codelineno-81-24" href="#__codelineno-81-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-25" name="__codelineno-81-25" href="#__codelineno-81-25"></a><span class="w"> </span><span class="n">Ordering</span>::<span class="n">Equal</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-26" name="__codelineno-81-26" href="#__codelineno-81-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-81-27" name="__codelineno-81-27" href="#__codelineno-81-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-28" name="__codelineno-81-28" href="#__codelineno-81-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-29" name="__codelineno-81-29" href="#__codelineno-81-29"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-81-30" name="__codelineno-81-30" href="#__codelineno-81-30"></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-81-31" name="__codelineno-81-31" href="#__codelineno-81-31"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)).</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-81-32" name="__codelineno-81-32" href="#__codelineno-81-32"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-81-33" name="__codelineno-81-33" href="#__codelineno-81-33"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-81-34" name="__codelineno-81-34" href="#__codelineno-81-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-35" name="__codelineno-81-35" href="#__codelineno-81-35"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">TreeNode</span>::<span class="n">new</span><span class="p">(</span><span class="n">val</span><span class="p">)),</span>
|
||
<a id="__codelineno-81-36" name="__codelineno-81-36" href="#__codelineno-81-36"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-37" name="__codelineno-81-37" href="#__codelineno-81-37"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">AVLTree</span><span class="w"> </span><span class="o">*</span><span class="n">tree</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-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="n">tree</span><span class="o">-></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">tree</span><span class="o">-></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-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a>
|
||
<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="cm">/* 递归插入节点（辅助函数） */</span>
|
||
<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></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="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></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="o">-></span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></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-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></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="o">-></span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></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-82-16" name="__codelineno-82-16" href="#__codelineno-82-16"></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-82-17" name="__codelineno-82-17" href="#__codelineno-82-17"></a><span class="w"> </span><span class="c1">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-82-18" name="__codelineno-82-18" href="#__codelineno-82-18"></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-82-19" name="__codelineno-82-19" href="#__codelineno-82-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-82-20" name="__codelineno-82-20" href="#__codelineno-82-20"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-82-21" name="__codelineno-82-21" href="#__codelineno-82-21"></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-82-22" name="__codelineno-82-22" href="#__codelineno-82-22"></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-82-23" name="__codelineno-82-23" href="#__codelineno-82-23"></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">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-82-24" name="__codelineno-82-24" href="#__codelineno-82-24"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-82-25" name="__codelineno-82-25" href="#__codelineno-82-25"></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-82-26" name="__codelineno-82-26" href="#__codelineno-82-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="c1">// 插入节点</span>
|
||
<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></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="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></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="p">(</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><span class="o">?</span><span class="p">;</span>
|
||
<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a>
|
||
<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="c1">// 递归插入节点（辅助方法）</span>
|
||
<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></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-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></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-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></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="p">{</span>
|
||
<a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></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-83-11" name="__codelineno-83-11" href="#__codelineno-83-11"></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-83-12" name="__codelineno-83-12" href="#__codelineno-83-12"></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-83-13" name="__codelineno-83-13" href="#__codelineno-83-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-83-14" name="__codelineno-83-14" href="#__codelineno-83-14"></a><span class="w"> </span><span class="c1">// 1. 查找插入位置，并插入节点</span>
|
||
<a id="__codelineno-83-15" name="__codelineno-83-15" href="#__codelineno-83-15"></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-83-16" name="__codelineno-83-16" href="#__codelineno-83-16"></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-83-17" name="__codelineno-83-17" href="#__codelineno-83-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="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-83-18" name="__codelineno-83-18" href="#__codelineno-83-18"></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-83-19" name="__codelineno-83-19" href="#__codelineno-83-19"></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-83-20" name="__codelineno-83-20" href="#__codelineno-83-20"></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">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-83-21" name="__codelineno-83-21" href="#__codelineno-83-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-83-22" name="__codelineno-83-22" href="#__codelineno-83-22"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-83-23" name="__codelineno-83-23" href="#__codelineno-83-23"></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-83-24" name="__codelineno-83-24" href="#__codelineno-83-24"></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">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-83-25" name="__codelineno-83-25" href="#__codelineno-83-25"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-83-26" name="__codelineno-83-26" href="#__codelineno-83-26"></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-83-27" name="__codelineno-83-27" href="#__codelineno-83-27"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2_2">2. 删除节点<a class="headerlink" href="#2_2" title="Permanent link">¶</a></h3>
|
||
<p>类似地，在二叉搜索树的删除节点方法的基础上，需要从底至顶执行旋转操作，使所有失衡节点恢复平衡。代码如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="9:12"><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" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></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-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="w"> </span><span class="sd">"""删除节点"""</span>
|
||
<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></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">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-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a>
|
||
<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></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">TreeNode</span> <span class="o">|</span> <span class="kc">None</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="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w"> </span><span class="sd">"""递归删除节点（辅助方法）"""</span>
|
||
<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></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-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a> <span class="k">return</span> <span class="kc">None</span>
|
||
<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a> <span class="c1"># 1. 查找节点，并删除之</span>
|
||
<a id="__codelineno-84-10" name="__codelineno-84-10" href="#__codelineno-84-10"></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-84-11" name="__codelineno-84-11" href="#__codelineno-84-11"></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-84-12" name="__codelineno-84-12" href="#__codelineno-84-12"></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-84-13" name="__codelineno-84-13" href="#__codelineno-84-13"></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-84-14" name="__codelineno-84-14" href="#__codelineno-84-14"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-84-15" name="__codelineno-84-15" href="#__codelineno-84-15"></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-84-16" name="__codelineno-84-16" href="#__codelineno-84-16"></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-84-17" name="__codelineno-84-17" href="#__codelineno-84-17"></a> <span class="c1"># 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-84-18" name="__codelineno-84-18" href="#__codelineno-84-18"></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-84-19" name="__codelineno-84-19" href="#__codelineno-84-19"></a> <span class="k">return</span> <span class="kc">None</span>
|
||
<a id="__codelineno-84-20" name="__codelineno-84-20" href="#__codelineno-84-20"></a> <span class="c1"># 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-84-21" name="__codelineno-84-21" href="#__codelineno-84-21"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-84-22" name="__codelineno-84-22" href="#__codelineno-84-22"></a> <span class="n">node</span> <span class="o">=</span> <span class="n">child</span>
|
||
<a id="__codelineno-84-23" name="__codelineno-84-23" href="#__codelineno-84-23"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-84-24" name="__codelineno-84-24" href="#__codelineno-84-24"></a> <span class="c1"># 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-84-25" name="__codelineno-84-25" href="#__codelineno-84-25"></a> <span class="n">temp</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
|
||
<a id="__codelineno-84-26" name="__codelineno-84-26" href="#__codelineno-84-26"></a> <span class="k">while</span> <span class="n">temp</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-84-27" name="__codelineno-84-27" href="#__codelineno-84-27"></a> <span class="n">temp</span> <span class="o">=</span> <span class="n">temp</span><span class="o">.</span><span class="n">left</span>
|
||
<a id="__codelineno-84-28" name="__codelineno-84-28" href="#__codelineno-84-28"></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-84-29" name="__codelineno-84-29" href="#__codelineno-84-29"></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-84-30" name="__codelineno-84-30" href="#__codelineno-84-30"></a> <span class="c1"># 更新节点高度</span>
|
||
<a id="__codelineno-84-31" name="__codelineno-84-31" href="#__codelineno-84-31"></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-84-32" name="__codelineno-84-32" href="#__codelineno-84-32"></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-84-33" name="__codelineno-84-33" href="#__codelineno-84-33"></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.cpp</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kt">void</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-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></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-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a>
|
||
<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></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>
|
||
<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></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-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></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-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></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-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></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-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></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-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></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-85-17" name="__codelineno-85-17" href="#__codelineno-85-17"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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-85-18" name="__codelineno-85-18" href="#__codelineno-85-18"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-85-19" name="__codelineno-85-19" href="#__codelineno-85-19"></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-85-20" name="__codelineno-85-20" href="#__codelineno-85-20"></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-85-21" name="__codelineno-85-21" href="#__codelineno-85-21"></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-85-22" name="__codelineno-85-22" href="#__codelineno-85-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-85-23" name="__codelineno-85-23" href="#__codelineno-85-23"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-85-24" name="__codelineno-85-24" href="#__codelineno-85-24"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-85-25" name="__codelineno-85-25" href="#__codelineno-85-25"></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-85-26" name="__codelineno-85-26" href="#__codelineno-85-26"></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-85-27" name="__codelineno-85-27" href="#__codelineno-85-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-85-28" name="__codelineno-85-28" href="#__codelineno-85-28"></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-85-29" name="__codelineno-85-29" href="#__codelineno-85-29"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-85-30" name="__codelineno-85-30" href="#__codelineno-85-30"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">temp</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-85-31" name="__codelineno-85-31" href="#__codelineno-85-31"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</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-85-32" name="__codelineno-85-32" href="#__codelineno-85-32"></a><span class="w"> </span><span class="n">temp</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">left</span><span class="p">;</span>
|
||
<a id="__codelineno-85-33" name="__codelineno-85-33" href="#__codelineno-85-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-85-34" name="__codelineno-85-34" href="#__codelineno-85-34"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tempVal</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-85-35" name="__codelineno-85-35" href="#__codelineno-85-35"></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-85-36" name="__codelineno-85-36" href="#__codelineno-85-36"></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">tempVal</span><span class="p">;</span>
|
||
<a id="__codelineno-85-37" name="__codelineno-85-37" href="#__codelineno-85-37"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-85-38" name="__codelineno-85-38" href="#__codelineno-85-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-85-39" name="__codelineno-85-39" href="#__codelineno-85-39"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-85-40" name="__codelineno-85-40" href="#__codelineno-85-40"></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-85-41" name="__codelineno-85-41" href="#__codelineno-85-41"></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-85-42" name="__codelineno-85-42" href="#__codelineno-85-42"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-85-43" name="__codelineno-85-43" href="#__codelineno-85-43"></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-85-44" name="__codelineno-85-44" href="#__codelineno-85-44"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">void</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-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></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-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a>
|
||
<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></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-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></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>
|
||
<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></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-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></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-86-12" name="__codelineno-86-12" href="#__codelineno-86-12"></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-86-13" name="__codelineno-86-13" href="#__codelineno-86-13"></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-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></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-86-15" name="__codelineno-86-15" href="#__codelineno-86-15"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-86-16" name="__codelineno-86-16" href="#__codelineno-86-16"></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-86-17" name="__codelineno-86-17" href="#__codelineno-86-17"></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-86-18" name="__codelineno-86-18" href="#__codelineno-86-18"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-86-19" name="__codelineno-86-19" href="#__codelineno-86-19"></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-86-20" name="__codelineno-86-20" href="#__codelineno-86-20"></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-86-21" name="__codelineno-86-21" href="#__codelineno-86-21"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-86-22" name="__codelineno-86-22" href="#__codelineno-86-22"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-86-23" name="__codelineno-86-23" href="#__codelineno-86-23"></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-86-24" name="__codelineno-86-24" href="#__codelineno-86-24"></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-86-25" name="__codelineno-86-25" href="#__codelineno-86-25"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-86-26" name="__codelineno-86-26" href="#__codelineno-86-26"></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">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
|
||
<a id="__codelineno-86-27" name="__codelineno-86-27" href="#__codelineno-86-27"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</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-86-28" name="__codelineno-86-28" href="#__codelineno-86-28"></a><span class="w"> </span><span class="n">temp</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">left</span><span class="p">;</span>
|
||
<a id="__codelineno-86-29" name="__codelineno-86-29" href="#__codelineno-86-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-86-30" name="__codelineno-86-30" href="#__codelineno-86-30"></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-86-31" name="__codelineno-86-31" href="#__codelineno-86-31"></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-86-32" name="__codelineno-86-32" href="#__codelineno-86-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-86-33" name="__codelineno-86-33" href="#__codelineno-86-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-86-34" name="__codelineno-86-34" href="#__codelineno-86-34"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-86-35" name="__codelineno-86-35" href="#__codelineno-86-35"></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-86-36" name="__codelineno-86-36" href="#__codelineno-86-36"></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-86-37" name="__codelineno-86-37" href="#__codelineno-86-37"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-86-38" name="__codelineno-86-38" href="#__codelineno-86-38"></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-86-39" name="__codelineno-86-39" href="#__codelineno-86-39"></a><span class="p">}</span>
|
||
</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-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="k">void</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-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></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-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a>
|
||
<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></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-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></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-87-11" name="__codelineno-87-11" href="#__codelineno-87-11"></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-87-12" name="__codelineno-87-12" href="#__codelineno-87-12"></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-87-13" name="__codelineno-87-13" href="#__codelineno-87-13"></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-87-14" name="__codelineno-87-14" href="#__codelineno-87-14"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-15" name="__codelineno-87-15" href="#__codelineno-87-15"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-16" name="__codelineno-87-16" href="#__codelineno-87-16"></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="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-87-17" name="__codelineno-87-17" href="#__codelineno-87-17"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-87-18" name="__codelineno-87-18" href="#__codelineno-87-18"></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-87-19" name="__codelineno-87-19" href="#__codelineno-87-19"></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-87-20" name="__codelineno-87-20" href="#__codelineno-87-20"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-87-21" name="__codelineno-87-21" href="#__codelineno-87-21"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-87-22" name="__codelineno-87-22" href="#__codelineno-87-22"></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-87-23" name="__codelineno-87-23" href="#__codelineno-87-23"></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-87-24" name="__codelineno-87-24" href="#__codelineno-87-24"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-87-25" name="__codelineno-87-25" href="#__codelineno-87-25"></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">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-87-26" name="__codelineno-87-26" href="#__codelineno-87-26"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-27" name="__codelineno-87-27" href="#__codelineno-87-27"></a><span class="w"> </span><span class="n">temp</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">left</span><span class="p">;</span>
|
||
<a id="__codelineno-87-28" name="__codelineno-87-28" href="#__codelineno-87-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-87-29" name="__codelineno-87-29" href="#__codelineno-87-29"></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="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
|
||
<a id="__codelineno-87-30" name="__codelineno-87-30" href="#__codelineno-87-30"></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-87-31" name="__codelineno-87-31" href="#__codelineno-87-31"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-87-32" name="__codelineno-87-32" href="#__codelineno-87-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-87-33" name="__codelineno-87-33" href="#__codelineno-87-33"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-87-34" name="__codelineno-87-34" href="#__codelineno-87-34"></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-87-35" name="__codelineno-87-35" href="#__codelineno-87-35"></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">Rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-87-36" name="__codelineno-87-36" href="#__codelineno-87-36"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-87-37" name="__codelineno-87-37" href="#__codelineno-87-37"></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-87-38" name="__codelineno-87-38" href="#__codelineno-87-38"></a><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-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></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="p">{</span>
|
||
<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></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">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>
|
||
<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a>
|
||
<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="cm">/* 递归删除节点（辅助函数） */</span>
|
||
<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></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>
|
||
<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></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-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||
<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-88-12" name="__codelineno-88-12" href="#__codelineno-88-12"></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="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-13" name="__codelineno-88-13" href="#__codelineno-88-13"></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">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-88-14" name="__codelineno-88-14" href="#__codelineno-88-14"></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="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="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-15" name="__codelineno-88-15" href="#__codelineno-88-15"></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>
|
||
<a id="__codelineno-88-16" name="__codelineno-88-16" href="#__codelineno-88-16"></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-88-17" name="__codelineno-88-17" href="#__codelineno-88-17"></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-88-18" name="__codelineno-88-18" href="#__codelineno-88-18"></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-88-19" name="__codelineno-88-19" href="#__codelineno-88-19"></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-88-20" name="__codelineno-88-20" href="#__codelineno-88-20"></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-88-21" name="__codelineno-88-21" href="#__codelineno-88-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-22" name="__codelineno-88-22" href="#__codelineno-88-22"></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-88-23" name="__codelineno-88-23" href="#__codelineno-88-23"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-88-24" name="__codelineno-88-24" href="#__codelineno-88-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||
<a id="__codelineno-88-25" name="__codelineno-88-25" href="#__codelineno-88-25"></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-88-26" name="__codelineno-88-26" href="#__codelineno-88-26"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-88-27" name="__codelineno-88-27" href="#__codelineno-88-27"></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-88-28" name="__codelineno-88-28" href="#__codelineno-88-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-29" name="__codelineno-88-29" href="#__codelineno-88-29"></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-88-30" name="__codelineno-88-30" href="#__codelineno-88-30"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-88-31" name="__codelineno-88-31" href="#__codelineno-88-31"></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">node</span><span class="p">.</span><span class="nx">Right</span>
|
||
<a id="__codelineno-88-32" name="__codelineno-88-32" href="#__codelineno-88-32"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">temp</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-88-33" name="__codelineno-88-33" href="#__codelineno-88-33"></a><span class="w"> </span><span class="nx">temp</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">Left</span>
|
||
<a id="__codelineno-88-34" name="__codelineno-88-34" href="#__codelineno-88-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-35" name="__codelineno-88-35" href="#__codelineno-88-35"></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><span class="kt">int</span><span class="p">))</span>
|
||
<a id="__codelineno-88-36" name="__codelineno-88-36" href="#__codelineno-88-36"></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-88-37" name="__codelineno-88-37" href="#__codelineno-88-37"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-38" name="__codelineno-88-38" href="#__codelineno-88-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-39" name="__codelineno-88-39" href="#__codelineno-88-39"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-88-40" name="__codelineno-88-40" href="#__codelineno-88-40"></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-88-41" name="__codelineno-88-41" href="#__codelineno-88-41"></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-88-42" name="__codelineno-88-42" href="#__codelineno-88-42"></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-88-43" name="__codelineno-88-43" href="#__codelineno-88-43"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-88-44" name="__codelineno-88-44" href="#__codelineno-88-44"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-88-45" name="__codelineno-88-45" href="#__codelineno-88-45"></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-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></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>
|
||
<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></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-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a>
|
||
<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></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-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></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-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a> <span class="k">return</span> <span class="kc">nil</span>
|
||
<a id="__codelineno-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-12" name="__codelineno-89-12" href="#__codelineno-89-12"></a> <span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-89-13" name="__codelineno-89-13" href="#__codelineno-89-13"></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-89-14" name="__codelineno-89-14" href="#__codelineno-89-14"></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-89-15" name="__codelineno-89-15" href="#__codelineno-89-15"></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-89-16" name="__codelineno-89-16" href="#__codelineno-89-16"></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-89-17" name="__codelineno-89-17" href="#__codelineno-89-17"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-18" name="__codelineno-89-18" href="#__codelineno-89-18"></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-89-19" name="__codelineno-89-19" href="#__codelineno-89-19"></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-89-20" name="__codelineno-89-20" href="#__codelineno-89-20"></a> <span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-89-21" name="__codelineno-89-21" href="#__codelineno-89-21"></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-89-22" name="__codelineno-89-22" href="#__codelineno-89-22"></a> <span class="k">return</span> <span class="kc">nil</span>
|
||
<a id="__codelineno-89-23" name="__codelineno-89-23" href="#__codelineno-89-23"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-24" name="__codelineno-89-24" href="#__codelineno-89-24"></a> <span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-89-25" name="__codelineno-89-25" href="#__codelineno-89-25"></a> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-26" name="__codelineno-89-26" href="#__codelineno-89-26"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">child</span>
|
||
<a id="__codelineno-89-27" name="__codelineno-89-27" href="#__codelineno-89-27"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-28" name="__codelineno-89-28" href="#__codelineno-89-28"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-29" name="__codelineno-89-29" href="#__codelineno-89-29"></a> <span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-89-30" name="__codelineno-89-30" href="#__codelineno-89-30"></a> <span class="kd">var</span> <span class="nv">temp</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
|
||
<a id="__codelineno-89-31" name="__codelineno-89-31" href="#__codelineno-89-31"></a> <span class="k">while</span> <span class="n">temp</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-89-32" name="__codelineno-89-32" href="#__codelineno-89-32"></a> <span class="n">temp</span> <span class="p">=</span> <span class="n">temp</span><span class="p">?.</span><span class="kr">left</span>
|
||
<a id="__codelineno-89-33" name="__codelineno-89-33" href="#__codelineno-89-33"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-34" name="__codelineno-89-34" href="#__codelineno-89-34"></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-89-35" name="__codelineno-89-35" href="#__codelineno-89-35"></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-89-36" name="__codelineno-89-36" href="#__codelineno-89-36"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-37" name="__codelineno-89-37" href="#__codelineno-89-37"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-38" name="__codelineno-89-38" href="#__codelineno-89-38"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-89-39" name="__codelineno-89-39" href="#__codelineno-89-39"></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-89-40" name="__codelineno-89-40" href="#__codelineno-89-40"></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-89-41" name="__codelineno-89-41" href="#__codelineno-89-41"></a> <span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-89-42" name="__codelineno-89-42" href="#__codelineno-89-42"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-89-43" name="__codelineno-89-43" href="#__codelineno-89-43"></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-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></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-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></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="err">#</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-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a>
|
||
<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="err">#</span><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-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></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-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></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="err">#</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-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></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>
|
||
<a id="__codelineno-90-12" name="__codelineno-90-12" href="#__codelineno-90-12"></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="err">#</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-90-13" name="__codelineno-90-13" href="#__codelineno-90-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-90-14" name="__codelineno-90-14" href="#__codelineno-90-14"></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-90-15" name="__codelineno-90-15" href="#__codelineno-90-15"></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-90-16" name="__codelineno-90-16" href="#__codelineno-90-16"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-90-17" name="__codelineno-90-17" href="#__codelineno-90-17"></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-90-18" name="__codelineno-90-18" href="#__codelineno-90-18"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-90-19" name="__codelineno-90-19" href="#__codelineno-90-19"></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-90-20" name="__codelineno-90-20" href="#__codelineno-90-20"></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-90-21" name="__codelineno-90-21" href="#__codelineno-90-21"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-90-22" name="__codelineno-90-22" href="#__codelineno-90-22"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</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-90-23" name="__codelineno-90-23" href="#__codelineno-90-23"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</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-90-24" name="__codelineno-90-24" href="#__codelineno-90-24"></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">temp</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
|
||
<a id="__codelineno-90-25" name="__codelineno-90-25" href="#__codelineno-90-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-90-26" name="__codelineno-90-26" href="#__codelineno-90-26"></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="err">#</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-90-27" name="__codelineno-90-27" href="#__codelineno-90-27"></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-90-28" name="__codelineno-90-28" href="#__codelineno-90-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-90-29" name="__codelineno-90-29" href="#__codelineno-90-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-90-30" name="__codelineno-90-30" href="#__codelineno-90-30"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</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">// 更新节点高度</span>
|
||
<a id="__codelineno-90-31" name="__codelineno-90-31" href="#__codelineno-90-31"></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-90-32" name="__codelineno-90-32" href="#__codelineno-90-32"></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="err">#</span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-90-33" name="__codelineno-90-33" href="#__codelineno-90-33"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-90-34" name="__codelineno-90-34" href="#__codelineno-90-34"></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-90-35" name="__codelineno-90-35" href="#__codelineno-90-35"></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-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></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="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></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-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a>
|
||
<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></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-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></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-91-9" name="__codelineno-91-9" href="#__codelineno-91-9"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-91-10" name="__codelineno-91-10" href="#__codelineno-91-10"></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-91-11" name="__codelineno-91-11" href="#__codelineno-91-11"></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-91-12" name="__codelineno-91-12" href="#__codelineno-91-12"></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-91-13" name="__codelineno-91-13" href="#__codelineno-91-13"></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-91-14" name="__codelineno-91-14" href="#__codelineno-91-14"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-15" name="__codelineno-91-15" href="#__codelineno-91-15"></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-91-16" name="__codelineno-91-16" href="#__codelineno-91-16"></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-91-17" name="__codelineno-91-17" href="#__codelineno-91-17"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-91-18" name="__codelineno-91-18" href="#__codelineno-91-18"></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-91-19" name="__codelineno-91-19" href="#__codelineno-91-19"></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-91-20" name="__codelineno-91-20" href="#__codelineno-91-20"></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-91-21" name="__codelineno-91-21" href="#__codelineno-91-21"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-91-22" name="__codelineno-91-22" href="#__codelineno-91-22"></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-91-23" name="__codelineno-91-23" href="#__codelineno-91-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-91-24" name="__codelineno-91-24" href="#__codelineno-91-24"></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-91-25" name="__codelineno-91-25" href="#__codelineno-91-25"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-91-26" name="__codelineno-91-26" href="#__codelineno-91-26"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">temp</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-91-27" name="__codelineno-91-27" href="#__codelineno-91-27"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">temp</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-91-28" name="__codelineno-91-28" href="#__codelineno-91-28"></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">temp</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
|
||
<a id="__codelineno-91-29" name="__codelineno-91-29" href="#__codelineno-91-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-91-30" name="__codelineno-91-30" href="#__codelineno-91-30"></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-91-31" name="__codelineno-91-31" href="#__codelineno-91-31"></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-91-32" name="__codelineno-91-32" href="#__codelineno-91-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-91-33" name="__codelineno-91-33" href="#__codelineno-91-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-91-34" name="__codelineno-91-34" href="#__codelineno-91-34"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-91-35" name="__codelineno-91-35" href="#__codelineno-91-35"></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-91-36" name="__codelineno-91-36" href="#__codelineno-91-36"></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-91-37" name="__codelineno-91-37" href="#__codelineno-91-37"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-91-38" name="__codelineno-91-38" href="#__codelineno-91-38"></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-91-39" name="__codelineno-91-39" href="#__codelineno-91-39"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">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-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></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-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a>
|
||
<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></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-92-9" name="__codelineno-92-9" href="#__codelineno-92-9"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></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-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></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-92-12" name="__codelineno-92-12" href="#__codelineno-92-12"></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="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-92-13" name="__codelineno-92-13" href="#__codelineno-92-13"></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-92-14" name="__codelineno-92-14" href="#__codelineno-92-14"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-92-15" name="__codelineno-92-15" href="#__codelineno-92-15"></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="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="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-92-16" name="__codelineno-92-16" href="#__codelineno-92-16"></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="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-92-17" name="__codelineno-92-17" href="#__codelineno-92-17"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-92-18" name="__codelineno-92-18" href="#__codelineno-92-18"></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-92-19" name="__codelineno-92-19" href="#__codelineno-92-19"></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-92-20" name="__codelineno-92-20" href="#__codelineno-92-20"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-92-21" name="__codelineno-92-21" href="#__codelineno-92-21"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-92-22" name="__codelineno-92-22" href="#__codelineno-92-22"></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-92-23" name="__codelineno-92-23" href="#__codelineno-92-23"></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-92-24" name="__codelineno-92-24" href="#__codelineno-92-24"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-92-25" name="__codelineno-92-25" href="#__codelineno-92-25"></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">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-92-26" name="__codelineno-92-26" href="#__codelineno-92-26"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</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-92-27" name="__codelineno-92-27" href="#__codelineno-92-27"></a><span class="w"> </span><span class="n">temp</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">left</span><span class="p">;</span>
|
||
<a id="__codelineno-92-28" name="__codelineno-92-28" href="#__codelineno-92-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-92-29" name="__codelineno-92-29" href="#__codelineno-92-29"></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-92-30" name="__codelineno-92-30" href="#__codelineno-92-30"></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-92-31" name="__codelineno-92-31" href="#__codelineno-92-31"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-92-32" name="__codelineno-92-32" href="#__codelineno-92-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-92-33" name="__codelineno-92-33" href="#__codelineno-92-33"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-92-34" name="__codelineno-92-34" href="#__codelineno-92-34"></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-92-35" name="__codelineno-92-35" href="#__codelineno-92-35"></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">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-92-36" name="__codelineno-92-36" href="#__codelineno-92-36"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-92-37" name="__codelineno-92-37" href="#__codelineno-92-37"></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-92-38" name="__codelineno-92-38" href="#__codelineno-92-38"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a><span class="k">fn</span> <span class="nf">remove</span><span class="p">(</span><span class="o">&</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a>
|
||
<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></a><span class="k">fn</span> <span class="nf">remove_helper</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-9" name="__codelineno-93-9" href="#__codelineno-93-9"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-10" name="__codelineno-93-10" href="#__codelineno-93-10"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="w"> </span><span class="k">if</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">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-12" name="__codelineno-93-12" href="#__codelineno-93-12"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-93-13" name="__codelineno-93-13" href="#__codelineno-93-13"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">remove_helper</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-93-14" name="__codelineno-93-14" href="#__codelineno-93-14"></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="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">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-15" name="__codelineno-93-15" href="#__codelineno-93-15"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-93-16" name="__codelineno-93-16" href="#__codelineno-93-16"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">remove_helper</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-93-17" name="__codelineno-93-17" href="#__codelineno-93-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</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">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-18" name="__codelineno-93-18" href="#__codelineno-93-18"></a><span class="w"> </span><span class="kd">let</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="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-19" name="__codelineno-93-19" href="#__codelineno-93-19"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span>
|
||
<a id="__codelineno-93-20" name="__codelineno-93-20" href="#__codelineno-93-20"></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-93-21" name="__codelineno-93-21" href="#__codelineno-93-21"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span>
|
||
<a id="__codelineno-93-22" name="__codelineno-93-22" href="#__codelineno-93-22"></a><span class="w"> </span><span class="p">};</span>
|
||
<a id="__codelineno-93-23" name="__codelineno-93-23" href="#__codelineno-93-23"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-24" name="__codelineno-93-24" href="#__codelineno-93-24"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-93-25" name="__codelineno-93-25" href="#__codelineno-93-25"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-26" name="__codelineno-93-26" href="#__codelineno-93-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
|
||
<a id="__codelineno-93-27" name="__codelineno-93-27" href="#__codelineno-93-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-28" name="__codelineno-93-28" href="#__codelineno-93-28"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-93-29" name="__codelineno-93-29" href="#__codelineno-93-29"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</span><span class="w"> </span><span class="o">=></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">child</span><span class="p">,</span>
|
||
<a id="__codelineno-93-30" name="__codelineno-93-30" href="#__codelineno-93-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-31" name="__codelineno-93-31" href="#__codelineno-93-31"></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-93-32" name="__codelineno-93-32" href="#__codelineno-93-32"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-93-33" name="__codelineno-93-33" href="#__codelineno-93-33"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</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">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-93-34" name="__codelineno-93-34" href="#__codelineno-93-34"></a><span class="w"> </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-35" name="__codelineno-93-35" href="#__codelineno-93-35"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">temp_left</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">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-93-36" name="__codelineno-93-36" href="#__codelineno-93-36"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">temp_left</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-37" name="__codelineno-93-37" href="#__codelineno-93-37"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-93-38" name="__codelineno-93-38" href="#__codelineno-93-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-39" name="__codelineno-93-39" href="#__codelineno-93-39"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp_left</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-93-40" name="__codelineno-93-40" href="#__codelineno-93-40"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-41" name="__codelineno-93-41" href="#__codelineno-93-41"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </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><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-93-42" name="__codelineno-93-42" href="#__codelineno-93-42"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">remove_helper</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">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-93-43" name="__codelineno-93-43" href="#__codelineno-93-43"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</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">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-93-44" name="__codelineno-93-44" href="#__codelineno-93-44"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-45" name="__codelineno-93-45" href="#__codelineno-93-45"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-93-46" name="__codelineno-93-46" href="#__codelineno-93-46"></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-93-47" name="__codelineno-93-47" href="#__codelineno-93-47"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)).</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-93-48" name="__codelineno-93-48" href="#__codelineno-93-48"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-93-49" name="__codelineno-93-49" href="#__codelineno-93-49"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-93-50" name="__codelineno-93-50" href="#__codelineno-93-50"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-51" name="__codelineno-93-51" href="#__codelineno-93-51"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
|
||
<a id="__codelineno-93-52" name="__codelineno-93-52" href="#__codelineno-93-52"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-53" name="__codelineno-93-53" href="#__codelineno-93-53"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="c1">// 由于引入了 stdio.h ，此处无法使用 remove 关键词</span>
|
||
<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">AVLTree</span><span class="w"> </span><span class="o">*</span><span class="n">tree</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-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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">tree</span><span class="o">-></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-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a>
|
||
<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="cm">/* 递归删除节点（辅助函数） */</span>
|
||
<a id="__codelineno-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-94-10" name="__codelineno-94-10" href="#__codelineno-94-10"></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="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-11" name="__codelineno-94-11" href="#__codelineno-94-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
|
||
<a id="__codelineno-94-12" name="__codelineno-94-12" href="#__codelineno-94-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-13" name="__codelineno-94-13" href="#__codelineno-94-13"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-94-14" name="__codelineno-94-14" href="#__codelineno-94-14"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-15" name="__codelineno-94-15" href="#__codelineno-94-15"></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-94-16" name="__codelineno-94-16" href="#__codelineno-94-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-17" name="__codelineno-94-17" href="#__codelineno-94-17"></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-94-18" name="__codelineno-94-18" href="#__codelineno-94-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-19" name="__codelineno-94-19" href="#__codelineno-94-19"></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="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</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="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-20" name="__codelineno-94-20" href="#__codelineno-94-20"></a><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-94-21" name="__codelineno-94-21" href="#__codelineno-94-21"></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">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-22" name="__codelineno-94-22" href="#__codelineno-94-22"></a><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-94-23" name="__codelineno-94-23" href="#__codelineno-94-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-24" name="__codelineno-94-24" href="#__codelineno-94-24"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-94-25" name="__codelineno-94-25" href="#__codelineno-94-25"></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="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-26" name="__codelineno-94-26" href="#__codelineno-94-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
|
||
<a id="__codelineno-94-27" name="__codelineno-94-27" href="#__codelineno-94-27"></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-94-28" name="__codelineno-94-28" href="#__codelineno-94-28"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-94-29" name="__codelineno-94-29" href="#__codelineno-94-29"></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-94-30" name="__codelineno-94-30" href="#__codelineno-94-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-31" name="__codelineno-94-31" href="#__codelineno-94-31"></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-94-32" name="__codelineno-94-32" href="#__codelineno-94-32"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-94-33" name="__codelineno-94-33" href="#__codelineno-94-33"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">temp</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-94-34" name="__codelineno-94-34" href="#__codelineno-94-34"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-35" name="__codelineno-94-35" href="#__codelineno-94-35"></a><span class="w"> </span><span class="n">temp</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">left</span><span class="p">;</span>
|
||
<a id="__codelineno-94-36" name="__codelineno-94-36" href="#__codelineno-94-36"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-37" name="__codelineno-94-37" href="#__codelineno-94-37"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tempVal</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-94-38" name="__codelineno-94-38" href="#__codelineno-94-38"></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-94-39" name="__codelineno-94-39" href="#__codelineno-94-39"></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">tempVal</span><span class="p">;</span>
|
||
<a id="__codelineno-94-40" name="__codelineno-94-40" href="#__codelineno-94-40"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-41" name="__codelineno-94-41" href="#__codelineno-94-41"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-42" name="__codelineno-94-42" href="#__codelineno-94-42"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-94-43" name="__codelineno-94-43" href="#__codelineno-94-43"></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-94-44" name="__codelineno-94-44" href="#__codelineno-94-44"></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-94-45" name="__codelineno-94-45" href="#__codelineno-94-45"></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-94-46" name="__codelineno-94-46" href="#__codelineno-94-46"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-94-47" name="__codelineno-94-47" href="#__codelineno-94-47"></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-94-48" name="__codelineno-94-48" href="#__codelineno-94-48"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></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="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></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><span class="o">?</span><span class="p">;</span>
|
||
<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a>
|
||
<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="c1">// 递归删除节点（辅助方法）</span>
|
||
<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></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-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></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-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></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-95-10" name="__codelineno-95-10" href="#__codelineno-95-10"></a><span class="w"> </span><span class="c1">// 1. 查找节点，并删除之</span>
|
||
<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></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="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-95-12" name="__codelineno-95-12" href="#__codelineno-95-12"></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">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-95-13" name="__codelineno-95-13" href="#__codelineno-95-13"></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="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-95-14" name="__codelineno-95-14" href="#__codelineno-95-14"></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-95-15" name="__codelineno-95-15" href="#__codelineno-95-15"></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-95-16" name="__codelineno-95-16" href="#__codelineno-95-16"></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="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-95-17" name="__codelineno-95-17" href="#__codelineno-95-17"></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-95-18" name="__codelineno-95-18" href="#__codelineno-95-18"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-95-19" name="__codelineno-95-19" href="#__codelineno-95-19"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-95-20" name="__codelineno-95-20" href="#__codelineno-95-20"></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-95-21" name="__codelineno-95-21" href="#__codelineno-95-21"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-95-22" name="__codelineno-95-22" href="#__codelineno-95-22"></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-95-23" name="__codelineno-95-23" href="#__codelineno-95-23"></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-95-24" name="__codelineno-95-24" href="#__codelineno-95-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-95-25" name="__codelineno-95-25" href="#__codelineno-95-25"></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-95-26" name="__codelineno-95-26" href="#__codelineno-95-26"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
|
||
<a id="__codelineno-95-27" name="__codelineno-95-27" href="#__codelineno-95-27"></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">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-95-28" name="__codelineno-95-28" href="#__codelineno-95-28"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</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-95-29" name="__codelineno-95-29" href="#__codelineno-95-29"></a><span class="w"> </span><span class="n">temp</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">left</span><span class="p">;</span>
|
||
<a id="__codelineno-95-30" name="__codelineno-95-30" href="#__codelineno-95-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-95-31" name="__codelineno-95-31" href="#__codelineno-95-31"></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-95-32" name="__codelineno-95-32" href="#__codelineno-95-32"></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-95-33" name="__codelineno-95-33" href="#__codelineno-95-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-95-34" name="__codelineno-95-34" href="#__codelineno-95-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-95-35" name="__codelineno-95-35" href="#__codelineno-95-35"></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">// 更新节点高度</span>
|
||
<a id="__codelineno-95-36" name="__codelineno-95-36" href="#__codelineno-95-36"></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-95-37" name="__codelineno-95-37" href="#__codelineno-95-37"></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">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-95-38" name="__codelineno-95-38" href="#__codelineno-95-38"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-95-39" name="__codelineno-95-39" href="#__codelineno-95-39"></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-95-40" name="__codelineno-95-40" href="#__codelineno-95-40"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="3_1">3. 查找节点<a class="headerlink" href="#3_1" title="Permanent link">¶</a></h3>
|
||
<p>AVL 树的节点查找操作与二叉搜索树一致，在此不再赘述。</p>
|
||
<h2 id="754-avl">7.5.4 AVL 树典型应用<a class="headerlink" href="#754-avl" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>组织和存储大型数据，适用于高频查找、低频增删的场景。</li>
|
||
<li>用于构建数据库中的索引系统。</li>
|
||
<li>红黑树在许多应用中比 AVL 树更受欢迎。这是因为红黑树的平衡条件相对宽松，在红黑树中插入与删除节点所需的旋转操作相对较少，其节点增删操作的平均效率更高。</li>
|
||
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