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0.1. 关于本书
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
|
||
0.2. 如何使用本书
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_preface/summary/" class="md-nav__link">
|
||
0.3. 小结
|
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</a>
|
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</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
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</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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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
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|
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|
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|
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<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
|
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1. 引言
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_2">
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<span class="md-nav__icon md-icon"></span>
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1. 引言
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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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|
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<li class="md-nav__item">
|
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<a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
|
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1.1. 算法无处不在
|
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</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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<li class="md-nav__item">
|
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<a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
|
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1.2. 算法是什么
|
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</a>
|
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</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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<li class="md-nav__item">
|
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<a href="../../chapter_introduction/summary/" class="md-nav__link">
|
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1.3. 小结
|
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</li>
|
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|
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|
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|
||
|
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</ul>
|
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</nav>
|
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</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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|
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
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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" for="__nav_3" id="__nav_3_label" tabindex="0">
|
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2. 复杂度分析
|
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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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_3">
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<span class="md-nav__icon md-icon"></span>
|
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2. 复杂度分析
|
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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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|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
|
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2.1. 算法效率评估
|
||
</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_computational_complexity/time_complexity/" class="md-nav__link">
|
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2.2. 时间复杂度
|
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</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
|
||
2.3. 空间复杂度
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
|
||
2.4. 小结
|
||
</a>
|
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</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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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_4" >
|
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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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|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
|
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3. 数据结构简介
|
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<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
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|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_4">
|
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<span class="md-nav__icon md-icon"></span>
|
||
3. 数据结构简介
|
||
</label>
|
||
<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">
|
||
<a href="../../chapter_data_structure/data_and_memory/" class="md-nav__link">
|
||
3.1. 数据与内存
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
|
||
3.2. 数据结构分类
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/summary/" class="md-nav__link">
|
||
3.3. 小结
|
||
</a>
|
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</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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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_5" >
|
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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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|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
|
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4. 数组与链表
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_5">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
4. 数组与链表
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
|
||
4.1. 数组
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
|
||
4.2. 链表
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
|
||
4.3. 列表
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
|
||
4.4. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section 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_6" >
|
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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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|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
|
||
5. 栈与队列
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_6">
|
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<span class="md-nav__icon md-icon"></span>
|
||
5. 栈与队列
|
||
</label>
|
||
<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">
|
||
<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
|
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5.1. 栈
|
||
</a>
|
||
</li>
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
|
||
5.2. 队列
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
||
5.3. 双向队列
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
|
||
5.4. 小结
|
||
</a>
|
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</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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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_7" >
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|
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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" for="__nav_7" id="__nav_7_label" tabindex="0">
|
||
6. 二分查找
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_7">
|
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<span class="md-nav__icon md-icon"></span>
|
||
6. 二分查找
|
||
</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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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_binary_search/binary_search/" class="md-nav__link">
|
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6.1. 二分查找
|
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</a>
|
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</li>
|
||
|
||
|
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|
||
|
||
</ul>
|
||
</nav>
|
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</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 md-nav__item--section md-nav__item--nested">
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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_8" >
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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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|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
|
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7. 散列表
|
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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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_8">
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<span class="md-nav__icon md-icon"></span>
|
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7. 散列表
|
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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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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
|
||
7.1. 哈希表
|
||
</a>
|
||
</li>
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
|
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7.2. 哈希冲突处理
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
||
7.3. 小结
|
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</a>
|
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</li>
|
||
|
||
|
||
|
||
|
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</ul>
|
||
</nav>
|
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</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
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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_9" checked>
|
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|
||
|
||
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
|
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8. 树
|
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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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
|
||
<label class="md-nav__title" for="__nav_9">
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<span class="md-nav__icon md-icon"></span>
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8. 树
|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../binary_tree/" class="md-nav__link">
|
||
8.1. 二叉树
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
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<a href="../binary_tree_traversal/" class="md-nav__link">
|
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8.2. 二叉树遍历
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../array_representation_of_tree/" class="md-nav__link">
|
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8.3. 二叉树数组表示
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../binary_search_tree/" class="md-nav__link">
|
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8.4. 二叉搜索树
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--active">
|
||
|
||
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link md-nav__link--active" for="__toc">
|
||
8.5. AVL 树 *
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<a href="./" class="md-nav__link md-nav__link--active">
|
||
8.5. AVL 树 *
|
||
</a>
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目录
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#851-avl" class="md-nav__link">
|
||
8.5.1. AVL 树常见术语
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="8.5.1. AVL 树常见术语">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_1" class="md-nav__link">
|
||
节点高度
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_2" class="md-nav__link">
|
||
节点平衡因子
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#852-avl" class="md-nav__link">
|
||
8.5.2. AVL 树旋转
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="8.5.2. AVL 树旋转">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_3" class="md-nav__link">
|
||
右旋
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_4" class="md-nav__link">
|
||
左旋
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_5" class="md-nav__link">
|
||
先左旋后右旋
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_6" class="md-nav__link">
|
||
先右旋后左旋
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_7" class="md-nav__link">
|
||
旋转的选择
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#853-avl" class="md-nav__link">
|
||
8.5.3. AVL 树常用操作
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="8.5.3. AVL 树常用操作">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_8" class="md-nav__link">
|
||
插入节点
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_9" class="md-nav__link">
|
||
删除节点
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_10" class="md-nav__link">
|
||
查找节点
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#854-avl" class="md-nav__link">
|
||
8.5.4. AVL 树典型应用
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../summary/" class="md-nav__link">
|
||
8.6. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
|
||
9. 堆
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
9. 堆
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
||
9.1. 堆
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
||
9.2. 建堆操作 *
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
||
9.3. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
|
||
10. 图
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
10. 图
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
||
10.1. 图
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
||
10.2. 图基础操作
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
||
10.3. 图的遍历
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/summary/" class="md-nav__link">
|
||
10.4. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
|
||
11. 排序算法
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
11. 排序算法
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
|
||
11.1. 排序算法
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
11.2. 冒泡排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
||
11.3. 插入排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
||
11.4. 快速排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
||
11.5. 归并排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
||
11.6. 桶排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
||
11.7. 计数排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
||
11.8. 基数排序
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
||
11.9. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_13" id="__nav_13_label" tabindex="0">
|
||
12. 搜索算法
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_13">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
12. 搜索算法
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
||
12.1. 搜索算法（New）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
||
12.2. 哈希优化策略
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
12.3. 小结
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_14" id="__nav_14_label" tabindex="0">
|
||
13. 回溯算法
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_14">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
13. 回溯算法
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
||
13.1. 回溯算法（New）
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__link" for="__nav_15" id="__nav_15_label" tabindex="0">
|
||
14. 附录
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_15">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
14. 附录
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
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|
||
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|
||
14.1. 编程环境安装
|
||
</a>
|
||
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|
||
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||
|
||
|
||
|
||
|
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||
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||
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|
||
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|
||
14.2. 一起参与创作
|
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<div class="md-nav__link md-nav__link--index ">
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<a href="#851-avl" class="md-nav__link">
|
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8.5.1. AVL 树常见术语
|
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节点高度
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|
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|
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8.5.2. AVL 树旋转
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先左旋后右旋
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先右旋后左旋
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|
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|
||
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|
||
<a href="#_7" class="md-nav__link">
|
||
旋转的选择
|
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|
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|
||
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||
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|
||
<a href="#853-avl" class="md-nav__link">
|
||
8.5.3. AVL 树常用操作
|
||
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|
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|
||
<a href="#_8" class="md-nav__link">
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插入节点
|
||
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|
||
|
||
<li class="md-nav__item">
|
||
<a href="#_9" class="md-nav__link">
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删除节点
|
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</li>
|
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|
||
<li class="md-nav__item">
|
||
<a href="#_10" class="md-nav__link">
|
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查找节点
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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="#854-avl" class="md-nav__link">
|
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8.5.4. AVL 树典型应用
|
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|
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</li>
|
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|
||
</ul>
|
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|
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</div>
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</div>
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<div class="md-content" data-md-component="content">
|
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<article class="md-content__inner md-typeset">
|
||
|
||
|
||
|
||
|
||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_tree/avl_tree.md" title="编辑此页" class="md-content__button md-icon">
|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
|
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|
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|
||
|
||
|
||
<h1 id="85-avl">8.5. AVL 树 *<a class="headerlink" href="#85-avl" title="Permanent link">¶</a></h1>
|
||
<p>在二叉搜索树章节中，我们提到了在多次插入和删除操作后，二叉搜索树可能退化为链表。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>如下图所示，经过两次删除节点操作，这个二叉搜索树便会退化为链表。</p>
|
||
<p><img alt="AVL 树在删除节点后发生退化" src="../avl_tree.assets/avltree_degradation_from_removing_node.png" /></p>
|
||
<p align="center"> Fig. AVL 树在删除节点后发生退化 </p>
|
||
|
||
<p>再例如，在以下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><img alt="AVL 树在插入节点后发生退化" src="../avl_tree.assets/avltree_degradation_from_inserting_node.png" /></p>
|
||
<p align="center"> Fig. AVL 树在插入节点后发生退化 </p>
|
||
|
||
<p>G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorithm for the organization of information" 中提出了「AVL 树」。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="851-avl">8.5.1. AVL 树常见术语<a class="headerlink" href="#851-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」。</p>
|
||
<h3 id="_1">节点高度<a class="headerlink" href="#_1" title="Permanent link">¶</a></h3>
|
||
<p>在操作 AVL 树时，我们需要获取节点的高度，因此需要为 AVL 树的节点类添加 <code>height</code> 变量。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:10"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label></div>
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<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* AVL 树节点类 */</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 节点值</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// 节点高度</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子节点</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子节点</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* AVL 树节点类 */</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="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w"> </span><span class="sd">"""AVL 树节点类"""</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="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-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="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-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 左子节点引用</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="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-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="kd">type</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="nx">Val</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="c1">// 节点值</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="nx">Height</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="c1">// 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="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-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="nx">Right</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 右子节点引用</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="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 节点值</span>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="nx">height</span><span class="p">;</span><span class="w"> </span><span class="c1">//节点高度</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子节点指针</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子节点指针</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">height</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">height</span><span class="p">;</span>
|
||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
|
||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
|
||
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 节点值</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="nx">height</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 节点高度</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子节点指针</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子节点指针</span>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">height?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">left?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">right?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">height</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">left</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">right</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* AVL 树节点类 */</span>
|
||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 节点值</span>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// 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="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</span>
|
||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子节点</span>
|
||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* AVL 树节点类 */</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span> <span class="p">{</span>
|
||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="kd">var</span> <span class="nv">val</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 节点值</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="kd">var</span> <span class="nv">height</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 节点高度</span>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="kd">var</span> <span class="nv">left</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="c1">// 左子节点</span>
|
||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="kd">var</span> <span class="nv">right</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="c1">// 右子节点</span>
|
||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a>
|
||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="n">val</span> <span class="p">=</span> <span class="n">x</span>
|
||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="n">height</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="p">}</span>
|
||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</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>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>「节点高度」是指从该节点到最远叶节点的距离，即所经过的“边”的数量。需要特别注意的是，叶节点的高度为 0 ，而空节点的高度为 -1 。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="2:10"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">height</span><span class="p">;</span>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
|
||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="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-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></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-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">height</span><span class="p">;</span>
|
||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
|
||
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="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-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></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-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="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.go</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">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-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">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Height</span>
|
||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>
|
||
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="w"> </span><span class="nx">lh</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span>
|
||
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w"> </span><span class="nx">rh</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
|
||
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></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-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">lh</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">rh</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Height</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">lh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Height</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">rh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -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="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">height</span><span class="p">;</span>
|
||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
|
||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></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-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="nx">node</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span>
|
||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></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-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></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-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="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="c1">// 空节点高度为 -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="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="nx">1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">node.height</span><span class="p">;</span>
|
||
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a>
|
||
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="c1">// 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="nx">node</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span>
|
||
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></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-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></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-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
|
||
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
|
||
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">updateHeight</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">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>
|
||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">{</span>
|
||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">height</span><span class="p">;</span>
|
||
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="p">}</span>
|
||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a>
|
||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="k">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="p">{</span>
|
||
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 获取节点高度 */</span>
|
||
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span> <span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a> <span class="c1">// 空节点高度为 -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="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">?</span> <span class="o">-</span><span class="mi">1</span> <span class="p">:</span> <span class="n">node</span><span class="p">!.</span><span class="n">height</span>
|
||
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a>
|
||
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="cm">/* 更新节点高度 */</span>
|
||
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="kd">func</span> <span class="nf">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?)</span> <span class="p">{</span>
|
||
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a> <span class="c1">// 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="n">node</span><span class="p">?.</span><span class="n">height</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">),</span> <span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">))</span> <span class="o">+</span> <span class="mi">1</span>
|
||
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// 获取节点高度</span>
|
||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">))</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">;</span>
|
||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w"> </span><span class="c1">// 空节点高度为 -1 ，叶节点高度为 0</span>
|
||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">height</span><span class="p">;</span>
|
||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="p">}</span>
|
||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a>
|
||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="k">fn</span><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">))</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w"> </span><span class="c1">// 节点高度等于最高子树高度 + 1</span>
|
||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">math</span><span class="p">.</span><span class="n">max</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="_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 0 。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="3:10"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Java</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Python</label><label for="__tabbed_3_4">Go</label><label for="__tabbed_3_5">JavaScript</label><label for="__tabbed_3_6">TypeScript</label><label for="__tabbed_3_7">C</label><label for="__tabbed_3_8">C#</label><label for="__tabbed_3_9">Swift</label><label for="__tabbed_3_10">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></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-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></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-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></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-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="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-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
|
||
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></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-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></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-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></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-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="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-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="w"> </span><span class="sd">"""获取平衡因子"""</span>
|
||
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a> <span class="c1"># 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a> <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a> <span class="c1"># 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
|
||
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
|
||
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 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="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
|
||
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">balanceFactor</span><span class="p">}</span>
|
||
</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>
|
||
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">{</span>
|
||
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w"> </span><span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 获取平衡因子 */</span>
|
||
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kd">func</span> <span class="nf">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a> <span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a> <span class="k">guard</span> <span class="kd">let</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span> <span class="k">else</span> <span class="p">{</span> <span class="k">return</span> <span class="mi">0</span> <span class="p">}</span>
|
||
<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a> <span class="c1">// 节点平衡因子 = 左子树高度 - 右子树高度</span>
|
||
<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a> <span class="k">return</span> <span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">.</span><span class="kr">left</span><span class="p">)</span> <span class="o">-</span> <span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">.</span><span class="kr">right</span><span class="p">)</span>
|
||
<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="c1">// 获取平衡因子</span>
|
||
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">))</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="c1">// 空节点平衡因子为 0</span>
|
||
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w"> </span><span class="c1">// 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="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="p">}</span>
|
||
</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="852-avl">8.5.2. AVL 树旋转<a class="headerlink" href="#852-avl" title="Permanent link">¶</a></h2>
|
||
<p>AVL 树的特点在于「旋转 Rotation」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>旋转操作既能保持树的「二叉搜索树」属性，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。下面我们将详细介绍这些旋转操作。</p>
|
||
<h3 id="_3">右旋<a class="headerlink" href="#_3" title="Permanent link">¶</a></h3>
|
||
<p>如下图所示，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，子树已经恢复平衡，并且仍然保持二叉搜索树的特性。</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><img alt="右旋操作步骤" src="../avl_tree.assets/avltree_right_rotate_step1.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="avltree_right_rotate_step2" src="../avl_tree.assets/avltree_right_rotate_step2.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="avltree_right_rotate_step3" src="../avl_tree.assets/avltree_right_rotate_step3.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="avltree_right_rotate_step4" src="../avl_tree.assets/avltree_right_rotate_step4.png" /></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>此外，如果节点 <code>child</code> 本身有右子节点（记为 <code>grandChild</code> ），则需要在「右旋」中添加一步：将 <code>grandChild</code> 作为 <code>node</code> 的左子节点。</p>
|
||
<p><img alt="有 grandChild 的右旋操作" src="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" /></p>
|
||
<p align="center"> Fig. 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="5:10"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Java</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Python</label><label for="__tabbed_5_4">Go</label><label for="__tabbed_5_5">JavaScript</label><label for="__tabbed_5_6">TypeScript</label><label for="__tabbed_5_7">C</label><label for="__tabbed_5_8">C#</label><label for="__tabbed_5_9">Swift</label><label for="__tabbed_5_10">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
|
||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
|
||
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="n">TreeNode</span><span class="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-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></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-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></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-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="n">child</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="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-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w"> </span><span class="sd">"""右旋操作"""</span>
|
||
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a> <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span>
|
||
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a> <span class="n">grand_child</span> <span class="o">=</span> <span class="n">child</span><span class="o">.</span><span class="n">right</span>
|
||
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a> <span class="c1"># 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a> <span class="n">child</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">grand_child</span>
|
||
<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a> <span class="c1"># 更新节点高度</span>
|
||
<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
|
||
<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a> <span class="c1"># 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a> <span class="k">return</span> <span class="n">child</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span>
|
||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">Right</span>
|
||
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">grandChild</span>
|
||
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
|
||
<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">)</span>
|
||
<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span>
|
||
<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="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-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
|
||
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
|
||
<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
|
||
<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
|
||
<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
|
||
<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
|
||
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
|
||
<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
|
||
<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
|
||
<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
|
||
<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rightRotate</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="p">{</span>
|
||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">?.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kd">func</span> <span class="nf">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?)</span> <span class="p">-></span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
|
||
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span>
|
||
<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a> <span class="kd">let</span> <span class="nv">grandChild</span> <span class="p">=</span> <span class="n">child</span><span class="p">?.</span><span class="kr">right</span>
|
||
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a> <span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a> <span class="n">child</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">grandChild</span>
|
||
<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a> <span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">child</span><span class="p">)</span>
|
||
<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a> <span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a> <span class="k">return</span> <span class="n">child</span>
|
||
<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="c1">// 右旋操作</span>
|
||
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">))</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向右旋转</span>
|
||
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</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>
|
||
</div>
|
||
<h3 id="_4">左旋<a class="headerlink" href="#_4" title="Permanent link">¶</a></h3>
|
||
<p>相应的，如果考虑上述失衡二叉树的“镜像”，则需要执行「左旋」操作。</p>
|
||
<p><img alt="左旋操作" src="../avl_tree.assets/avltree_left_rotate.png" /></p>
|
||
<p align="center"> Fig. 左旋操作 </p>
|
||
|
||
<p>同理，若节点 <code>child</code> 本身有左子节点（记为 <code>grandChild</code> ），则需要在「左旋」中添加一步：将 <code>grandChild</code> 作为 <code>node</code> 的右子节点。</p>
|
||
<p><img alt="有 grandChild 的左旋操作" src="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" /></p>
|
||
<p align="center"> Fig. 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，我们可以轻松地从右旋的代码推导出左旋的代码。具体地，只需将「右旋」代码中的把所有的 <code>left</code> 替换为 <code>right</code> ，将所有的 <code>right</code> 替换为 <code>left</code> ，即可得到「左旋」代码。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Java</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Python</label><label for="__tabbed_6_4">Go</label><label for="__tabbed_6_5">JavaScript</label><label for="__tabbed_6_6">TypeScript</label><label for="__tabbed_6_7">C</label><label for="__tabbed_6_8">C#</label><label for="__tabbed_6_9">Swift</label><label for="__tabbed_6_10">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
|
||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
|
||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</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="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="n">TreeNode</span><span class="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-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></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-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></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-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w"> </span><span class="n">child</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="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-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="sd">"""左旋操作"""</span>
|
||
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a> <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
|
||
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a> <span class="n">grand_child</span> <span class="o">=</span> <span class="n">child</span><span class="o">.</span><span class="n">left</span>
|
||
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a> <span class="c1"># 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a> <span class="n">child</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">grand_child</span>
|
||
<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a> <span class="c1"># 更新节点高度</span>
|
||
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
|
||
<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a> <span class="c1"># 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a> <span class="k">return</span> <span class="n">child</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span>
|
||
<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">Left</span>
|
||
<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">grandChild</span>
|
||
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
|
||
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">)</span>
|
||
<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>
|
||
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="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-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
|
||
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
|
||
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
|
||
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w"> </span><span class="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-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
|
||
<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</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="nx">child</span><span class="p">;</span>
|
||
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
|
||
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
|
||
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="nx">child</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
|
||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
|
||
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
|
||
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">leftRotate</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="p">{</span>
|
||
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">?.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</span>
|
||
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="kd">func</span> <span class="nf">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?)</span> <span class="p">-></span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
|
||
<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
|
||
<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a> <span class="kd">let</span> <span class="nv">grandChild</span> <span class="p">=</span> <span class="n">child</span><span class="p">?.</span><span class="kr">left</span>
|
||
<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a> <span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a> <span class="n">child</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">grandChild</span>
|
||
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a> <span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">child</span><span class="p">)</span>
|
||
<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a> <span class="c1">// 返回旋转后子树的根节点</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>
|
||
<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="c1">// 左旋操作</span>
|
||
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">))</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="c1">// 以 child 为原点，将 node 向左旋转</span>
|
||
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w"> </span><span class="c1">// 返回旋转后子树的根节点</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>
|
||
</div>
|
||
<h3 id="_5">先左旋后右旋<a class="headerlink" href="#_5" title="Permanent link">¶</a></h3>
|
||
<p>对于下图中的失衡节点 3，仅使用左旋或右旋都无法使子树恢复平衡。此时需要先左旋后右旋，即先对 <code>child</code> 执行「左旋」，再对 <code>node</code> 执行「右旋」。</p>
|
||
<p><img alt="先左旋后右旋" src="../avl_tree.assets/avltree_left_right_rotate.png" /></p>
|
||
<p align="center"> Fig. 先左旋后右旋 </p>
|
||
|
||
<h3 id="_6">先右旋后左旋<a class="headerlink" href="#_6" title="Permanent link">¶</a></h3>
|
||
<p>同理，对于上述失衡二叉树的镜像情况，需要先右旋后左旋，即先对 <code>child</code> 执行「右旋」，然后对 <code>node</code> 执行「左旋」。</p>
|
||
<p><img alt="先右旋后左旋" src="../avl_tree.assets/avltree_right_left_rotate.png" /></p>
|
||
<p align="center"> Fig. 先右旋后左旋 </p>
|
||
|
||
<h3 id="_7">旋转的选择<a class="headerlink" href="#_7" title="Permanent link">¶</a></h3>
|
||
<p>下图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、左旋、先右后左、先左后右的旋转操作。</p>
|
||
<p><img alt="AVL 树的四种旋转情况" src="../avl_tree.assets/avltree_rotation_cases.png" /></p>
|
||
<p align="center"> Fig. AVL 树的四种旋转情况 </p>
|
||
|
||
<p>在代码中，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上图中的哪种情况。</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">\(>0\)</span> （即左偏树）</td>
|
||
<td><span class="arithmatex">\(\geq 0\)</span></td>
|
||
<td>右旋</td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(>0\)</span> （即左偏树）</td>
|
||
<td><span class="arithmatex">\(<0\)</span></td>
|
||
<td>先左旋后右旋</td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(<0\)</span> （即右偏树）</td>
|
||
<td><span class="arithmatex">\(\leq 0\)</span></td>
|
||
<td>左旋</td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(<0\)</span> （即右偏树）</td>
|
||
<td><span class="arithmatex">\(>0\)</span></td>
|
||
<td>先右旋后左旋</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<p>为了便于使用，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>。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="7:10"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Java</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Python</label><label for="__tabbed_7_4">Go</label><label for="__tabbed_7_5">JavaScript</label><label for="__tabbed_7_6">TypeScript</label><label for="__tabbed_7_7">C</label><label for="__tabbed_7_8">C#</label><label for="__tabbed_7_9">Swift</label><label for="__tabbed_7_10">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
|
||
<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-50-23" name="__codelineno-50-23" href="#__codelineno-50-23"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
|
||
<a id="__codelineno-50-24" name="__codelineno-50-24" href="#__codelineno-50-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-50-25" name="__codelineno-50-25" href="#__codelineno-50-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-50-26" name="__codelineno-50-26" href="#__codelineno-50-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-50-27" name="__codelineno-50-27" href="#__codelineno-50-27"></a><span class="w"> </span><span class="c1">// 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-50-28" name="__codelineno-50-28" href="#__codelineno-50-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-50-29" name="__codelineno-50-29" href="#__codelineno-50-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="n">TreeNode</span><span class="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-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-22" name="__codelineno-51-22" href="#__codelineno-51-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-51-23" name="__codelineno-51-23" href="#__codelineno-51-23"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-51-24" name="__codelineno-51-24" href="#__codelineno-51-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-51-25" name="__codelineno-51-25" href="#__codelineno-51-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-51-26" name="__codelineno-51-26" href="#__codelineno-51-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-51-27" name="__codelineno-51-27" href="#__codelineno-51-27"></a><span class="w"> </span><span class="c1">// 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-51-28" name="__codelineno-51-28" href="#__codelineno-51-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-51-29" name="__codelineno-51-29" href="#__codelineno-51-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="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-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></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-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a> <span class="c1"># 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a> <span class="n">balance_factor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a> <span class="c1"># 左偏树</span>
|
||
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a> <span class="k">if</span> <span class="n">balance_factor</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">:</span>
|
||
<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a> <span class="c1"># 右旋</span>
|
||
<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a> <span class="c1"># 先左旋后右旋</span>
|
||
<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__left_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
|
||
<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a> <span class="c1"># 右偏树</span>
|
||
<a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a> <span class="k">elif</span> <span class="n">balance_factor</span> <span class="o"><</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span> <span class="o"><=</span> <span class="mi">0</span><span class="p">:</span>
|
||
<a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a> <span class="c1"># 左旋</span>
|
||
<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a> <span class="c1"># 先右旋后左旋</span>
|
||
<a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__right_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
||
<a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a> <span class="c1"># 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a> <span class="k">return</span> <span class="n">node</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w"> </span><span class="c1">// Go 推荐短变量，这里 bf 指代 t.balanceFactor</span>
|
||
<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w"> </span><span class="nx">bf</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
|
||
<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">bf</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
|
||
<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">)</span>
|
||
<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
|
||
<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">bf</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
|
||
<a id="__codelineno-53-22" name="__codelineno-53-22" href="#__codelineno-53-22"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-23" name="__codelineno-53-23" href="#__codelineno-53-23"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-53-24" name="__codelineno-53-24" href="#__codelineno-53-24"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
|
||
<a id="__codelineno-53-25" name="__codelineno-53-25" href="#__codelineno-53-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">)</span>
|
||
<a id="__codelineno-53-26" name="__codelineno-53-26" href="#__codelineno-53-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-53-27" name="__codelineno-53-27" href="#__codelineno-53-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-53-28" name="__codelineno-53-28" href="#__codelineno-53-28"></a><span class="w"> </span><span class="c1">// 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-53-29" name="__codelineno-53-29" href="#__codelineno-53-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-53-30" name="__codelineno-53-30" href="#__codelineno-53-30"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="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-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="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-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-22" name="__codelineno-54-22" href="#__codelineno-54-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-54-23" name="__codelineno-54-23" href="#__codelineno-54-23"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="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-54-24" name="__codelineno-54-24" href="#__codelineno-54-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-54-25" name="__codelineno-54-25" href="#__codelineno-54-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-54-26" name="__codelineno-54-26" href="#__codelineno-54-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-54-27" name="__codelineno-54-27" href="#__codelineno-54-27"></a><span class="w"> </span><span class="c1">// 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-54-28" name="__codelineno-54-28" href="#__codelineno-54-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
|
||
<a id="__codelineno-54-29" name="__codelineno-54-29" href="#__codelineno-54-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="p">);</span>
|
||
<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">balanceFactor</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">balanceFactor</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-55-23" name="__codelineno-55-23" href="#__codelineno-55-23"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">rightRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">);</span>
|
||
<a id="__codelineno-55-24" name="__codelineno-55-24" href="#__codelineno-55-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">leftRotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-55-25" name="__codelineno-55-25" href="#__codelineno-55-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-55-26" name="__codelineno-55-26" href="#__codelineno-55-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-55-27" name="__codelineno-55-27" href="#__codelineno-55-27"></a><span class="w"> </span><span class="c1">// 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-55-28" name="__codelineno-55-28" href="#__codelineno-55-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
|
||
<a id="__codelineno-55-29" name="__codelineno-55-29" href="#__codelineno-55-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="p">{</span>
|
||
<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
|
||
<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
|
||
<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span>
|
||
<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
|
||
<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-57-32" name="__codelineno-57-32" href="#__codelineno-57-32"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-57-33" name="__codelineno-57-33" href="#__codelineno-57-33"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-57-34" name="__codelineno-57-34" href="#__codelineno-57-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-35" name="__codelineno-57-35" href="#__codelineno-57-35"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-36" name="__codelineno-57-36" href="#__codelineno-57-36"></a><span class="w"> </span><span class="c1">// 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-57-37" name="__codelineno-57-37" href="#__codelineno-57-37"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-57-38" name="__codelineno-57-38" href="#__codelineno-57-38"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">func</span> <span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?)</span> <span class="p">-></span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
|
||
<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a> <span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a> <span class="kd">let</span> <span class="nv">balanceFactor</span> <span class="p">=</span> <span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a> <span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a> <span class="k">if</span> <span class="n">balanceFactor</span> <span class="o">></span> <span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a> <span class="k">if</span> <span class="kc">self</span><span class="p">.</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">)</span> <span class="o">>=</span> <span class="mi">0</span> <span class="p">{</span>
|
||
<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a> <span class="c1">// 右旋</span>
|
||
<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a> <span class="k">return</span> <span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a> <span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">)</span>
|
||
<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a> <span class="k">return</span> <span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a> <span class="p">}</span>
|
||
<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a> <span class="p">}</span>
|
||
<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a> <span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a> <span class="k">if</span> <span class="n">balanceFactor</span> <span class="o"><</span> <span class="o">-</span><span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a> <span class="k">if</span> <span class="kc">self</span><span class="p">.</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">)</span> <span class="o"><=</span> <span class="mi">0</span> <span class="p">{</span>
|
||
<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a> <span class="c1">// 左旋</span>
|
||
<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a> <span class="k">return</span> <span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a> <span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">)</span>
|
||
<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a> <span class="k">return</span> <span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a> <span class="p">}</span>
|
||
<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a> <span class="p">}</span>
|
||
<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a> <span class="c1">// 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="c1">// 执行旋转操作，使该子树重新恢复平衡</span>
|
||
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">))</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="c1">// 获取节点 node 的平衡因子</span>
|
||
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="c1">// 左偏树</span>
|
||
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balance_factor</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="c1">// 先左旋后右旋</span>
|
||
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a><span class="w"> </span><span class="c1">// 右偏树</span>
|
||
<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balance_factor</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-22" name="__codelineno-59-22" href="#__codelineno-59-22"></a><span class="w"> </span><span class="c1">// 先右旋后左旋</span>
|
||
<a id="__codelineno-59-23" name="__codelineno-59-23" href="#__codelineno-59-23"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-59-24" name="__codelineno-59-24" href="#__codelineno-59-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-59-25" name="__codelineno-59-25" href="#__codelineno-59-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-59-26" name="__codelineno-59-26" href="#__codelineno-59-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-59-27" name="__codelineno-59-27" href="#__codelineno-59-27"></a><span class="w"> </span><span class="c1">// 平衡树，无需旋转，直接返回</span>
|
||
<a id="__codelineno-59-28" name="__codelineno-59-28" href="#__codelineno-59-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-59-29" name="__codelineno-59-29" href="#__codelineno-59-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h2 id="853-avl">8.5.3. AVL 树常用操作<a class="headerlink" href="#853-avl" title="Permanent link">¶</a></h2>
|
||
<h3 id="_8">插入节点<a class="headerlink" href="#_8" 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>。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="8:10"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Java</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Python</label><label for="__tabbed_8_4">Go</label><label for="__tabbed_8_5">JavaScript</label><label for="__tabbed_8_6">TypeScript</label><label for="__tabbed_8_7">C</label><label for="__tabbed_8_8">C#</label><label for="__tabbed_8_9">Swift</label><label for="__tabbed_8_10">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></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-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a>
|
||
<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></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-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></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-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></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-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
|
||
<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
|
||
<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-60-16" name="__codelineno-60-16" href="#__codelineno-60-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-60-17" name="__codelineno-60-17" href="#__codelineno-60-17"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-60-18" name="__codelineno-60-18" href="#__codelineno-60-18"></a><span class="w"> </span><span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-60-19" name="__codelineno-60-19" href="#__codelineno-60-19"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-60-20" name="__codelineno-60-20" href="#__codelineno-60-20"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-60-21" name="__codelineno-60-21" href="#__codelineno-60-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-60-22" name="__codelineno-60-22" href="#__codelineno-60-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></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-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a>
|
||
<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></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-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></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-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="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a><span class="w"> </span><span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="k">def</span> <span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span> <span class="o">-></span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="w"> </span><span class="sd">"""插入节点"""</span>
|
||
<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__root</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__root</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a>
|
||
<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></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-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w"> </span><span class="sd">"""递归插入节点（辅助方法）"""</span>
|
||
<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></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-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></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-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a> <span class="c1"># 1. 查找插入位置，并插入节点</span>
|
||
<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></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-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></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-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></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-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></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-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a> <span class="c1"># 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-62-16" name="__codelineno-62-16" href="#__codelineno-62-16"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-62-17" name="__codelineno-62-17" href="#__codelineno-62-17"></a> <span class="c1"># 更新节点高度</span>
|
||
<a id="__codelineno-62-18" name="__codelineno-62-18" href="#__codelineno-62-18"></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-62-19" name="__codelineno-62-19" href="#__codelineno-62-19"></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-62-20" name="__codelineno-62-20" href="#__codelineno-62-20"></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.go</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
|
||
<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a>
|
||
<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></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-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></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-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="nx">NewTreeNode</span><span class="p">(</span><span class="nx">val</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>
|
||
<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></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="w"> </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="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
|
||
<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></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="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="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
|
||
<a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></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-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a><span class="w"> </span><span class="c1">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-63-18" name="__codelineno-63-18" href="#__codelineno-63-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-63-21" name="__codelineno-63-21" href="#__codelineno-63-21"></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-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></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-63-23" name="__codelineno-63-23" href="#__codelineno-63-23"></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-63-24" name="__codelineno-63-24" href="#__codelineno-63-24"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-63-25" name="__codelineno-63-25" href="#__codelineno-63-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-63-26" name="__codelineno-63-26" href="#__codelineno-63-26"></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-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="nx">insert</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="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-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a>
|
||
<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></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-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="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
|
||
<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></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-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></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-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></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-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重复节点不插入，直接返回</span>
|
||
<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="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-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a><span class="w"> </span><span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-64-16" name="__codelineno-64-16" href="#__codelineno-64-16"></a><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">rotate</span><span class="p">(</span><span class="nx">node</span><span class="p">);</span>
|
||
<a id="__codelineno-64-17" name="__codelineno-64-17" href="#__codelineno-64-17"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-64-18" name="__codelineno-64-18" href="#__codelineno-64-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
|
||
<a id="__codelineno-64-19" name="__codelineno-64-19" href="#__codelineno-64-19"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="nx">insert</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
|
||
<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a>
|
||
<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></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-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></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-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-65-10" name="__codelineno-65-10" href="#__codelineno-65-10"></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-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></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-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></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-65-13" name="__codelineno-65-13" href="#__codelineno-65-13"></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-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></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-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></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-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-65-17" name="__codelineno-65-17" href="#__codelineno-65-17"></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-65-18" name="__codelineno-65-18" href="#__codelineno-65-18"></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-65-19" name="__codelineno-65-19" href="#__codelineno-65-19"></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-65-20" name="__codelineno-65-20" href="#__codelineno-65-20"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-65-21" name="__codelineno-65-21" href="#__codelineno-65-21"></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-65-22" name="__codelineno-65-22" href="#__codelineno-65-22"></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-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
|
||
<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a>
|
||
<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertHelper</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></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>
|
||
<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="p">{</span>
|
||
<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a>
|
||
<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></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>
|
||
<a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></a><span class="p">{</span>
|
||
<a id="__codelineno-67-10" name="__codelineno-67-10" href="#__codelineno-67-10"></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="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w"> </span><span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-67-12" name="__codelineno-67-12" href="#__codelineno-67-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</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="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-67-14" name="__codelineno-67-14" href="#__codelineno-67-14"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-67-15" name="__codelineno-67-15" href="#__codelineno-67-15"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-67-16" name="__codelineno-67-16" href="#__codelineno-67-16"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-67-17" name="__codelineno-67-17" href="#__codelineno-67-17"></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-67-18" name="__codelineno-67-18" href="#__codelineno-67-18"></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-67-19" name="__codelineno-67-19" href="#__codelineno-67-19"></a><span class="w"> </span><span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-67-20" name="__codelineno-67-20" href="#__codelineno-67-20"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-67-21" name="__codelineno-67-21" href="#__codelineno-67-21"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-67-22" name="__codelineno-67-22" href="#__codelineno-67-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-67-23" name="__codelineno-67-23" href="#__codelineno-67-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 插入节点 */</span>
|
||
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="p">@</span><span class="n">discardableResult</span>
|
||
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="kd">func</span> <span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">root</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a>
|
||
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
|
||
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="kd">func</span> <span class="nf">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
|
||
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a> <span class="k">if</span> <span class="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a> <span class="k">return</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></a> <span class="p">}</span>
|
||
<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></a> <span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
|
||
<a id="__codelineno-68-14" name="__codelineno-68-14" href="#__codelineno-68-14"></a> <span class="k">if</span> <span class="n">val</span> <span class="o"><</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
|
||
<a id="__codelineno-68-15" name="__codelineno-68-15" href="#__codelineno-68-15"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-68-16" name="__codelineno-68-16" href="#__codelineno-68-16"></a> <span class="p">}</span> <span class="k">else</span> <span class="k">if</span> <span class="n">val</span> <span class="o">></span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
|
||
<a id="__codelineno-68-17" name="__codelineno-68-17" href="#__codelineno-68-17"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-68-18" name="__codelineno-68-18" href="#__codelineno-68-18"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-68-19" name="__codelineno-68-19" href="#__codelineno-68-19"></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-68-20" name="__codelineno-68-20" href="#__codelineno-68-20"></a> <span class="p">}</span>
|
||
<a id="__codelineno-68-21" name="__codelineno-68-21" href="#__codelineno-68-21"></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-68-22" name="__codelineno-68-22" href="#__codelineno-68-22"></a> <span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-68-23" name="__codelineno-68-23" href="#__codelineno-68-23"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-68-24" name="__codelineno-68-24" href="#__codelineno-68-24"></a> <span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-68-25" name="__codelineno-68-25" href="#__codelineno-68-25"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-68-26" name="__codelineno-68-26" href="#__codelineno-68-26"></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-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="c1">// 插入节点</span>
|
||
<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">insertHelper</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a>
|
||
<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="c1">// 递归插入节点（辅助方法）</span>
|
||
<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></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-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></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-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></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-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></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-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></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-69-12" name="__codelineno-69-12" href="#__codelineno-69-12"></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-69-13" name="__codelineno-69-13" href="#__codelineno-69-13"></a><span class="w"> </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="c1">// 1. 查找插入位置，并插入节点</span>
|
||
<a id="__codelineno-69-15" name="__codelineno-69-15" href="#__codelineno-69-15"></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-69-16" name="__codelineno-69-16" href="#__codelineno-69-16"></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-69-17" name="__codelineno-69-17" href="#__codelineno-69-17"></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-69-18" name="__codelineno-69-18" href="#__codelineno-69-18"></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-69-19" name="__codelineno-69-19" href="#__codelineno-69-19"></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-69-20" name="__codelineno-69-20" href="#__codelineno-69-20"></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-69-21" name="__codelineno-69-21" href="#__codelineno-69-21"></a><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="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-69-23" name="__codelineno-69-23" href="#__codelineno-69-23"></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-69-24" name="__codelineno-69-24" href="#__codelineno-69-24"></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-69-25" name="__codelineno-69-25" href="#__codelineno-69-25"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-69-26" name="__codelineno-69-26" href="#__codelineno-69-26"></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-69-27" name="__codelineno-69-27" href="#__codelineno-69-27"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="_9">删除节点<a class="headerlink" href="#_9" 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，需要从底至顶地执行旋转操作，使所有失衡节点恢复平衡。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="9:10"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Java</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Python</label><label for="__tabbed_9_4">Go</label><label for="__tabbed_9_5">JavaScript</label><label for="__tabbed_9_6">TypeScript</label><label for="__tabbed_9_7">C</label><label for="__tabbed_9_8">C#</label><label for="__tabbed_9_9">Swift</label><label for="__tabbed_9_10">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></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-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a>
|
||
<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></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-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></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-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="kc">null</span><span class="p">;</span>
|
||
<a id="__codelineno-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
|
||
<a id="__codelineno-70-12" name="__codelineno-70-12" href="#__codelineno-70-12"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-70-13" name="__codelineno-70-13" href="#__codelineno-70-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
|
||
<a id="__codelineno-70-14" name="__codelineno-70-14" href="#__codelineno-70-14"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-70-15" name="__codelineno-70-15" href="#__codelineno-70-15"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-70-16" name="__codelineno-70-16" href="#__codelineno-70-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-70-17" name="__codelineno-70-17" href="#__codelineno-70-17"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
|
||
<a id="__codelineno-70-18" name="__codelineno-70-18" href="#__codelineno-70-18"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-70-19" name="__codelineno-70-19" href="#__codelineno-70-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-70-20" name="__codelineno-70-20" href="#__codelineno-70-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||
<a id="__codelineno-70-21" name="__codelineno-70-21" href="#__codelineno-70-21"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-70-22" name="__codelineno-70-22" href="#__codelineno-70-22"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-70-23" name="__codelineno-70-23" href="#__codelineno-70-23"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-70-24" name="__codelineno-70-24" href="#__codelineno-70-24"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-70-25" name="__codelineno-70-25" href="#__codelineno-70-25"></a><span class="w"> </span><span class="c1">// 子节点数量 = 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-70-26" name="__codelineno-70-26" href="#__codelineno-70-26"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
|
||
<a id="__codelineno-70-27" name="__codelineno-70-27" href="#__codelineno-70-27"></a><span class="w"> </span><span class="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-70-28" name="__codelineno-70-28" href="#__codelineno-70-28"></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-70-29" name="__codelineno-70-29" href="#__codelineno-70-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-70-30" name="__codelineno-70-30" href="#__codelineno-70-30"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
|
||
<a id="__codelineno-70-31" name="__codelineno-70-31" href="#__codelineno-70-31"></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-70-32" name="__codelineno-70-32" href="#__codelineno-70-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-70-33" name="__codelineno-70-33" href="#__codelineno-70-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-70-34" name="__codelineno-70-34" href="#__codelineno-70-34"></a><span class="w"> </span><span class="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-70-35" name="__codelineno-70-35" href="#__codelineno-70-35"></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-70-36" name="__codelineno-70-36" href="#__codelineno-70-36"></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-70-37" name="__codelineno-70-37" href="#__codelineno-70-37"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-70-38" name="__codelineno-70-38" href="#__codelineno-70-38"></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-70-39" name="__codelineno-70-39" href="#__codelineno-70-39"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></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-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a>
|
||
<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></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-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></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-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="k">nullptr</span><span class="p">;</span>
|
||
<a id="__codelineno-71-10" name="__codelineno-71-10" href="#__codelineno-71-10"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-71-11" name="__codelineno-71-11" href="#__codelineno-71-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-71-12" name="__codelineno-71-12" href="#__codelineno-71-12"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-71-13" name="__codelineno-71-13" href="#__codelineno-71-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-71-14" name="__codelineno-71-14" href="#__codelineno-71-14"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-71-15" name="__codelineno-71-15" href="#__codelineno-71-15"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-16" name="__codelineno-71-16" href="#__codelineno-71-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-17" name="__codelineno-71-17" href="#__codelineno-71-17"></a><span class="w"> </span><span class="n">TreeNode</span><span class="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-71-18" name="__codelineno-71-18" href="#__codelineno-71-18"></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-71-19" name="__codelineno-71-19" href="#__codelineno-71-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-20" name="__codelineno-71-20" href="#__codelineno-71-20"></a><span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-71-21" name="__codelineno-71-21" href="#__codelineno-71-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
|
||
<a id="__codelineno-71-22" name="__codelineno-71-22" href="#__codelineno-71-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-23" name="__codelineno-71-23" href="#__codelineno-71-23"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-71-24" name="__codelineno-71-24" href="#__codelineno-71-24"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-25" name="__codelineno-71-25" href="#__codelineno-71-25"></a><span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-71-26" name="__codelineno-71-26" href="#__codelineno-71-26"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-71-27" name="__codelineno-71-27" href="#__codelineno-71-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-28" name="__codelineno-71-28" href="#__codelineno-71-28"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-29" name="__codelineno-71-29" href="#__codelineno-71-29"></a><span class="w"> </span><span class="c1">// 子节点数量 = 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-71-30" name="__codelineno-71-30" href="#__codelineno-71-30"></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-71-31" name="__codelineno-71-31" href="#__codelineno-71-31"></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-71-32" name="__codelineno-71-32" href="#__codelineno-71-32"></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-71-33" name="__codelineno-71-33" href="#__codelineno-71-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-34" name="__codelineno-71-34" href="#__codelineno-71-34"></a><span class="w"> </span><span class="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-71-35" name="__codelineno-71-35" href="#__codelineno-71-35"></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-71-36" name="__codelineno-71-36" href="#__codelineno-71-36"></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-71-37" name="__codelineno-71-37" href="#__codelineno-71-37"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-38" name="__codelineno-71-38" href="#__codelineno-71-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-39" name="__codelineno-71-39" href="#__codelineno-71-39"></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-71-40" name="__codelineno-71-40" href="#__codelineno-71-40"></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-71-41" name="__codelineno-71-41" href="#__codelineno-71-41"></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-71-42" name="__codelineno-71-42" href="#__codelineno-71-42"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-71-43" name="__codelineno-71-43" href="#__codelineno-71-43"></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-71-44" name="__codelineno-71-44" href="#__codelineno-71-44"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></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> <span class="o">-></span> <span class="kc">None</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">"""删除节点"""</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">__remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__root</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a>
|
||
<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></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-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w"> </span><span class="sd">"""递归删除节点（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="kc">None</span>
|
||
<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a> <span class="c1"># 1. 查找节点，并删除之</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">__remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-72-12" 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">__remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-72-14" 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="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-72-16" name="__codelineno-72-16" href="#__codelineno-72-16"></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-72-17" name="__codelineno-72-17" href="#__codelineno-72-17"></a> <span class="c1"># 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-72-18" name="__codelineno-72-18" href="#__codelineno-72-18"></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-72-19" name="__codelineno-72-19" href="#__codelineno-72-19"></a> <span class="k">return</span> <span class="kc">None</span>
|
||
<a id="__codelineno-72-20" name="__codelineno-72-20" href="#__codelineno-72-20"></a> <span class="c1"># 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-72-21" name="__codelineno-72-21" href="#__codelineno-72-21"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-72-22" name="__codelineno-72-22" href="#__codelineno-72-22"></a> <span class="n">node</span> <span class="o">=</span> <span class="n">child</span>
|
||
<a id="__codelineno-72-23" name="__codelineno-72-23" href="#__codelineno-72-23"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-72-24" name="__codelineno-72-24" href="#__codelineno-72-24"></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-72-25" name="__codelineno-72-25" href="#__codelineno-72-25"></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-72-26" name="__codelineno-72-26" href="#__codelineno-72-26"></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-72-27" name="__codelineno-72-27" href="#__codelineno-72-27"></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-72-28" name="__codelineno-72-28" href="#__codelineno-72-28"></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-72-29" name="__codelineno-72-29" href="#__codelineno-72-29"></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-72-30" name="__codelineno-72-30" href="#__codelineno-72-30"></a> <span class="c1"># 更新节点高度</span>
|
||
<a id="__codelineno-72-31" name="__codelineno-72-31" href="#__codelineno-72-31"></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-72-32" name="__codelineno-72-32" href="#__codelineno-72-32"></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-72-33" name="__codelineno-72-33" href="#__codelineno-72-33"></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.go</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></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-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">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></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-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="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||
<a id="__codelineno-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-11" name="__codelineno-73-11" href="#__codelineno-73-11"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-73-12" name="__codelineno-73-12" href="#__codelineno-73-12"></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="w"> </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="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-73-14" name="__codelineno-73-14" href="#__codelineno-73-14"></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="w"> </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="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-73-16" name="__codelineno-73-16" href="#__codelineno-73-16"></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-73-17" name="__codelineno-73-17" href="#__codelineno-73-17"></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-73-18" name="__codelineno-73-18" href="#__codelineno-73-18"></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-73-19" name="__codelineno-73-19" href="#__codelineno-73-19"></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-73-20" name="__codelineno-73-20" href="#__codelineno-73-20"></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-73-21" name="__codelineno-73-21" href="#__codelineno-73-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-22" name="__codelineno-73-22" href="#__codelineno-73-22"></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-73-23" name="__codelineno-73-23" href="#__codelineno-73-23"></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-73-24" name="__codelineno-73-24" href="#__codelineno-73-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||
<a id="__codelineno-73-25" name="__codelineno-73-25" href="#__codelineno-73-25"></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-73-26" name="__codelineno-73-26" href="#__codelineno-73-26"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-73-27" name="__codelineno-73-27" href="#__codelineno-73-27"></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-73-28" name="__codelineno-73-28" href="#__codelineno-73-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-29" name="__codelineno-73-29" href="#__codelineno-73-29"></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-73-30" name="__codelineno-73-30" href="#__codelineno-73-30"></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-73-31" name="__codelineno-73-31" href="#__codelineno-73-31"></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-73-32" name="__codelineno-73-32" href="#__codelineno-73-32"></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-73-33" name="__codelineno-73-33" href="#__codelineno-73-33"></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-73-34" name="__codelineno-73-34" href="#__codelineno-73-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-35" name="__codelineno-73-35" href="#__codelineno-73-35"></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>
|
||
<a id="__codelineno-73-36" name="__codelineno-73-36" href="#__codelineno-73-36"></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-73-37" name="__codelineno-73-37" href="#__codelineno-73-37"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-38" name="__codelineno-73-38" href="#__codelineno-73-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-39" name="__codelineno-73-39" href="#__codelineno-73-39"></a><span class="w"> </span><span class="c1">// 更新节点高度</span>
|
||
<a id="__codelineno-73-40" name="__codelineno-73-40" href="#__codelineno-73-40"></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-73-41" name="__codelineno-73-41" href="#__codelineno-73-41"></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-73-42" name="__codelineno-73-42" href="#__codelineno-73-42"></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-73-43" name="__codelineno-73-43" href="#__codelineno-73-43"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-73-44" name="__codelineno-73-44" href="#__codelineno-73-44"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-73-45" name="__codelineno-73-45" href="#__codelineno-73-45"></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-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="nx">remove</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="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-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">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></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-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="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||
<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></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-74-11" name="__codelineno-74-11" href="#__codelineno-74-11"></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-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></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-74-13" name="__codelineno-74-13" href="#__codelineno-74-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
|
||
<a id="__codelineno-74-16" name="__codelineno-74-16" href="#__codelineno-74-16"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-74-17" name="__codelineno-74-17" href="#__codelineno-74-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">child</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||
<a id="__codelineno-74-18" name="__codelineno-74-18" href="#__codelineno-74-18"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-74-19" name="__codelineno-74-19" href="#__codelineno-74-19"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
|
||
<a id="__codelineno-74-20" name="__codelineno-74-20" href="#__codelineno-74-20"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-74-21" name="__codelineno-74-21" href="#__codelineno-74-21"></a><span class="w"> </span><span class="c1">// 子节点数量 = 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-74-22" name="__codelineno-74-22" href="#__codelineno-74-22"></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-74-23" name="__codelineno-74-23" href="#__codelineno-74-23"></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-74-24" name="__codelineno-74-24" href="#__codelineno-74-24"></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-74-25" name="__codelineno-74-25" href="#__codelineno-74-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-74-26" name="__codelineno-74-26" href="#__codelineno-74-26"></a><span class="w"> </span><span class="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-74-27" name="__codelineno-74-27" href="#__codelineno-74-27"></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-74-28" name="__codelineno-74-28" href="#__codelineno-74-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-74-29" name="__codelineno-74-29" href="#__codelineno-74-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-74-30" name="__codelineno-74-30" href="#__codelineno-74-30"></a><span class="w"> </span><span class="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-74-31" name="__codelineno-74-31" href="#__codelineno-74-31"></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-74-32" name="__codelineno-74-32" href="#__codelineno-74-32"></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-74-33" name="__codelineno-74-33" href="#__codelineno-74-33"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-74-34" name="__codelineno-74-34" href="#__codelineno-74-34"></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-74-35" name="__codelineno-74-35" href="#__codelineno-74-35"></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-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="nx">remove</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span>
|
||
<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="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">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></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-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="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||
<a id="__codelineno-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</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="nx">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-75-11" name="__codelineno-75-11" href="#__codelineno-75-11"></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-75-12" name="__codelineno-75-12" href="#__codelineno-75-12"></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-75-13" name="__codelineno-75-13" href="#__codelineno-75-13"></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-75-14" name="__codelineno-75-14" href="#__codelineno-75-14"></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-75-15" name="__codelineno-75-15" href="#__codelineno-75-15"></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-75-16" name="__codelineno-75-16" href="#__codelineno-75-16"></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-75-17" name="__codelineno-75-17" href="#__codelineno-75-17"></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-75-18" name="__codelineno-75-18" href="#__codelineno-75-18"></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-75-19" name="__codelineno-75-19" href="#__codelineno-75-19"></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-75-20" name="__codelineno-75-20" href="#__codelineno-75-20"></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-75-21" name="__codelineno-75-21" href="#__codelineno-75-21"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-75-22" name="__codelineno-75-22" href="#__codelineno-75-22"></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-75-23" name="__codelineno-75-23" href="#__codelineno-75-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-75-24" name="__codelineno-75-24" href="#__codelineno-75-24"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-75-25" name="__codelineno-75-25" href="#__codelineno-75-25"></a><span class="w"> </span><span class="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-75-26" name="__codelineno-75-26" href="#__codelineno-75-26"></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-75-27" name="__codelineno-75-27" href="#__codelineno-75-27"></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-75-28" name="__codelineno-75-28" href="#__codelineno-75-28"></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-75-29" name="__codelineno-75-29" href="#__codelineno-75-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-75-30" name="__codelineno-75-30" href="#__codelineno-75-30"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
|
||
<a id="__codelineno-75-31" name="__codelineno-75-31" href="#__codelineno-75-31"></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-75-32" name="__codelineno-75-32" href="#__codelineno-75-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-75-33" name="__codelineno-75-33" href="#__codelineno-75-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-75-34" name="__codelineno-75-34" href="#__codelineno-75-34"></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-75-35" name="__codelineno-75-35" href="#__codelineno-75-35"></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-75-36" name="__codelineno-75-36" href="#__codelineno-75-36"></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-75-37" name="__codelineno-75-37" href="#__codelineno-75-37"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-75-38" name="__codelineno-75-38" href="#__codelineno-75-38"></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-75-39" name="__codelineno-75-39" href="#__codelineno-75-39"></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-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
|
||
<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a>
|
||
<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeHelper</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></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>
|
||
<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="p">{</span>
|
||
<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a>
|
||
<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></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>
|
||
<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a><span class="p">{</span>
|
||
<a id="__codelineno-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></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="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
|
||
<a id="__codelineno-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a><span class="w"> </span><span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-77-12" name="__codelineno-77-12" href="#__codelineno-77-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-77-13" name="__codelineno-77-13" href="#__codelineno-77-13"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-77-14" name="__codelineno-77-14" href="#__codelineno-77-14"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-77-15" name="__codelineno-77-15" href="#__codelineno-77-15"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-77-16" name="__codelineno-77-16" href="#__codelineno-77-16"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-77-17" name="__codelineno-77-17" href="#__codelineno-77-17"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-77-18" name="__codelineno-77-18" href="#__codelineno-77-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
|
||
<a id="__codelineno-77-19" name="__codelineno-77-19" href="#__codelineno-77-19"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-77-20" name="__codelineno-77-20" href="#__codelineno-77-20"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-77-21" name="__codelineno-77-21" href="#__codelineno-77-21"></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-77-22" name="__codelineno-77-22" href="#__codelineno-77-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
|
||
<a id="__codelineno-77-23" name="__codelineno-77-23" href="#__codelineno-77-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
|
||
<a id="__codelineno-77-24" name="__codelineno-77-24" href="#__codelineno-77-24"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-77-25" name="__codelineno-77-25" href="#__codelineno-77-25"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-77-26" name="__codelineno-77-26" href="#__codelineno-77-26"></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-77-27" name="__codelineno-77-27" href="#__codelineno-77-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-77-28" name="__codelineno-77-28" href="#__codelineno-77-28"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-77-29" name="__codelineno-77-29" href="#__codelineno-77-29"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-77-30" name="__codelineno-77-30" href="#__codelineno-77-30"></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-77-31" name="__codelineno-77-31" href="#__codelineno-77-31"></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-77-32" name="__codelineno-77-32" href="#__codelineno-77-32"></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>
|
||
<a id="__codelineno-77-33" name="__codelineno-77-33" href="#__codelineno-77-33"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-77-34" name="__codelineno-77-34" href="#__codelineno-77-34"></a><span class="w"> </span><span class="n">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-77-35" name="__codelineno-77-35" href="#__codelineno-77-35"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-77-36" name="__codelineno-77-36" href="#__codelineno-77-36"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-77-37" name="__codelineno-77-37" href="#__codelineno-77-37"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-77-38" name="__codelineno-77-38" href="#__codelineno-77-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-77-39" name="__codelineno-77-39" href="#__codelineno-77-39"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-77-40" name="__codelineno-77-40" href="#__codelineno-77-40"></a><span class="w"> </span><span class="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-77-41" name="__codelineno-77-41" href="#__codelineno-77-41"></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-77-42" name="__codelineno-77-42" href="#__codelineno-77-42"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-77-43" name="__codelineno-77-43" href="#__codelineno-77-43"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-77-44" name="__codelineno-77-44" href="#__codelineno-77-44"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-77-45" name="__codelineno-77-45" href="#__codelineno-77-45"></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-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="cm">/* 删除节点 */</span>
|
||
<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="p">@</span><span class="n">discardableResult</span>
|
||
<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a><span class="kd">func</span> <span class="nf">remove</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">root</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a>
|
||
<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
|
||
<a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a><span class="kd">func</span> <span class="nf">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-78-10" name="__codelineno-78-10" href="#__codelineno-78-10"></a> <span class="k">if</span> <span class="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-11" name="__codelineno-78-11" href="#__codelineno-78-11"></a> <span class="k">return</span> <span class="kc">nil</span>
|
||
<a id="__codelineno-78-12" name="__codelineno-78-12" href="#__codelineno-78-12"></a> <span class="p">}</span>
|
||
<a id="__codelineno-78-13" name="__codelineno-78-13" href="#__codelineno-78-13"></a> <span class="cm">/* 1. 查找节点，并删除之 */</span>
|
||
<a id="__codelineno-78-14" name="__codelineno-78-14" href="#__codelineno-78-14"></a> <span class="k">if</span> <span class="n">val</span> <span class="o"><</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-15" name="__codelineno-78-15" href="#__codelineno-78-15"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-78-16" name="__codelineno-78-16" href="#__codelineno-78-16"></a> <span class="p">}</span> <span class="k">else</span> <span class="k">if</span> <span class="n">val</span> <span class="o">></span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-17" name="__codelineno-78-17" href="#__codelineno-78-17"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-78-18" name="__codelineno-78-18" href="#__codelineno-78-18"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-19" name="__codelineno-78-19" href="#__codelineno-78-19"></a> <span class="k">if</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-20" name="__codelineno-78-20" href="#__codelineno-78-20"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">?</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
|
||
<a id="__codelineno-78-21" name="__codelineno-78-21" href="#__codelineno-78-21"></a> <span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
|
||
<a id="__codelineno-78-22" name="__codelineno-78-22" href="#__codelineno-78-22"></a> <span class="k">if</span> <span class="n">child</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-23" name="__codelineno-78-23" href="#__codelineno-78-23"></a> <span class="k">return</span> <span class="kc">nil</span>
|
||
<a id="__codelineno-78-24" name="__codelineno-78-24" href="#__codelineno-78-24"></a> <span class="p">}</span>
|
||
<a id="__codelineno-78-25" name="__codelineno-78-25" href="#__codelineno-78-25"></a> <span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-78-26" name="__codelineno-78-26" href="#__codelineno-78-26"></a> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-27" name="__codelineno-78-27" href="#__codelineno-78-27"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">child</span>
|
||
<a id="__codelineno-78-28" name="__codelineno-78-28" href="#__codelineno-78-28"></a> <span class="p">}</span>
|
||
<a id="__codelineno-78-29" name="__codelineno-78-29" href="#__codelineno-78-29"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-78-30" name="__codelineno-78-30" href="#__codelineno-78-30"></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-78-31" name="__codelineno-78-31" href="#__codelineno-78-31"></a> <span class="kd">let</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-78-32" name="__codelineno-78-32" href="#__codelineno-78-32"></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-78-33" name="__codelineno-78-33" href="#__codelineno-78-33"></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-78-34" name="__codelineno-78-34" href="#__codelineno-78-34"></a> <span class="p">}</span>
|
||
<a id="__codelineno-78-35" name="__codelineno-78-35" href="#__codelineno-78-35"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">temp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-78-36" name="__codelineno-78-36" href="#__codelineno-78-36"></a> <span class="n">node</span><span class="p">?.</span><span class="n">val</span> <span class="p">=</span> <span class="n">temp</span><span class="p">!.</span><span class="n">val</span>
|
||
<a id="__codelineno-78-37" name="__codelineno-78-37" href="#__codelineno-78-37"></a> <span class="p">}</span>
|
||
<a id="__codelineno-78-38" name="__codelineno-78-38" href="#__codelineno-78-38"></a> <span class="p">}</span>
|
||
<a id="__codelineno-78-39" name="__codelineno-78-39" href="#__codelineno-78-39"></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-78-40" name="__codelineno-78-40" href="#__codelineno-78-40"></a> <span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
|
||
<a id="__codelineno-78-41" name="__codelineno-78-41" href="#__codelineno-78-41"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-78-42" name="__codelineno-78-42" href="#__codelineno-78-42"></a> <span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-78-43" name="__codelineno-78-43" href="#__codelineno-78-43"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-78-44" name="__codelineno-78-44" href="#__codelineno-78-44"></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-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="c1">// 删除节点</span>
|
||
<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="kt">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="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">removeHelper</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="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="c1">// 递归删除节点（辅助方法）</span>
|
||
<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></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-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></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-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></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-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w"> </span><span class="c1">// 1. 查找节点，并删除之</span>
|
||
<a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></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-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></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-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></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-79-14" name="__codelineno-79-14" href="#__codelineno-79-14"></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-79-15" name="__codelineno-79-15" href="#__codelineno-79-15"></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-79-16" name="__codelineno-79-16" href="#__codelineno-79-16"></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-79-17" name="__codelineno-79-17" href="#__codelineno-79-17"></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-79-18" name="__codelineno-79-18" href="#__codelineno-79-18"></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-79-19" name="__codelineno-79-19" href="#__codelineno-79-19"></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-79-20" name="__codelineno-79-20" href="#__codelineno-79-20"></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-79-21" name="__codelineno-79-21" href="#__codelineno-79-21"></a><span class="w"> </span><span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
|
||
<a id="__codelineno-79-22" name="__codelineno-79-22" href="#__codelineno-79-22"></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-79-23" name="__codelineno-79-23" href="#__codelineno-79-23"></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-79-24" name="__codelineno-79-24" href="#__codelineno-79-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-79-25" name="__codelineno-79-25" href="#__codelineno-79-25"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-26" name="__codelineno-79-26" href="#__codelineno-79-26"></a><span class="w"> </span><span class="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-79-27" name="__codelineno-79-27" href="#__codelineno-79-27"></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-79-28" name="__codelineno-79-28" href="#__codelineno-79-28"></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-79-29" name="__codelineno-79-29" href="#__codelineno-79-29"></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-79-30" name="__codelineno-79-30" href="#__codelineno-79-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-79-31" name="__codelineno-79-31" href="#__codelineno-79-31"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-79-32" name="__codelineno-79-32" href="#__codelineno-79-32"></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-79-33" name="__codelineno-79-33" href="#__codelineno-79-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-79-34" name="__codelineno-79-34" href="#__codelineno-79-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-79-35" name="__codelineno-79-35" href="#__codelineno-79-35"></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-79-36" name="__codelineno-79-36" href="#__codelineno-79-36"></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-79-37" name="__codelineno-79-37" href="#__codelineno-79-37"></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-79-38" name="__codelineno-79-38" href="#__codelineno-79-38"></a><span class="w"> </span><span class="c1">// 返回子树的根节点</span>
|
||
<a id="__codelineno-79-39" name="__codelineno-79-39" href="#__codelineno-79-39"></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-79-40" name="__codelineno-79-40" href="#__codelineno-79-40"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="_10">查找节点<a class="headerlink" href="#_10" 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="854-avl">8.5.4. AVL 树典型应用<a class="headerlink" href="#854-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>
|
||
</ul>
|
||
<div class="admonition question">
|
||
<p class="admonition-title">为什么红黑树比 AVL 树更受欢迎？</p>
|
||
<p>红黑树的平衡条件相对宽松，因此在红黑树中插入与删除节点所需的旋转操作相对较少，在节点增删操作上的平均效率高于 AVL 树。</p>
|
||
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|
||
|
||
|
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|
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|
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|
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