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第 0 章 前言
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0.2 如何使用本書
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0.3 小結
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第 1 章 初識演算法
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1.1 演算法無處不在
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第 2 章 複雜度分析
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2.1 演算法效率評估
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2.2 迭代與遞迴
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2.3 時間複雜度
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2.4 空間複雜度
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</a>
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 3 章 資料結構
|
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</a>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 3 章 資料結構
|
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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<span class="md-ellipsis">
|
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3.1 資料結構分類
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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|
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|
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<span class="md-ellipsis">
|
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3.2 基本資料型別
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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<span class="md-ellipsis">
|
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3.3 數字編碼 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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|
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3.4 字元編碼 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_data_structure/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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3.5 小結
|
||
</span>
|
||
|
||
|
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</a>
|
||
</li>
|
||
|
||
|
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|
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|
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</ul>
|
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</nav>
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|
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|
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|
||
|
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|
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<li class="md-nav__item md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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|
||
|
||
<span class="md-ellipsis">
|
||
第 4 章 陣列與鏈結串列
|
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</span>
|
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|
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|
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</a>
|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 4 章 陣列與鏈結串列
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
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<span class="md-ellipsis">
|
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4.1 陣列
|
||
</span>
|
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|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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4.2 鏈結串列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
|
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|
||
|
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<span class="md-ellipsis">
|
||
4.3 串列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
4.4 記憶體與快取 *
|
||
</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近新增">
|
||
</span>
|
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|
||
|
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|
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|
||
</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_array_and_linkedlist/summary/" class="md-nav__link">
|
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|
||
|
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<span class="md-ellipsis">
|
||
4.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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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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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_stack_and_queue/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 5 章 堆疊與佇列
|
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</span>
|
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|
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|
||
</a>
|
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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">
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 5 章 堆疊與佇列
|
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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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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
5.1 堆疊
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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5.2 佇列
|
||
</span>
|
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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_stack_and_queue/deque/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
5.3 雙向佇列
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
5.4 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
||
|
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|
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|
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</ul>
|
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</nav>
|
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|
||
</li>
|
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|
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|
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|
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|
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|
||
|
||
|
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|
||
|
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|
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|
||
|
||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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|
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<span class="md-ellipsis">
|
||
第 6 章 雜湊表
|
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</span>
|
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|
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|
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</a>
|
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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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 6 章 雜湊表
|
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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6.1 雜湊表
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
|
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<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
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<span class="md-ellipsis">
|
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6.2 雜湊衝突
|
||
</span>
|
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|
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|
||
</a>
|
||
</li>
|
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|
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
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<span class="md-ellipsis">
|
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6.3 雜湊演算法
|
||
</span>
|
||
|
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|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
|
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<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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6.4 小結
|
||
</span>
|
||
|
||
|
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</a>
|
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</li>
|
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|
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|
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</ul>
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</nav>
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--active md-nav__item--nested">
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|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 7 章 樹
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
|
||
<label class="md-nav__title" for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 7 章 樹
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../binary_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.1 二元樹
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../binary_tree_traversal/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.2 二元樹走訪
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../array_representation_of_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.3 二元樹陣列表示
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../binary_search_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.4 二元搜尋樹
|
||
</span>
|
||
|
||
|
||
</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">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.5 AVL *
|
||
</span>
|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
<a href="./" class="md-nav__link md-nav__link--active">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.5 AVL *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
|
||
<nav class="md-nav md-nav--secondary" aria-label="目錄">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<label class="md-nav__title" for="__toc">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
目錄
|
||
</label>
|
||
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#751-avl" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
7.5.1 AVL 樹常見術語
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="7.5.1 AVL 樹常見術語">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 節點高度
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 節點平衡因子
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#752-avl" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
7.5.2 AVL 樹旋轉
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="7.5.2 AVL 樹旋轉">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 右旋
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 左旋
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#3" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
3. 先左旋後右旋
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#4" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
4. 先右旋後左旋
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#5" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
5. 旋轉的選擇
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#753-avl" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
7.5.3 AVL 樹常用操作
|
||
</span>
|
||
</a>
|
||
|
||
<nav class="md-nav" aria-label="7.5.3 AVL 樹常用操作">
|
||
<ul class="md-nav__list">
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#1_2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
1. 插入節點
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#2_2" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
2. 刪除節點
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#3_1" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
3. 查詢節點
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#754-avl" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
7.5.4 AVL 樹典型應用
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.6 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_heap/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 8 章 堆積
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 8 章 堆積
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.1 堆積
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.2 建堆積操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/top_k/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.3 Top-k 問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.4 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_graph/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 9 章 圖
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
|
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第 9 章 圖
|
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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_graph/graph/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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9.1 圖
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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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_graph/graph_operations/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
9.2 圖基礎操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
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|
||
|
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<span class="md-ellipsis">
|
||
9.3 圖的走訪
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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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_graph/summary/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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9.4 小結
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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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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<li class="md-nav__item md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_searching/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
|
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|
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<span class="md-ellipsis">
|
||
第 10 章 搜尋
|
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</span>
|
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|
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</a>
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<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_12">
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<span class="md-nav__icon md-icon"></span>
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第 10 章 搜尋
|
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
10.1 二分搜尋
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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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_searching/binary_search_insertion/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
10.2 二分搜尋插入點
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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|
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|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.3 二分搜尋邊界
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
10.4 雜湊最佳化策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.5 重識搜尋演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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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_searching/summary/" class="md-nav__link">
|
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|
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|
||
<span class="md-ellipsis">
|
||
10.6 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
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|
||
|
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|
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|
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||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
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<div class="md-nav__link md-nav__container">
|
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<a href="../../chapter_sorting/" class="md-nav__link ">
|
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|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 11 章 排序
|
||
</span>
|
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|
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|
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</a>
|
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|
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|
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<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_13">
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<span class="md-nav__icon md-icon"></span>
|
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第 11 章 排序
|
||
</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
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<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
11.1 排序演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
11.2 選擇排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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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_sorting/bubble_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.3 泡沫排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.4 插入排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.5 快速排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.6 合併排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.7 堆積排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.8 桶排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.9 計數排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.10 基數排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.11 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
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|
||
|
||
|
||
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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|
||
|
||
<span class="md-ellipsis">
|
||
第 12 章 分治
|
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</span>
|
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|
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|
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</a>
|
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|
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|
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<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
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<span class="md-nav__icon md-icon"></span>
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第 12 章 分治
|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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12.1 分治演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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12.2 分治搜尋策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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12.3 構建樹問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
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|
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<span class="md-ellipsis">
|
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12.4 河內塔問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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12.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
||
|
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|
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|
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</ul>
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</nav>
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</li>
|
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|
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第 13 章 回溯
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第 13 章 回溯
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13.1 回溯演算法
|
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|
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|
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|
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</a>
|
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|
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13.2 全排列問題
|
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|
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</a>
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13.3 子集和問題
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|
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|
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</a>
|
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</li>
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13.4 N 皇后問題
|
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|
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13.5 小結
|
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|
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|
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第 14 章 動態規劃
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14.1 初探動態規劃
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|
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|
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14.2 DP 問題特性
|
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</a>
|
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</li>
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14.3 DP 解題思路
|
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|
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</a>
|
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</li>
|
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14.4 0-1 背包問題
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|
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</a>
|
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</li>
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14.5 完全背包問題
|
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|
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</a>
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</li>
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14.6 編輯距離問題
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|
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</a>
|
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</li>
|
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14.7 小結
|
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|
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|
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第 15 章 貪婪
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15.1 貪婪演算法
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|
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|
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15.3 最大容量問題
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15.4 最大切分乘積問題
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|
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</a>
|
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</li>
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15.5 小結
|
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|
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|
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第 16 章 附錄
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16.1 程式設計環境安裝
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</a>
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16.2 一起參與創作
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</a>
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</li>
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16.3 術語表
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</a>
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</li>
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|
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|
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7.5.4 AVL 樹典型應用
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<h1 id="75-avl">7.5 AVL 樹 *<a class="headerlink" href="#75-avl" title="Permanent link">¶</a></h1>
|
||
<p>在“二元搜尋樹”章節中我們提到，在多次插入和刪除操作後，二元搜尋樹可能退化為鏈結串列。在這種情況下，所有操作的時間複雜度將從 <span class="arithmatex">\(O(\log n)\)</span> 劣化為 <span class="arithmatex">\(O(n)\)</span> 。</p>
|
||
<p>如圖 7-24 所示，經過兩次刪除節點操作，這棵二元搜尋樹便會退化為鏈結串列。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_degradation_from_removing_node.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="AVL 樹在刪除節點後發生退化" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_removing_node.png" /></a></p>
|
||
<p align="center"> 圖 7-24 AVL 樹在刪除節點後發生退化 </p>
|
||
|
||
<p>再例如，在圖 7-25 所示的完美二元樹中插入兩個節點後，樹將嚴重向左傾斜，查詢操作的時間複雜度也隨之劣化。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_degradation_from_inserting_node.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="AVL 樹在插入節點後發生退化" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_inserting_node.png" /></a></p>
|
||
<p align="center"> 圖 7-25 AVL 樹在插入節點後發生退化 </p>
|
||
|
||
<p>1962 年 G. M. Adelson-Velsky 和 E. M. Landis 在論文“An algorithm for the organization of information”中提出了 <u>AVL 樹</u>。論文中詳細描述了一系列操作，確保在持續新增和刪除節點後，AVL 樹不會退化，從而使得各種操作的時間複雜度保持在 <span class="arithmatex">\(O(\log n)\)</span> 級別。換句話說，在需要頻繁進行增刪查改操作的場景中，AVL 樹能始終保持高效的資料操作效能，具有很好的應用價值。</p>
|
||
<h2 id="751-avl">7.5.1 AVL 樹常見術語<a class="headerlink" href="#751-avl" title="Permanent link">¶</a></h2>
|
||
<p>AVL 樹既是二元搜尋樹，也是平衡二元樹，同時滿足這兩類二元樹的所有性質，因此是一種<u>平衡二元搜尋樹（balanced binary search tree）</u>。</p>
|
||
<h3 id="1">1. 節點高度<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
||
<p>由於 AVL 樹的相關操作需要獲取節點高度，因此我們需要為節點類別新增 <code>height</code> 變數：</p>
|
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<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""AVL 樹節點類別"""</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 節點值</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 節點高度</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 左子節點引用</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右子節點引用</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* AVL 樹節點類別 */</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">// 節點值</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">// 節點高度</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">// 左子節點</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">// 右子節點</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="p">()</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">default</span><span class="p">;</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="k">explicit</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">){}</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="p">};</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* AVL 樹節點類別 */</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點高度</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子節點</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子節點</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* AVL 樹節點類別 */</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int?</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點高度</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子節點引用</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子節點引用</span>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* AVL 樹節點結構體 */</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="nx">Val</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">Height</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="c1">// 節點高度</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">Left</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 左子節點引用</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="nx">Right</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 右子節點引用</span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* AVL 樹節點類別 */</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a> <span class="kd">var</span> <span class="nv">val</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 節點值</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="kd">var</span> <span class="nv">height</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 節點高度</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a> <span class="kd">var</span> <span class="nv">left</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="c1">// 左子節點</span>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="kd">var</span> <span class="nv">right</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="c1">// 右子節點</span>
|
||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a> <span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a> <span class="n">val</span> <span class="p">=</span> <span class="n">x</span>
|
||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a> <span class="n">height</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a> <span class="p">}</span>
|
||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* AVL 樹節點類別 */</span>
|
||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="nx">height</span><span class="p">;</span><span class="w"> </span><span class="c1">//節點高度</span>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子節點指標</span>
|
||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子節點指標</span>
|
||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">height</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
|
||
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">height</span><span class="p">;</span>
|
||
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
|
||
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
|
||
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* AVL 樹節點類別 */</span>
|
||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="nx">height</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點高度</span>
|
||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子節點指標</span>
|
||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子節點指標</span>
|
||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">height?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">left?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">right?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span>
|
||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">height</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">left</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">right</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* AVL 樹節點類別 */</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// 節點高度</span>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子節點</span>
|
||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子節點</span>
|
||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">right</span><span class="p">]);</span>
|
||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">rc</span>::<span class="n">Rc</span><span class="p">;</span>
|
||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">cell</span>::<span class="n">RefCell</span><span class="p">;</span>
|
||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
|
||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* AVL 樹節點結構體 */</span>
|
||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="n">height</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 節點高度</span>
|
||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="n">left</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="c1">// 左子節點</span>
|
||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="n">right</span>: <span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="p">,</span><span class="w"> </span><span class="c1">// 右子節點</span>
|
||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a>
|
||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="k">impl</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="cm">/* 建構子 */</span>
|
||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="k">fn</span> <span class="nf">new</span><span class="p">(</span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="bp">Self</span><span class="o">>></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="n">Rc</span>::<span class="n">new</span><span class="p">(</span><span class="n">RefCell</span>::<span class="n">new</span><span class="p">(</span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="n">val</span><span class="p">,</span>
|
||
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="n">height</span>: <span class="mi">0</span><span class="p">,</span>
|
||
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="n">left</span>: <span class="nb">None</span><span class="p">,</span>
|
||
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="n">right</span>: <span class="nb">None</span>
|
||
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a> <span class="p">}))</span>
|
||
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* AVL 樹節點結構體 */</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">}</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">;</span>
|
||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
|
||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="cm">/* 建構子 */</span>
|
||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newTreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a>
|
||
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">));</span>
|
||
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
|
||
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
|
||
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* AVL 樹節點類別 */</span>
|
||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">(</span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">height</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="c1">// 節點高度</span>
|
||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="c1">// 左子節點</span>
|
||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="c1">// 右子節點</span>
|
||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>“節點高度”是指從該節點到它的最遠葉節點的距離，即所經過的“邊”的數量。需要特別注意的是，葉節點的高度為 <span class="arithmatex">\(0\)</span> ，而空節點的高度為 <span class="arithmatex">\(-1\)</span> 。我們將建立兩個工具函式，分別用於獲取和更新節點的高度：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></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-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w"> </span><span class="sd">"""獲取節點高度"""</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a> <span class="c1"># 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></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-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a> <span class="k">return</span> <span class="n">node</span><span class="o">.</span><span class="n">height</span>
|
||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a> <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
|
||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></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-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="sd">"""更新節點高度"""</span>
|
||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a> <span class="c1"># 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a> <span class="n">node</span><span class="o">.</span><span class="n">height</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)])</span> <span class="o">+</span> <span class="mi">1</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="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-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">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-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">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></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-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w"> </span><span class="n">node</span><span class="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-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></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-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></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-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a>
|
||
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></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-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></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-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 獲取節點高度 */</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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>
|
||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="k">void</span><span class="w"> </span><span class="nf">UpdateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">Height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">Height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></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-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></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-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></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-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></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-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a>
|
||
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></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-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></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-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></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-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></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-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></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-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></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-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></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-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></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-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="n">node</span><span class="p">?.</span><span class="n">height</span> <span class="p">??</span> <span class="o">-</span><span class="mi">1</span>
|
||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a>
|
||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></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-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a> <span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></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-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></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-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a>
|
||
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></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-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></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-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></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-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></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-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></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-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></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-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a>
|
||
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></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-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></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-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></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-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">height</span><span class="p">;</span>
|
||
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a>
|
||
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="kt">void</span><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span> <span class="nf">height</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">height</span><span class="p">,</span>
|
||
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">,</span>
|
||
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a>
|
||
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="k">fn</span> <span class="nf">update_height</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">max</span><span class="p">(</span><span class="bp">Self</span>::<span class="n">height</span><span class="p">(</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">height</span><span class="p">(</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></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-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 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="n">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">height</span><span class="p">;</span>
|
||
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
|
||
<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a>
|
||
<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="kt">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">lh</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">rh</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">lh</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rh</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">lh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></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-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rh</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 獲取節點高度 */</span>
|
||
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">fun</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="w"> </span><span class="n">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-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="na">height</span><span class="w"> </span><span class="o">?:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
|
||
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a>
|
||
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="cm">/* 更新節點高度 */</span>
|
||
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="na">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="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="o">?.</span><span class="na">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
|
||
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">height</span><span class="p">}</span>
|
||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
|
||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">update_height</span><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-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="c1">// 獲取節點高度</span>
|
||
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></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-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></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-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w"> </span><span class="c1">// 空節點高度為 -1 ，葉節點高度為 0</span>
|
||
<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></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-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="p">}</span>
|
||
<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>
|
||
<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></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-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w"> </span><span class="c1">// 節點高度等於最高子樹高度 + 1</span>
|
||
<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">@max</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2">2. 節點平衡因子<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||
<p>節點的<u>平衡因子（balance factor）</u>定義為節點左子樹的高度減去右子樹的高度，同時規定空節點的平衡因子為 <span class="arithmatex">\(0\)</span> 。我們同樣將獲取節點平衡因子的功能封裝成函式，方便後續使用：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></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-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w"> </span><span class="sd">"""獲取平衡因子"""</span>
|
||
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a> <span class="c1"># 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></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-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a> <span class="c1"># 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">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-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 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="k">nullptr</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="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></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-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></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-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="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-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></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-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></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-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">BalanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="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-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></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-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="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-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></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-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></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-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a> <span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></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-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a> <span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></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-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></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-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="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-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></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-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></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-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></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-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="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-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">fn</span> <span class="nf">balance_factor</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
|
||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span>
|
||
<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></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-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></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-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 獲取平衡因子 */</span>
|
||
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">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-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
|
||
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w"> </span><span class="k">return</span><span class="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-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">balance_factor</span><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-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="c1">// 獲取平衡因子</span>
|
||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></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-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w"> </span><span class="c1">// 空節點平衡因子為 0</span>
|
||
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">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-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w"> </span><span class="c1">// 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
|
||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></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-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="admonition note">
|
||
<p class="admonition-title">Note</p>
|
||
<p>設平衡因子為 <span class="arithmatex">\(f\)</span> ，則一棵 AVL 樹的任意節點的平衡因子皆滿足 <span class="arithmatex">\(-1 \le f \le 1\)</span> 。</p>
|
||
</div>
|
||
<h2 id="752-avl">7.5.2 AVL 樹旋轉<a class="headerlink" href="#752-avl" title="Permanent link">¶</a></h2>
|
||
<p>AVL 樹的特點在於“旋轉”操作，它能夠在不影響二元樹的中序走訪序列的前提下，使失衡節點重新恢復平衡。換句話說，<strong>旋轉操作既能保持“二元搜尋樹”的性質，也能使樹重新變為“平衡二元樹”</strong>。</p>
|
||
<p>我們將平衡因子絕對值 <span class="arithmatex">\(> 1\)</span> 的節點稱為“失衡節點”。根據節點失衡情況的不同，旋轉操作分為四種：右旋、左旋、先右旋後左旋、先左旋後右旋。下面詳細介紹這些旋轉操作。</p>
|
||
<h3 id="1_1">1. 右旋<a class="headerlink" href="#1_1" title="Permanent link">¶</a></h3>
|
||
<p>如圖 7-26 所示，節點下方為平衡因子。從底至頂看，二元樹中首個失衡節點是“節點 3”。我們關注以該失衡節點為根節點的子樹，將該節點記為 <code>node</code> ，其左子節點記為 <code>child</code> ，執行“右旋”操作。完成右旋後，子樹恢復平衡，並且仍然保持二元搜尋樹的性質。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="4:4"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1"><1></label><label for="__tabbed_4_2"><2></label><label for="__tabbed_4_3"><3></label><label for="__tabbed_4_4"><4></label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="右旋操作步驟" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step2" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step3" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step4" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step4.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 圖 7-26 右旋操作步驟 </p>
|
||
|
||
<p>如圖 7-27 所示，當節點 <code>child</code> 有右子節點（記為 <code>grand_child</code> ）時，需要在右旋中新增一步：將 <code>grand_child</code> 作為 <code>node</code> 的左子節點。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="有 grand_child 的右旋操作" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" /></a></p>
|
||
<p align="center"> 圖 7-27 有 grand_child 的右旋操作 </p>
|
||
|
||
<p>“向右旋轉”是一種形象化的說法，實際上需要透過修改節點指標來實現，程式碼如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></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-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="sd">"""右旋操作"""</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">left</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">right</span>
|
||
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a> <span class="c1"># 以 child 為原點，將 node 向右旋轉</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">right</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">left</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"># 更新節點高度</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"># 返回旋轉後子樹的根節點</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.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="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-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></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-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></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-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></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-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></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-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></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-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></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-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</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="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="n">TreeNode</span><span class="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-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></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-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></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-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="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-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="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-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">RightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">?.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></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-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></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-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</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="n">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.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="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-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></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-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></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-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></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-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></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-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></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-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></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-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span>
|
||
<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></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-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></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-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></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-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></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-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a> <span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></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-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></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-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a> <span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></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-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></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-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a> <span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a> <span class="k">return</span> <span class="n">child</span>
|
||
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></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-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></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-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></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-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></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-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></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-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></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-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></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-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">child</span><span class="p">);</span>
|
||
<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span><span class="p">;</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.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></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-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></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-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></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-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></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-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></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-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></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-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">updateHeight</span><span class="p">(</span><span class="nx">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">// 返回旋轉後子樹的根節點</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="nx">child</span><span class="p">;</span>
|
||
<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="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-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="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-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">fn</span> <span class="nf">right_rotate</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||
<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span><span class="p">;</span>
|
||
<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">));</span>
|
||
<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span>
|
||
<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
|
||
<a id="__codelineno-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="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
|
||
<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></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-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">-></span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="w"> </span><span class="n">child</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></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-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></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-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></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-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 右旋操作 */</span>
|
||
<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="n">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="kd">val</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span>
|
||
<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">!!</span><span class="p">.</span><span class="na">right</span>
|
||
<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></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>
|
||
<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></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>
|
||
<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></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-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></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-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span>
|
||
<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right_rotate</span><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-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="c1">// 右旋操作</span>
|
||
<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></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-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></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-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></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-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向右旋轉</span>
|
||
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></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-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></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-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></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-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></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-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2_1">2. 左旋<a class="headerlink" href="#2_1" title="Permanent link">¶</a></h3>
|
||
<p>相應地，如果考慮上述失衡二元樹的“映象”，則需要執行圖 7-28 所示的“左旋”操作。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_left_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="左旋操作" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate.png" /></a></p>
|
||
<p align="center"> 圖 7-28 左旋操作 </p>
|
||
|
||
<p>同理，如圖 7-29 所示，當節點 <code>child</code> 有左子節點（記為 <code>grand_child</code> ）時，需要在左旋中新增一步：將 <code>grand_child</code> 作為 <code>node</code> 的右子節點。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="有 grand_child 的左旋操作" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" /></a></p>
|
||
<p align="center"> 圖 7-29 有 grand_child 的左旋操作 </p>
|
||
|
||
<p>可以觀察到，<strong>右旋和左旋操作在邏輯上是映象對稱的，它們分別解決的兩種失衡情況也是對稱的</strong>。基於對稱性，我們只需將右旋的實現程式碼中的所有的 <code>left</code> 替換為 <code>right</code> ，將所有的 <code>right</code> 替換為 <code>left</code> ，即可得到左旋的實現程式碼：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></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-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w"> </span><span class="sd">"""左旋操作"""</span>
|
||
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></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-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></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-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a> <span class="c1"># 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></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-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></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-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a> <span class="c1"># 更新節點高度</span>
|
||
<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></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-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></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-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a> <span class="c1"># 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a> <span class="k">return</span> <span class="n">child</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="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-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></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-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></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-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></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-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></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-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></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-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></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-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</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="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="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-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="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-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></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-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></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-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></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-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></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-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
|
||
<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></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-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">LeftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">?.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">?.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></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-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></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-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></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-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></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-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></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-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></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-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></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-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></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-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></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-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">child</span>
|
||
<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></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-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></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-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></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-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></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-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a> <span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></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-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></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-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a> <span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></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-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></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-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a> <span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a> <span class="k">return</span> <span class="n">child</span>
|
||
<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></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-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></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-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></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-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></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-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></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-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></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-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></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-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></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-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></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-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></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-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></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-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></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-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></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-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></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-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></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-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></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-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></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-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></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-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></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-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></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-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></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-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="k">fn</span> <span class="nf">left_rotate</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||
<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span><span class="p">;</span>
|
||
<a id="__codelineno-65-10" name="__codelineno-65-10" href="#__codelineno-65-10"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">));</span>
|
||
<a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span>
|
||
<a id="__codelineno-65-13" name="__codelineno-65-13" href="#__codelineno-65-13"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
|
||
<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
|
||
<a id="__codelineno-65-17" name="__codelineno-65-17" href="#__codelineno-65-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-65-18" name="__codelineno-65-18" href="#__codelineno-65-18"></a><span class="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="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></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-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">-></span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="w"> </span><span class="n">child</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-66-9" name="__codelineno-66-9" href="#__codelineno-66-9"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-66-10" name="__codelineno-66-10" href="#__codelineno-66-10"></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-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></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-66-12" name="__codelineno-66-12" href="#__codelineno-66-12"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-66-13" name="__codelineno-66-13" href="#__codelineno-66-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-66-14" name="__codelineno-66-14" href="#__codelineno-66-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 左旋操作 */</span>
|
||
<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">!!</span><span class="p">.</span><span class="na">right</span>
|
||
<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">!!</span><span class="p">.</span><span class="na">left</span>
|
||
<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></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>
|
||
<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></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>
|
||
<a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></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-67-10" name="__codelineno-67-10" href="#__codelineno-67-10"></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-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</span>
|
||
<a id="__codelineno-67-12" name="__codelineno-67-12" href="#__codelineno-67-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">child</span>
|
||
<a id="__codelineno-67-13" name="__codelineno-67-13" href="#__codelineno-67-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left_rotate</span><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">// 左旋操作</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">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-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></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-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></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-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w"> </span><span class="c1">// 以 child 為原點，將 node 向左旋轉</span>
|
||
<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></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-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></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-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></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-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></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-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="w"> </span><span class="c1">// 返回旋轉後子樹的根節點</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">child</span><span class="p">;</span>
|
||
<a id="__codelineno-69-13" name="__codelineno-69-13" href="#__codelineno-69-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="3">3. 先左旋後右旋<a class="headerlink" href="#3" title="Permanent link">¶</a></h3>
|
||
<p>對於圖 7-30 中的失衡節點 3 ，僅使用左旋或右旋都無法使子樹恢復平衡。此時需要先對 <code>child</code> 執行“左旋”，再對 <code>node</code> 執行“右旋”。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_left_right_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="先左旋後右旋" class="animation-figure" src="../avl_tree.assets/avltree_left_right_rotate.png" /></a></p>
|
||
<p align="center"> 圖 7-30 先左旋後右旋 </p>
|
||
|
||
<h3 id="4">4. 先右旋後左旋<a class="headerlink" href="#4" title="Permanent link">¶</a></h3>
|
||
<p>如圖 7-31 所示，對於上述失衡二元樹的映象情況，需要先對 <code>child</code> 執行“右旋”，再對 <code>node</code> 執行“左旋”。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_right_left_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="先右旋後左旋" class="animation-figure" src="../avl_tree.assets/avltree_right_left_rotate.png" /></a></p>
|
||
<p align="center"> 圖 7-31 先右旋後左旋 </p>
|
||
|
||
<h3 id="5">5. 旋轉的選擇<a class="headerlink" href="#5" title="Permanent link">¶</a></h3>
|
||
<p>圖 7-32 展示的四種失衡情況與上述案例逐個對應，分別需要採用右旋、先左旋後右旋、先右旋後左旋、左旋的操作。</p>
|
||
<p><a class="glightbox" href="../avl_tree.assets/avltree_rotation_cases.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="AVL 樹的四種旋轉情況" class="animation-figure" src="../avl_tree.assets/avltree_rotation_cases.png" /></a></p>
|
||
<p align="center"> 圖 7-32 AVL 樹的四種旋轉情況 </p>
|
||
|
||
<p>如下表所示，我們透過判斷失衡節點的平衡因子以及較高一側子節點的平衡因子的正負號，來確定失衡節點屬於圖 7-32 中的哪種情況。</p>
|
||
<p align="center"> 表 7-3 四種旋轉情況的選擇條件 </p>
|
||
|
||
<div class="center-table">
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>失衡節點的平衡因子</th>
|
||
<th>子節點的平衡因子</th>
|
||
<th>應採用的旋轉方法</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td><span class="arithmatex">\(> 1\)</span> （左偏樹）</td>
|
||
<td><span class="arithmatex">\(\geq 0\)</span></td>
|
||
<td>右旋</td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(> 1\)</span> （左偏樹）</td>
|
||
<td><span class="arithmatex">\(<0\)</span></td>
|
||
<td>先左旋後右旋</td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(< -1\)</span> （右偏樹）</td>
|
||
<td><span class="arithmatex">\(\leq 0\)</span></td>
|
||
<td>左旋</td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(< -1\)</span> （右偏樹）</td>
|
||
<td><span class="arithmatex">\(>0\)</span></td>
|
||
<td>先右旋後左旋</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<p>為了便於使用，我們將旋轉操作封裝成一個函式。<strong>有了這個函式，我們就能對各種失衡情況進行旋轉，使失衡節點重新恢復平衡</strong>。程式碼如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></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-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="w"> </span><span class="sd">"""執行旋轉操作，使該子樹重新恢復平衡"""</span>
|
||
<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a> <span class="c1"># 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></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-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a> <span class="c1"># 左偏樹</span>
|
||
<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></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-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></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-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a> <span class="c1"># 右旋</span>
|
||
<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></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-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a> <span class="c1"># 先左旋後右旋</span>
|
||
<a id="__codelineno-70-12" name="__codelineno-70-12" href="#__codelineno-70-12"></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-70-13" name="__codelineno-70-13" href="#__codelineno-70-13"></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-70-14" name="__codelineno-70-14" href="#__codelineno-70-14"></a> <span class="c1"># 右偏樹</span>
|
||
<a id="__codelineno-70-15" name="__codelineno-70-15" href="#__codelineno-70-15"></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-70-16" name="__codelineno-70-16" href="#__codelineno-70-16"></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-70-17" name="__codelineno-70-17" href="#__codelineno-70-17"></a> <span class="c1"># 左旋</span>
|
||
<a id="__codelineno-70-18" name="__codelineno-70-18" href="#__codelineno-70-18"></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-70-19" name="__codelineno-70-19" href="#__codelineno-70-19"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-70-20" name="__codelineno-70-20" href="#__codelineno-70-20"></a> <span class="c1"># 先右旋後左旋</span>
|
||
<a id="__codelineno-70-21" name="__codelineno-70-21" href="#__codelineno-70-21"></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-70-22" name="__codelineno-70-22" href="#__codelineno-70-22"></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-70-23" name="__codelineno-70-23" href="#__codelineno-70-23"></a> <span class="c1"># 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-70-24" name="__codelineno-70-24" href="#__codelineno-70-24"></a> <span class="k">return</span> <span class="n">node</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></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-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w"> </span><span class="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-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_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-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">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-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-71-9" name="__codelineno-71-9" href="#__codelineno-71-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-71-10" name="__codelineno-71-10" href="#__codelineno-71-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-11" name="__codelineno-71-11" href="#__codelineno-71-11"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-71-12" name="__codelineno-71-12" href="#__codelineno-71-12"></a><span class="w"> </span><span class="n">node</span><span class="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-71-13" name="__codelineno-71-13" href="#__codelineno-71-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-71-14" name="__codelineno-71-14" href="#__codelineno-71-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-15" name="__codelineno-71-15" href="#__codelineno-71-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-16" name="__codelineno-71-16" href="#__codelineno-71-16"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-71-17" name="__codelineno-71-17" href="#__codelineno-71-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_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-71-18" name="__codelineno-71-18" href="#__codelineno-71-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">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-71-19" name="__codelineno-71-19" href="#__codelineno-71-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-71-20" name="__codelineno-71-20" href="#__codelineno-71-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-71-21" name="__codelineno-71-21" href="#__codelineno-71-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-22" name="__codelineno-71-22" href="#__codelineno-71-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-71-23" name="__codelineno-71-23" href="#__codelineno-71-23"></a><span class="w"> </span><span class="n">node</span><span class="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-71-24" name="__codelineno-71-24" href="#__codelineno-71-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-71-25" name="__codelineno-71-25" href="#__codelineno-71-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-26" name="__codelineno-71-26" href="#__codelineno-71-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-27" name="__codelineno-71-27" href="#__codelineno-71-27"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-71-28" name="__codelineno-71-28" href="#__codelineno-71-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-71-29" name="__codelineno-71-29" href="#__codelineno-71-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></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-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></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-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></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-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></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-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></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-72-10" name="__codelineno-72-10" href="#__codelineno-72-10"></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-72-11" name="__codelineno-72-11" href="#__codelineno-72-11"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-72-12" name="__codelineno-72-12" href="#__codelineno-72-12"></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-72-13" name="__codelineno-72-13" href="#__codelineno-72-13"></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-72-14" name="__codelineno-72-14" href="#__codelineno-72-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-72-15" name="__codelineno-72-15" href="#__codelineno-72-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-72-16" name="__codelineno-72-16" href="#__codelineno-72-16"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-72-17" name="__codelineno-72-17" href="#__codelineno-72-17"></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-72-18" name="__codelineno-72-18" href="#__codelineno-72-18"></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-72-19" name="__codelineno-72-19" href="#__codelineno-72-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-72-20" name="__codelineno-72-20" href="#__codelineno-72-20"></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-72-21" name="__codelineno-72-21" href="#__codelineno-72-21"></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-72-22" name="__codelineno-72-22" href="#__codelineno-72-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-72-23" name="__codelineno-72-23" href="#__codelineno-72-23"></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-72-24" name="__codelineno-72-24" href="#__codelineno-72-24"></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-72-25" name="__codelineno-72-25" href="#__codelineno-72-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-72-26" name="__codelineno-72-26" href="#__codelineno-72-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-72-27" name="__codelineno-72-27" href="#__codelineno-72-27"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-72-28" name="__codelineno-72-28" href="#__codelineno-72-28"></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-72-29" name="__codelineno-72-29" href="#__codelineno-72-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">Rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BalanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">BalanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="w"> </span><span class="c1">// 右旋</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="nf">RightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-73-10" name="__codelineno-73-10" href="#__codelineno-73-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><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="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-73-12" name="__codelineno-73-12" href="#__codelineno-73-12"></a><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">LeftRotate</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-73-13" name="__codelineno-73-13" href="#__codelineno-73-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">RightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-73-14" name="__codelineno-73-14" href="#__codelineno-73-14"></a><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="p">}</span>
|
||
<a id="__codelineno-73-16" name="__codelineno-73-16" href="#__codelineno-73-16"></a><span class="w"> </span><span class="c1">// 右偏樹</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="p">(</span><span class="n">balanceFactorInt</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-18" name="__codelineno-73-18" href="#__codelineno-73-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">BalanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">?.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-19" name="__codelineno-73-19" href="#__codelineno-73-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-73-20" name="__codelineno-73-20" href="#__codelineno-73-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">LeftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-73-21" name="__codelineno-73-21" href="#__codelineno-73-21"></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-73-22" name="__codelineno-73-22" href="#__codelineno-73-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-73-23" name="__codelineno-73-23" href="#__codelineno-73-23"></a><span class="w"> </span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RightRotate</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-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="nf">LeftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-73-25" name="__codelineno-73-25" href="#__codelineno-73-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-26" name="__codelineno-73-26" href="#__codelineno-73-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-27" name="__codelineno-73-27" href="#__codelineno-73-27"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-73-28" name="__codelineno-73-28" href="#__codelineno-73-28"></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-73-29" name="__codelineno-73-29" href="#__codelineno-73-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></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-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w"> </span><span class="c1">// Go 推薦短變數，這裡 bf 指代 t.balanceFactor</span>
|
||
<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></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-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></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-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="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-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></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-74-11" name="__codelineno-74-11" href="#__codelineno-74-11"></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-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-74-13" name="__codelineno-74-13" href="#__codelineno-74-13"></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-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></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-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a><span class="w"> </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="p">}</span>
|
||
<a id="__codelineno-74-17" name="__codelineno-74-17" href="#__codelineno-74-17"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-74-18" name="__codelineno-74-18" href="#__codelineno-74-18"></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-74-19" name="__codelineno-74-19" href="#__codelineno-74-19"></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-74-20" name="__codelineno-74-20" href="#__codelineno-74-20"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-74-21" name="__codelineno-74-21" href="#__codelineno-74-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-74-22" name="__codelineno-74-22" href="#__codelineno-74-22"></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-74-23" name="__codelineno-74-23" href="#__codelineno-74-23"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-74-24" name="__codelineno-74-24" href="#__codelineno-74-24"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">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-74-25" name="__codelineno-74-25" href="#__codelineno-74-25"></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-74-26" name="__codelineno-74-26" href="#__codelineno-74-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-74-27" name="__codelineno-74-27" href="#__codelineno-74-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-74-28" name="__codelineno-74-28" href="#__codelineno-74-28"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-74-29" name="__codelineno-74-29" href="#__codelineno-74-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-74-30" name="__codelineno-74-30" href="#__codelineno-74-30"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></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-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a> <span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></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-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a> <span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></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-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></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-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a> <span class="c1">// 右旋</span>
|
||
<a id="__codelineno-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></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-75-10" name="__codelineno-75-10" href="#__codelineno-75-10"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-75-11" name="__codelineno-75-11" href="#__codelineno-75-11"></a> <span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-75-12" name="__codelineno-75-12" href="#__codelineno-75-12"></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-75-13" name="__codelineno-75-13" href="#__codelineno-75-13"></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-75-14" name="__codelineno-75-14" href="#__codelineno-75-14"></a> <span class="p">}</span>
|
||
<a id="__codelineno-75-15" name="__codelineno-75-15" href="#__codelineno-75-15"></a> <span class="p">}</span>
|
||
<a id="__codelineno-75-16" name="__codelineno-75-16" href="#__codelineno-75-16"></a> <span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-75-17" name="__codelineno-75-17" href="#__codelineno-75-17"></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-75-18" name="__codelineno-75-18" href="#__codelineno-75-18"></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-75-19" name="__codelineno-75-19" href="#__codelineno-75-19"></a> <span class="c1">// 左旋</span>
|
||
<a id="__codelineno-75-20" name="__codelineno-75-20" href="#__codelineno-75-20"></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-75-21" name="__codelineno-75-21" href="#__codelineno-75-21"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-75-22" name="__codelineno-75-22" href="#__codelineno-75-22"></a> <span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-75-23" name="__codelineno-75-23" href="#__codelineno-75-23"></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-75-24" name="__codelineno-75-24" href="#__codelineno-75-24"></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-75-25" name="__codelineno-75-25" href="#__codelineno-75-25"></a> <span class="p">}</span>
|
||
<a id="__codelineno-75-26" name="__codelineno-75-26" href="#__codelineno-75-26"></a> <span class="p">}</span>
|
||
<a id="__codelineno-75-27" name="__codelineno-75-27" href="#__codelineno-75-27"></a> <span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-75-28" name="__codelineno-75-28" href="#__codelineno-75-28"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-75-29" name="__codelineno-75-29" href="#__codelineno-75-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></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-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></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-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></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-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></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-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-76-10" name="__codelineno-76-10" href="#__codelineno-76-10"></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-76-11" name="__codelineno-76-11" href="#__codelineno-76-11"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-76-12" name="__codelineno-76-12" href="#__codelineno-76-12"></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-76-13" name="__codelineno-76-13" href="#__codelineno-76-13"></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-76-14" name="__codelineno-76-14" href="#__codelineno-76-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-76-15" name="__codelineno-76-15" href="#__codelineno-76-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-76-16" name="__codelineno-76-16" href="#__codelineno-76-16"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-76-17" name="__codelineno-76-17" href="#__codelineno-76-17"></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-76-18" name="__codelineno-76-18" href="#__codelineno-76-18"></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-76-19" name="__codelineno-76-19" href="#__codelineno-76-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-76-20" name="__codelineno-76-20" href="#__codelineno-76-20"></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-76-21" name="__codelineno-76-21" href="#__codelineno-76-21"></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-76-22" name="__codelineno-76-22" href="#__codelineno-76-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-76-23" name="__codelineno-76-23" href="#__codelineno-76-23"></a><span class="w"> </span><span class="nx">node</span><span class="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-76-24" name="__codelineno-76-24" href="#__codelineno-76-24"></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-76-25" name="__codelineno-76-25" href="#__codelineno-76-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-76-26" name="__codelineno-76-26" href="#__codelineno-76-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-76-27" name="__codelineno-76-27" href="#__codelineno-76-27"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-76-28" name="__codelineno-76-28" href="#__codelineno-76-28"></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-76-29" name="__codelineno-76-29" href="#__codelineno-76-29"></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-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></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-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></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-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></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-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></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-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></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-77-10" name="__codelineno-77-10" href="#__codelineno-77-10"></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-77-11" name="__codelineno-77-11" href="#__codelineno-77-11"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-77-12" name="__codelineno-77-12" href="#__codelineno-77-12"></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-77-13" name="__codelineno-77-13" href="#__codelineno-77-13"></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-77-14" name="__codelineno-77-14" href="#__codelineno-77-14"></a><span class="w"> </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="p">}</span>
|
||
<a id="__codelineno-77-16" name="__codelineno-77-16" href="#__codelineno-77-16"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-77-17" name="__codelineno-77-17" href="#__codelineno-77-17"></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-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="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-77-19" name="__codelineno-77-19" href="#__codelineno-77-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-77-20" name="__codelineno-77-20" href="#__codelineno-77-20"></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-77-21" name="__codelineno-77-21" href="#__codelineno-77-21"></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-77-22" name="__codelineno-77-22" href="#__codelineno-77-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-77-23" name="__codelineno-77-23" href="#__codelineno-77-23"></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-77-24" name="__codelineno-77-24" href="#__codelineno-77-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">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-77-25" name="__codelineno-77-25" href="#__codelineno-77-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-77-26" name="__codelineno-77-26" href="#__codelineno-77-26"></a><span class="w"> </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="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-77-28" name="__codelineno-77-28" href="#__codelineno-77-28"></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-77-29" name="__codelineno-77-29" href="#__codelineno-77-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">factor</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></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-78-10" name="__codelineno-78-10" href="#__codelineno-78-10"></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-78-11" name="__codelineno-78-11" href="#__codelineno-78-11"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-78-12" name="__codelineno-78-12" href="#__codelineno-78-12"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-78-13" name="__codelineno-78-13" href="#__codelineno-78-13"></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-78-14" name="__codelineno-78-14" href="#__codelineno-78-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-78-15" name="__codelineno-78-15" href="#__codelineno-78-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-78-16" name="__codelineno-78-16" href="#__codelineno-78-16"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-78-17" name="__codelineno-78-17" href="#__codelineno-78-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">factor</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-78-18" name="__codelineno-78-18" href="#__codelineno-78-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">!</span><span class="p">.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-78-19" name="__codelineno-78-19" href="#__codelineno-78-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-78-20" name="__codelineno-78-20" href="#__codelineno-78-20"></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-78-21" name="__codelineno-78-21" href="#__codelineno-78-21"></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-78-22" name="__codelineno-78-22" href="#__codelineno-78-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-78-23" name="__codelineno-78-23" href="#__codelineno-78-23"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-78-24" name="__codelineno-78-24" href="#__codelineno-78-24"></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-78-25" name="__codelineno-78-25" href="#__codelineno-78-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-78-26" name="__codelineno-78-26" href="#__codelineno-78-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-78-27" name="__codelineno-78-27" href="#__codelineno-78-27"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-78-28" name="__codelineno-78-28" href="#__codelineno-78-28"></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-78-29" name="__codelineno-78-29" href="#__codelineno-78-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">fn</span> <span class="nf">rotate</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
|
||
<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">right_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
|
||
<a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></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-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-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="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">left_rotate</span><span class="p">(</span><span class="n">left</span><span class="p">);</span>
|
||
<a id="__codelineno-79-15" name="__codelineno-79-15" href="#__codelineno-79-15"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">right_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
|
||
<a id="__codelineno-79-16" name="__codelineno-79-16" href="#__codelineno-79-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-79-17" name="__codelineno-79-17" href="#__codelineno-79-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-79-18" name="__codelineno-79-18" href="#__codelineno-79-18"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-79-19" name="__codelineno-79-19" href="#__codelineno-79-19"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-20" name="__codelineno-79-20" href="#__codelineno-79-20"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-79-21" name="__codelineno-79-21" href="#__codelineno-79-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">())</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-22" name="__codelineno-79-22" href="#__codelineno-79-22"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-79-23" name="__codelineno-79-23" href="#__codelineno-79-23"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">left_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
|
||
<a id="__codelineno-79-24" name="__codelineno-79-24" href="#__codelineno-79-24"></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-79-25" name="__codelineno-79-25" href="#__codelineno-79-25"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-79-26" name="__codelineno-79-26" href="#__codelineno-79-26"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-79-27" name="__codelineno-79-27" href="#__codelineno-79-27"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">right_rotate</span><span class="p">(</span><span class="n">right</span><span class="p">);</span>
|
||
<a id="__codelineno-79-28" name="__codelineno-79-28" href="#__codelineno-79-28"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">left_rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">))</span>
|
||
<a id="__codelineno-79-29" name="__codelineno-79-29" href="#__codelineno-79-29"></a><span class="w"> </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><span class="w"> </span><span class="k">else</span><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="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-79-32" name="__codelineno-79-32" href="#__codelineno-79-32"></a><span class="w"> </span><span class="n">node</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="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-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></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-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">bf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bf</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></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-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></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-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></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-80-11" name="__codelineno-80-11" href="#__codelineno-80-11"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-80-12" name="__codelineno-80-12" href="#__codelineno-80-12"></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-80-13" name="__codelineno-80-13" href="#__codelineno-80-13"></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-80-14" name="__codelineno-80-14" href="#__codelineno-80-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-80-15" name="__codelineno-80-15" href="#__codelineno-80-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-80-16" name="__codelineno-80-16" href="#__codelineno-80-16"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-80-17" name="__codelineno-80-17" href="#__codelineno-80-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bf</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-80-18" name="__codelineno-80-18" href="#__codelineno-80-18"></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-80-19" name="__codelineno-80-19" href="#__codelineno-80-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-80-20" name="__codelineno-80-20" href="#__codelineno-80-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-80-21" name="__codelineno-80-21" href="#__codelineno-80-21"></a><span class="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-80-22" name="__codelineno-80-22" href="#__codelineno-80-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-80-23" name="__codelineno-80-23" href="#__codelineno-80-23"></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-80-24" name="__codelineno-80-24" href="#__codelineno-80-24"></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-80-25" name="__codelineno-80-25" href="#__codelineno-80-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-80-26" name="__codelineno-80-26" href="#__codelineno-80-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-80-27" name="__codelineno-80-27" href="#__codelineno-80-27"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-80-28" name="__codelineno-80-28" href="#__codelineno-80-28"></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-80-29" name="__codelineno-80-29" href="#__codelineno-80-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">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-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></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="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></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="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></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-81-10" name="__codelineno-81-10" href="#__codelineno-81-10"></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-81-11" name="__codelineno-81-11" href="#__codelineno-81-11"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-81-12" name="__codelineno-81-12" href="#__codelineno-81-12"></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-81-13" name="__codelineno-81-13" href="#__codelineno-81-13"></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-81-14" name="__codelineno-81-14" href="#__codelineno-81-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-15" name="__codelineno-81-15" href="#__codelineno-81-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-16" name="__codelineno-81-16" href="#__codelineno-81-16"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-81-17" name="__codelineno-81-17" href="#__codelineno-81-17"></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="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-18" name="__codelineno-81-18" href="#__codelineno-81-18"></a><span class="w"> </span><span class="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="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-19" name="__codelineno-81-19" href="#__codelineno-81-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-81-20" name="__codelineno-81-20" href="#__codelineno-81-20"></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-81-21" name="__codelineno-81-21" href="#__codelineno-81-21"></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-81-22" name="__codelineno-81-22" href="#__codelineno-81-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-81-23" name="__codelineno-81-23" href="#__codelineno-81-23"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="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-81-24" name="__codelineno-81-24" href="#__codelineno-81-24"></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-81-25" name="__codelineno-81-25" href="#__codelineno-81-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-26" name="__codelineno-81-26" href="#__codelineno-81-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-27" name="__codelineno-81-27" href="#__codelineno-81-27"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-81-28" name="__codelineno-81-28" href="#__codelineno-81-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
|
||
<a id="__codelineno-81-29" name="__codelineno-81-29" href="#__codelineno-81-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</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.zig</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="c1">// 執行旋轉操作，使該子樹重新恢復平衡</span>
|
||
<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">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-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w"> </span><span class="c1">// 獲取節點 node 的平衡因子</span>
|
||
<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></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-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w"> </span><span class="c1">// 左偏樹</span>
|
||
<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></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-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></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-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w"> </span><span class="c1">// 右旋</span>
|
||
<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></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-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></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-83-11" name="__codelineno-83-11" href="#__codelineno-83-11"></a><span class="w"> </span><span class="c1">// 先左旋後右旋</span>
|
||
<a id="__codelineno-83-12" name="__codelineno-83-12" href="#__codelineno-83-12"></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-83-13" name="__codelineno-83-13" href="#__codelineno-83-13"></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-83-14" name="__codelineno-83-14" href="#__codelineno-83-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-83-15" name="__codelineno-83-15" href="#__codelineno-83-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-83-16" name="__codelineno-83-16" href="#__codelineno-83-16"></a><span class="w"> </span><span class="c1">// 右偏樹</span>
|
||
<a id="__codelineno-83-17" name="__codelineno-83-17" href="#__codelineno-83-17"></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-83-18" name="__codelineno-83-18" href="#__codelineno-83-18"></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-83-19" name="__codelineno-83-19" href="#__codelineno-83-19"></a><span class="w"> </span><span class="c1">// 左旋</span>
|
||
<a id="__codelineno-83-20" name="__codelineno-83-20" href="#__codelineno-83-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">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-83-21" name="__codelineno-83-21" href="#__codelineno-83-21"></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-83-22" name="__codelineno-83-22" href="#__codelineno-83-22"></a><span class="w"> </span><span class="c1">// 先右旋後左旋</span>
|
||
<a id="__codelineno-83-23" name="__codelineno-83-23" href="#__codelineno-83-23"></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-83-24" name="__codelineno-83-24" href="#__codelineno-83-24"></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-83-25" name="__codelineno-83-25" href="#__codelineno-83-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-83-26" name="__codelineno-83-26" href="#__codelineno-83-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-83-27" name="__codelineno-83-27" href="#__codelineno-83-27"></a><span class="w"> </span><span class="c1">// 平衡樹，無須旋轉，直接返回</span>
|
||
<a id="__codelineno-83-28" name="__codelineno-83-28" href="#__codelineno-83-28"></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-83-29" name="__codelineno-83-29" href="#__codelineno-83-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h2 id="753-avl">7.5.3 AVL 樹常用操作<a class="headerlink" href="#753-avl" title="Permanent link">¶</a></h2>
|
||
<h3 id="1_2">1. 插入節點<a class="headerlink" href="#1_2" title="Permanent link">¶</a></h3>
|
||
<p>AVL 樹的節點插入操作與二元搜尋樹在主體上類似。唯一的區別在於，在 AVL 樹中插入節點後，從該節點到根節點的路徑上可能會出現一系列失衡節點。因此，<strong>我們需要從這個節點開始，自底向上執行旋轉操作，使所有失衡節點恢復平衡</strong>。程式碼如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="8:14"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><input id="__tabbed_8_14" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label><label for="__tabbed_8_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="k">def</span> <span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">):</span>
|
||
<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="w"> </span><span class="sd">"""插入節點"""</span>
|
||
<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">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-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a>
|
||
<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="k">def</span> <span class="nf">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-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w"> </span><span class="sd">"""遞迴插入節點（輔助方法）"""</span>
|
||
<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a> <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||
<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a> <span class="k">return</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a> <span class="c1"># 1. 查詢插入位置並插入節點</span>
|
||
<a id="__codelineno-84-10" name="__codelineno-84-10" href="#__codelineno-84-10"></a> <span class="k">if</span> <span class="n">val</span> <span class="o"><</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
|
||
<a id="__codelineno-84-11" name="__codelineno-84-11" href="#__codelineno-84-11"></a> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">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-84-12" name="__codelineno-84-12" href="#__codelineno-84-12"></a> <span class="k">elif</span> <span class="n">val</span> <span class="o">></span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
|
||
<a id="__codelineno-84-13" name="__codelineno-84-13" href="#__codelineno-84-13"></a> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">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-84-14" name="__codelineno-84-14" href="#__codelineno-84-14"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-84-15" name="__codelineno-84-15" href="#__codelineno-84-15"></a> <span class="c1"># 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-84-16" name="__codelineno-84-16" href="#__codelineno-84-16"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-84-17" name="__codelineno-84-17" href="#__codelineno-84-17"></a> <span class="c1"># 更新節點高度</span>
|
||
<a id="__codelineno-84-18" name="__codelineno-84-18" href="#__codelineno-84-18"></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-84-19" name="__codelineno-84-19" href="#__codelineno-84-19"></a> <span class="c1"># 2. 執行旋轉操作，使該子樹重新恢復平衡</span>
|
||
<a id="__codelineno-84-20" name="__codelineno-84-20" href="#__codelineno-84-20"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">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-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a>
|
||
<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">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-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
|
||
<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">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-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></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">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-85-17" name="__codelineno-85-17" href="#__codelineno-85-17"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-85-18" name="__codelineno-85-18" href="#__codelineno-85-18"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-85-19" name="__codelineno-85-19" href="#__codelineno-85-19"></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-85-20" name="__codelineno-85-20" href="#__codelineno-85-20"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-85-21" name="__codelineno-85-21" href="#__codelineno-85-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-85-22" name="__codelineno-85-22" href="#__codelineno-85-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">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-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a>
|
||
<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">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-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
|
||
<a id="__codelineno-86-12" name="__codelineno-86-12" href="#__codelineno-86-12"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-86-13" name="__codelineno-86-13" href="#__codelineno-86-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
|
||
<a id="__codelineno-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-86-15" name="__codelineno-86-15" href="#__codelineno-86-15"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-86-16" name="__codelineno-86-16" href="#__codelineno-86-16"></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">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-86-17" name="__codelineno-86-17" href="#__codelineno-86-17"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-86-18" name="__codelineno-86-18" href="#__codelineno-86-18"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-86-19" name="__codelineno-86-19" href="#__codelineno-86-19"></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-86-20" name="__codelineno-86-20" href="#__codelineno-86-20"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-86-21" name="__codelineno-86-21" href="#__codelineno-86-21"></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-86-22" name="__codelineno-86-22" href="#__codelineno-86-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">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-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a>
|
||
<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">InsertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">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-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-87-11" name="__codelineno-87-11" href="#__codelineno-87-11"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-87-12" name="__codelineno-87-12" href="#__codelineno-87-12"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-87-13" name="__codelineno-87-13" href="#__codelineno-87-13"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-87-14" name="__codelineno-87-14" href="#__codelineno-87-14"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-87-15" name="__codelineno-87-15" href="#__codelineno-87-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-87-16" name="__codelineno-87-16" href="#__codelineno-87-16"></a><span class="w"> </span><span class="n">UpdateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-87-17" name="__codelineno-87-17" href="#__codelineno-87-17"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-87-18" name="__codelineno-87-18" href="#__codelineno-87-18"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-87-19" name="__codelineno-87-19" href="#__codelineno-87-19"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-87-20" name="__codelineno-87-20" href="#__codelineno-87-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-87-21" name="__codelineno-87-21" href="#__codelineno-87-21"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">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-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">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-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a>
|
||
<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="cm">/* 遞迴插入節點（輔助函式） */</span>
|
||
<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">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-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span>
|
||
<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-88-12" name="__codelineno-88-12" href="#__codelineno-88-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-13" name="__codelineno-88-13" href="#__codelineno-88-13"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">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-88-14" name="__codelineno-88-14" href="#__codelineno-88-14"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-15" name="__codelineno-88-15" href="#__codelineno-88-15"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">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-88-16" name="__codelineno-88-16" href="#__codelineno-88-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-17" name="__codelineno-88-17" href="#__codelineno-88-17"></a><span class="w"> </span><span class="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-88-18" name="__codelineno-88-18" href="#__codelineno-88-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-88-19" name="__codelineno-88-19" href="#__codelineno-88-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-20" name="__codelineno-88-20" href="#__codelineno-88-20"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-88-21" name="__codelineno-88-21" href="#__codelineno-88-21"></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-88-22" name="__codelineno-88-22" href="#__codelineno-88-22"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-88-23" name="__codelineno-88-23" href="#__codelineno-88-23"></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-88-24" name="__codelineno-88-24" href="#__codelineno-88-24"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-88-25" name="__codelineno-88-25" href="#__codelineno-88-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-88-26" name="__codelineno-88-26" href="#__codelineno-88-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">func</span> <span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">root</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a>
|
||
<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="kd">func</span> <span class="nf">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-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a> <span class="k">if</span> <span class="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a> <span class="k">return</span> <span class="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-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-12" name="__codelineno-89-12" href="#__codelineno-89-12"></a> <span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-89-13" name="__codelineno-89-13" href="#__codelineno-89-13"></a> <span class="k">if</span> <span class="n">val</span> <span class="o"><</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-14" name="__codelineno-89-14" href="#__codelineno-89-14"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">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-89-15" name="__codelineno-89-15" href="#__codelineno-89-15"></a> <span class="p">}</span> <span class="k">else</span> <span class="k">if</span> <span class="n">val</span> <span class="o">></span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-16" name="__codelineno-89-16" href="#__codelineno-89-16"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">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-89-17" name="__codelineno-89-17" href="#__codelineno-89-17"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-18" name="__codelineno-89-18" href="#__codelineno-89-18"></a> <span class="k">return</span> <span class="n">node</span> <span class="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-89-19" name="__codelineno-89-19" href="#__codelineno-89-19"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-20" name="__codelineno-89-20" href="#__codelineno-89-20"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span> <span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-89-21" name="__codelineno-89-21" href="#__codelineno-89-21"></a> <span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-89-22" name="__codelineno-89-22" href="#__codelineno-89-22"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-89-23" name="__codelineno-89-23" href="#__codelineno-89-23"></a> <span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-89-24" name="__codelineno-89-24" href="#__codelineno-89-24"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-89-25" name="__codelineno-89-25" href="#__codelineno-89-25"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></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-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">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-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a>
|
||
<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="err">#</span><span class="nx">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-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">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-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span>
|
||
<a id="__codelineno-90-12" name="__codelineno-90-12" href="#__codelineno-90-12"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">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-90-13" name="__codelineno-90-13" href="#__codelineno-90-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-90-14" name="__codelineno-90-14" href="#__codelineno-90-14"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-90-15" name="__codelineno-90-15" href="#__codelineno-90-15"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-90-16" name="__codelineno-90-16" href="#__codelineno-90-16"></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-90-17" name="__codelineno-90-17" href="#__codelineno-90-17"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-90-18" name="__codelineno-90-18" href="#__codelineno-90-18"></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-90-19" name="__codelineno-90-19" href="#__codelineno-90-19"></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-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></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-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">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-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a>
|
||
<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></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-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="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-91-9" name="__codelineno-91-9" href="#__codelineno-91-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-91-10" name="__codelineno-91-10" href="#__codelineno-91-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-11" name="__codelineno-91-11" href="#__codelineno-91-11"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">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-91-12" name="__codelineno-91-12" href="#__codelineno-91-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-13" name="__codelineno-91-13" href="#__codelineno-91-13"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">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-91-14" name="__codelineno-91-14" href="#__codelineno-91-14"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-15" name="__codelineno-91-15" href="#__codelineno-91-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-91-16" name="__codelineno-91-16" href="#__codelineno-91-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-91-17" name="__codelineno-91-17" href="#__codelineno-91-17"></a><span class="w"> </span><span class="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">// 更新節點高度</span>
|
||
<a id="__codelineno-91-18" name="__codelineno-91-18" href="#__codelineno-91-18"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-91-19" name="__codelineno-91-19" href="#__codelineno-91-19"></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-91-20" name="__codelineno-91-20" href="#__codelineno-91-20"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-91-21" name="__codelineno-91-21" href="#__codelineno-91-21"></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-91-22" name="__codelineno-91-22" href="#__codelineno-91-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">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-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a>
|
||
<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-92-9" name="__codelineno-92-9" href="#__codelineno-92-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-92-12" name="__codelineno-92-12" href="#__codelineno-92-12"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-92-13" name="__codelineno-92-13" href="#__codelineno-92-13"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">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-92-14" name="__codelineno-92-14" href="#__codelineno-92-14"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-92-15" name="__codelineno-92-15" href="#__codelineno-92-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-92-16" name="__codelineno-92-16" href="#__codelineno-92-16"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-92-17" name="__codelineno-92-17" href="#__codelineno-92-17"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-92-18" name="__codelineno-92-18" href="#__codelineno-92-18"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-92-19" name="__codelineno-92-19" href="#__codelineno-92-19"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-92-20" name="__codelineno-92-20" href="#__codelineno-92-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-92-21" name="__codelineno-92-21" href="#__codelineno-92-21"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a><span class="k">fn</span> <span class="nf">insert</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a>
|
||
<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></a><span class="k">fn</span> <span class="nf">insert_helper</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-9" name="__codelineno-93-9" href="#__codelineno-93-9"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-10" name="__codelineno-93-10" href="#__codelineno-93-10"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-12" name="__codelineno-93-12" href="#__codelineno-93-12"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">node_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-93-13" name="__codelineno-93-13" href="#__codelineno-93-13"></a><span class="w"> </span><span class="n">node_val</span>
|
||
<a id="__codelineno-93-14" name="__codelineno-93-14" href="#__codelineno-93-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-15" name="__codelineno-93-15" href="#__codelineno-93-15"></a><span class="w"> </span><span class="p">.</span><span class="n">cmp</span><span class="p">(</span><span class="o">&</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-93-16" name="__codelineno-93-16" href="#__codelineno-93-16"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-17" name="__codelineno-93-17" href="#__codelineno-93-17"></a><span class="w"> </span><span class="n">Ordering</span>::<span class="n">Greater</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-18" name="__codelineno-93-18" href="#__codelineno-93-18"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-93-19" name="__codelineno-93-19" href="#__codelineno-93-19"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">insert_helper</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-93-20" name="__codelineno-93-20" href="#__codelineno-93-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-21" name="__codelineno-93-21" href="#__codelineno-93-21"></a><span class="w"> </span><span class="n">Ordering</span>::<span class="n">Less</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-22" name="__codelineno-93-22" href="#__codelineno-93-22"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-93-23" name="__codelineno-93-23" href="#__codelineno-93-23"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">insert_helper</span><span class="p">(</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-93-24" name="__codelineno-93-24" href="#__codelineno-93-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-25" name="__codelineno-93-25" href="#__codelineno-93-25"></a><span class="w"> </span><span class="n">Ordering</span>::<span class="n">Equal</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-26" name="__codelineno-93-26" href="#__codelineno-93-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-93-27" name="__codelineno-93-27" href="#__codelineno-93-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-28" name="__codelineno-93-28" href="#__codelineno-93-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-29" name="__codelineno-93-29" href="#__codelineno-93-29"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-93-30" name="__codelineno-93-30" href="#__codelineno-93-30"></a>
|
||
<a id="__codelineno-93-31" name="__codelineno-93-31" href="#__codelineno-93-31"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-93-32" name="__codelineno-93-32" href="#__codelineno-93-32"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)).</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-93-33" name="__codelineno-93-33" href="#__codelineno-93-33"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-93-34" name="__codelineno-93-34" href="#__codelineno-93-34"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-93-35" name="__codelineno-93-35" href="#__codelineno-93-35"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-36" name="__codelineno-93-36" href="#__codelineno-93-36"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">TreeNode</span>::<span class="n">new</span><span class="p">(</span><span class="n">val</span><span class="p">)),</span>
|
||
<a id="__codelineno-93-37" name="__codelineno-93-37" href="#__codelineno-93-37"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-38" name="__codelineno-93-38" href="#__codelineno-93-38"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">AVLTree</span><span class="w"> </span><span class="o">*</span><span class="n">tree</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="w"> </span><span class="n">tree</span><span class="o">-></span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">tree</span><span class="o">-></span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a>
|
||
<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="cm">/* 遞迴插入節點（輔助函式） */</span>
|
||
<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></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-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-94-10" name="__codelineno-94-10" href="#__codelineno-94-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-11" name="__codelineno-94-11" href="#__codelineno-94-11"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-94-12" name="__codelineno-94-12" href="#__codelineno-94-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-13" name="__codelineno-94-13" href="#__codelineno-94-13"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-94-14" name="__codelineno-94-14" href="#__codelineno-94-14"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-15" name="__codelineno-94-15" href="#__codelineno-94-15"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">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-94-16" name="__codelineno-94-16" href="#__codelineno-94-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-17" name="__codelineno-94-17" href="#__codelineno-94-17"></a><span class="w"> </span><span class="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-94-18" name="__codelineno-94-18" href="#__codelineno-94-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-94-19" name="__codelineno-94-19" href="#__codelineno-94-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-20" name="__codelineno-94-20" href="#__codelineno-94-20"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-94-21" name="__codelineno-94-21" href="#__codelineno-94-21"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-94-22" name="__codelineno-94-22" href="#__codelineno-94-22"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-94-23" name="__codelineno-94-23" href="#__codelineno-94-23"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-94-24" name="__codelineno-94-24" href="#__codelineno-94-24"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-94-25" name="__codelineno-94-25" href="#__codelineno-94-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-94-26" name="__codelineno-94-26" href="#__codelineno-94-26"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="cm">/* 插入節點 */</span>
|
||
<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">_val</span><span class="p">:</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-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></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-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a>
|
||
<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="cm">/* 遞迴插入節點（輔助方法） */</span>
|
||
<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</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-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">_val</span><span class="p">)</span>
|
||
<a id="__codelineno-95-10" name="__codelineno-95-10" href="#__codelineno-95-10"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span>
|
||
<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></a><span class="w"> </span><span class="cm">/* 1. 查詢插入位置並插入節點 */</span>
|
||
<a id="__codelineno-95-12" name="__codelineno-95-12" href="#__codelineno-95-12"></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="na">_val</span><span class="p">)</span>
|
||
<a id="__codelineno-95-13" name="__codelineno-95-13" href="#__codelineno-95-13"></a><span class="w"> </span><span class="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-95-14" name="__codelineno-95-14" href="#__codelineno-95-14"></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-95-15" name="__codelineno-95-15" href="#__codelineno-95-15"></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-95-16" name="__codelineno-95-16" href="#__codelineno-95-16"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-95-17" name="__codelineno-95-17" href="#__codelineno-95-17"></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="c1">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-95-18" name="__codelineno-95-18" href="#__codelineno-95-18"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-95-19" name="__codelineno-95-19" href="#__codelineno-95-19"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-95-20" name="__codelineno-95-20" href="#__codelineno-95-20"></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-95-21" name="__codelineno-95-21" href="#__codelineno-95-21"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-95-22" name="__codelineno-95-22" href="#__codelineno-95-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
|
||
<a id="__codelineno-95-23" name="__codelineno-95-23" href="#__codelineno-95-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
|
||
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a>
|
||
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert_helper</span><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-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="c1">// 插入節點</span>
|
||
<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">insertHelper</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)).</span><span class="o">?</span><span class="p">;</span>
|
||
<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a>
|
||
<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="c1">// 遞迴插入節點（輔助方法）</span>
|
||
<a id="__codelineno-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></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-97-8" name="__codelineno-97-8" href="#__codelineno-97-8"></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-97-9" name="__codelineno-97-9" href="#__codelineno-97-9"></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-97-10" name="__codelineno-97-10" href="#__codelineno-97-10"></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-97-11" name="__codelineno-97-11" href="#__codelineno-97-11"></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-97-12" name="__codelineno-97-12" href="#__codelineno-97-12"></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-97-13" name="__codelineno-97-13" href="#__codelineno-97-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-97-14" name="__codelineno-97-14" href="#__codelineno-97-14"></a><span class="w"> </span><span class="c1">// 1. 查詢插入位置並插入節點</span>
|
||
<a id="__codelineno-97-15" name="__codelineno-97-15" href="#__codelineno-97-15"></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-97-16" name="__codelineno-97-16" href="#__codelineno-97-16"></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-97-17" name="__codelineno-97-17" href="#__codelineno-97-17"></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-97-18" name="__codelineno-97-18" href="#__codelineno-97-18"></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-97-19" name="__codelineno-97-19" href="#__codelineno-97-19"></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-97-20" name="__codelineno-97-20" href="#__codelineno-97-20"></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">// 重複節點不插入，直接返回</span>
|
||
<a id="__codelineno-97-21" name="__codelineno-97-21" href="#__codelineno-97-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-97-22" name="__codelineno-97-22" href="#__codelineno-97-22"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-97-23" name="__codelineno-97-23" href="#__codelineno-97-23"></a><span class="w"> </span><span class="c1">// 2. 執行旋轉操作，使該子樹重新恢復平衡</span>
|
||
<a id="__codelineno-97-24" name="__codelineno-97-24" href="#__codelineno-97-24"></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-97-25" name="__codelineno-97-25" href="#__codelineno-97-25"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-97-26" name="__codelineno-97-26" href="#__codelineno-97-26"></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-97-27" name="__codelineno-97-27" href="#__codelineno-97-27"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2_2">2. 刪除節點<a class="headerlink" href="#2_2" title="Permanent link">¶</a></h3>
|
||
<p>類似地，在二元搜尋樹的刪除節點方法的基礎上，需要從底至頂執行旋轉操作，使所有失衡節點恢復平衡。程式碼如下所示：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="9:14"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><input id="__tabbed_9_13" name="__tabbed_9" type="radio" /><input id="__tabbed_9_14" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Kotlin</label><label for="__tabbed_9_13">Ruby</label><label for="__tabbed_9_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="k">def</span> <span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="w"> </span><span class="sd">"""刪除節點"""</span>
|
||
<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></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-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a>
|
||
<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></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-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a><span class="w"> </span><span class="sd">"""遞迴刪除節點（輔助方法）"""</span>
|
||
<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></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-98-8" name="__codelineno-98-8" href="#__codelineno-98-8"></a> <span class="k">return</span> <span class="kc">None</span>
|
||
<a id="__codelineno-98-9" name="__codelineno-98-9" href="#__codelineno-98-9"></a> <span class="c1"># 1. 查詢節點並刪除</span>
|
||
<a id="__codelineno-98-10" name="__codelineno-98-10" href="#__codelineno-98-10"></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-98-11" name="__codelineno-98-11" href="#__codelineno-98-11"></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-98-12" name="__codelineno-98-12" href="#__codelineno-98-12"></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-98-13" name="__codelineno-98-13" href="#__codelineno-98-13"></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-98-14" name="__codelineno-98-14" href="#__codelineno-98-14"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-98-15" name="__codelineno-98-15" href="#__codelineno-98-15"></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-98-16" name="__codelineno-98-16" href="#__codelineno-98-16"></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-98-17" name="__codelineno-98-17" href="#__codelineno-98-17"></a> <span class="c1"># 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-98-18" name="__codelineno-98-18" href="#__codelineno-98-18"></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-98-19" name="__codelineno-98-19" href="#__codelineno-98-19"></a> <span class="k">return</span> <span class="kc">None</span>
|
||
<a id="__codelineno-98-20" name="__codelineno-98-20" href="#__codelineno-98-20"></a> <span class="c1"># 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-98-21" name="__codelineno-98-21" href="#__codelineno-98-21"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-98-22" name="__codelineno-98-22" href="#__codelineno-98-22"></a> <span class="n">node</span> <span class="o">=</span> <span class="n">child</span>
|
||
<a id="__codelineno-98-23" name="__codelineno-98-23" href="#__codelineno-98-23"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-98-24" name="__codelineno-98-24" href="#__codelineno-98-24"></a> <span class="c1"># 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-98-25" name="__codelineno-98-25" href="#__codelineno-98-25"></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-98-26" name="__codelineno-98-26" href="#__codelineno-98-26"></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-98-27" name="__codelineno-98-27" href="#__codelineno-98-27"></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-98-28" name="__codelineno-98-28" href="#__codelineno-98-28"></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-98-29" name="__codelineno-98-29" href="#__codelineno-98-29"></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-98-30" name="__codelineno-98-30" href="#__codelineno-98-30"></a> <span class="c1"># 更新節點高度</span>
|
||
<a id="__codelineno-98-31" name="__codelineno-98-31" href="#__codelineno-98-31"></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-98-32" name="__codelineno-98-32" href="#__codelineno-98-32"></a> <span class="c1"># 2. 執行旋轉操作，使該子樹重新恢復平衡</span>
|
||
<a id="__codelineno-98-33" name="__codelineno-98-33" href="#__codelineno-98-33"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></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-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></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-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a>
|
||
<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></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-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></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-99-9" name="__codelineno-99-9" href="#__codelineno-99-9"></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-99-10" name="__codelineno-99-10" href="#__codelineno-99-10"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-99-11" name="__codelineno-99-11" href="#__codelineno-99-11"></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-99-12" name="__codelineno-99-12" href="#__codelineno-99-12"></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-99-13" name="__codelineno-99-13" href="#__codelineno-99-13"></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-99-14" name="__codelineno-99-14" href="#__codelineno-99-14"></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-99-15" name="__codelineno-99-15" href="#__codelineno-99-15"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-99-16" name="__codelineno-99-16" href="#__codelineno-99-16"></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-99-17" name="__codelineno-99-17" href="#__codelineno-99-17"></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-99-18" name="__codelineno-99-18" href="#__codelineno-99-18"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-99-19" name="__codelineno-99-19" href="#__codelineno-99-19"></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-99-20" name="__codelineno-99-20" href="#__codelineno-99-20"></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-99-21" name="__codelineno-99-21" href="#__codelineno-99-21"></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-99-22" name="__codelineno-99-22" href="#__codelineno-99-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-99-23" name="__codelineno-99-23" href="#__codelineno-99-23"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-99-24" name="__codelineno-99-24" href="#__codelineno-99-24"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-99-25" name="__codelineno-99-25" href="#__codelineno-99-25"></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-99-26" name="__codelineno-99-26" href="#__codelineno-99-26"></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-99-27" name="__codelineno-99-27" href="#__codelineno-99-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-99-28" name="__codelineno-99-28" href="#__codelineno-99-28"></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-99-29" name="__codelineno-99-29" href="#__codelineno-99-29"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-99-30" name="__codelineno-99-30" href="#__codelineno-99-30"></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-99-31" name="__codelineno-99-31" href="#__codelineno-99-31"></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-99-32" name="__codelineno-99-32" href="#__codelineno-99-32"></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-99-33" name="__codelineno-99-33" href="#__codelineno-99-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-99-34" name="__codelineno-99-34" href="#__codelineno-99-34"></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-99-35" name="__codelineno-99-35" href="#__codelineno-99-35"></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-99-36" name="__codelineno-99-36" href="#__codelineno-99-36"></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-99-37" name="__codelineno-99-37" href="#__codelineno-99-37"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-99-38" name="__codelineno-99-38" href="#__codelineno-99-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-99-39" name="__codelineno-99-39" href="#__codelineno-99-39"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-99-40" name="__codelineno-99-40" href="#__codelineno-99-40"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-99-41" name="__codelineno-99-41" href="#__codelineno-99-41"></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-99-42" name="__codelineno-99-42" href="#__codelineno-99-42"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-99-43" name="__codelineno-99-43" href="#__codelineno-99-43"></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-99-44" name="__codelineno-99-44" href="#__codelineno-99-44"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></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-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></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-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a>
|
||
<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></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-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></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-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></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-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></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-100-12" name="__codelineno-100-12" href="#__codelineno-100-12"></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-100-13" name="__codelineno-100-13" href="#__codelineno-100-13"></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-100-14" name="__codelineno-100-14" href="#__codelineno-100-14"></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-100-15" name="__codelineno-100-15" href="#__codelineno-100-15"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-100-16" name="__codelineno-100-16" href="#__codelineno-100-16"></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-100-17" name="__codelineno-100-17" href="#__codelineno-100-17"></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-100-18" name="__codelineno-100-18" href="#__codelineno-100-18"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-100-19" name="__codelineno-100-19" href="#__codelineno-100-19"></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-100-20" name="__codelineno-100-20" href="#__codelineno-100-20"></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-100-21" name="__codelineno-100-21" href="#__codelineno-100-21"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-100-22" name="__codelineno-100-22" href="#__codelineno-100-22"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-100-23" name="__codelineno-100-23" href="#__codelineno-100-23"></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-100-24" name="__codelineno-100-24" href="#__codelineno-100-24"></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-100-25" name="__codelineno-100-25" href="#__codelineno-100-25"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-100-26" name="__codelineno-100-26" href="#__codelineno-100-26"></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-100-27" name="__codelineno-100-27" href="#__codelineno-100-27"></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-100-28" name="__codelineno-100-28" href="#__codelineno-100-28"></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-100-29" name="__codelineno-100-29" href="#__codelineno-100-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-100-30" name="__codelineno-100-30" href="#__codelineno-100-30"></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-100-31" name="__codelineno-100-31" href="#__codelineno-100-31"></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-100-32" name="__codelineno-100-32" href="#__codelineno-100-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-100-33" name="__codelineno-100-33" href="#__codelineno-100-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-100-34" name="__codelineno-100-34" href="#__codelineno-100-34"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-100-35" name="__codelineno-100-35" href="#__codelineno-100-35"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-100-36" name="__codelineno-100-36" href="#__codelineno-100-36"></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-100-37" name="__codelineno-100-37" href="#__codelineno-100-37"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-100-38" name="__codelineno-100-38" href="#__codelineno-100-38"></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-100-39" name="__codelineno-100-39" href="#__codelineno-100-39"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></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-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a>
|
||
<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
|
||
<a id="__codelineno-101-9" name="__codelineno-101-9" href="#__codelineno-101-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-101-10" name="__codelineno-101-10" href="#__codelineno-101-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-101-11" name="__codelineno-101-11" href="#__codelineno-101-11"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-101-12" name="__codelineno-101-12" href="#__codelineno-101-12"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-101-13" name="__codelineno-101-13" href="#__codelineno-101-13"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-101-14" name="__codelineno-101-14" href="#__codelineno-101-14"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-101-15" name="__codelineno-101-15" href="#__codelineno-101-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-101-16" name="__codelineno-101-16" href="#__codelineno-101-16"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-101-17" name="__codelineno-101-17" href="#__codelineno-101-17"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-101-18" name="__codelineno-101-18" href="#__codelineno-101-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
|
||
<a id="__codelineno-101-19" name="__codelineno-101-19" href="#__codelineno-101-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
|
||
<a id="__codelineno-101-20" name="__codelineno-101-20" href="#__codelineno-101-20"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-101-21" name="__codelineno-101-21" href="#__codelineno-101-21"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-101-22" name="__codelineno-101-22" href="#__codelineno-101-22"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-101-23" name="__codelineno-101-23" href="#__codelineno-101-23"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-101-24" name="__codelineno-101-24" href="#__codelineno-101-24"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-101-25" name="__codelineno-101-25" href="#__codelineno-101-25"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-101-26" name="__codelineno-101-26" href="#__codelineno-101-26"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-101-27" name="__codelineno-101-27" href="#__codelineno-101-27"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-101-28" name="__codelineno-101-28" href="#__codelineno-101-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-101-29" name="__codelineno-101-29" href="#__codelineno-101-29"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">RemoveHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="o">!</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
|
||
<a id="__codelineno-101-30" name="__codelineno-101-30" href="#__codelineno-101-30"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-101-31" name="__codelineno-101-31" href="#__codelineno-101-31"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-101-32" name="__codelineno-101-32" href="#__codelineno-101-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-101-33" name="__codelineno-101-33" href="#__codelineno-101-33"></a><span class="w"> </span><span class="n">UpdateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-101-34" name="__codelineno-101-34" href="#__codelineno-101-34"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-101-35" name="__codelineno-101-35" href="#__codelineno-101-35"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-101-36" name="__codelineno-101-36" href="#__codelineno-101-36"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-101-37" name="__codelineno-101-37" href="#__codelineno-101-37"></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-101-38" name="__codelineno-101-38" href="#__codelineno-101-38"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></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-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></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-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a>
|
||
<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="cm">/* 遞迴刪除節點（輔助函式） */</span>
|
||
<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></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-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></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-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||
<a id="__codelineno-102-10" name="__codelineno-102-10" href="#__codelineno-102-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-11" name="__codelineno-102-11" href="#__codelineno-102-11"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-102-12" name="__codelineno-102-12" href="#__codelineno-102-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-102-13" name="__codelineno-102-13" href="#__codelineno-102-13"></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-102-14" name="__codelineno-102-14" href="#__codelineno-102-14"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-102-15" name="__codelineno-102-15" href="#__codelineno-102-15"></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-102-16" name="__codelineno-102-16" href="#__codelineno-102-16"></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-102-17" name="__codelineno-102-17" href="#__codelineno-102-17"></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-102-18" name="__codelineno-102-18" href="#__codelineno-102-18"></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-102-19" name="__codelineno-102-19" href="#__codelineno-102-19"></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-102-20" name="__codelineno-102-20" href="#__codelineno-102-20"></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-102-21" name="__codelineno-102-21" href="#__codelineno-102-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-22" name="__codelineno-102-22" href="#__codelineno-102-22"></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-102-23" name="__codelineno-102-23" href="#__codelineno-102-23"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-102-24" name="__codelineno-102-24" href="#__codelineno-102-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||
<a id="__codelineno-102-25" name="__codelineno-102-25" href="#__codelineno-102-25"></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-102-26" name="__codelineno-102-26" href="#__codelineno-102-26"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-102-27" name="__codelineno-102-27" href="#__codelineno-102-27"></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-102-28" name="__codelineno-102-28" href="#__codelineno-102-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-29" name="__codelineno-102-29" href="#__codelineno-102-29"></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-102-30" name="__codelineno-102-30" href="#__codelineno-102-30"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-102-31" name="__codelineno-102-31" href="#__codelineno-102-31"></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-102-32" name="__codelineno-102-32" href="#__codelineno-102-32"></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-102-33" name="__codelineno-102-33" href="#__codelineno-102-33"></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-102-34" name="__codelineno-102-34" href="#__codelineno-102-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-35" name="__codelineno-102-35" href="#__codelineno-102-35"></a><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">temp</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">))</span>
|
||
<a id="__codelineno-102-36" name="__codelineno-102-36" href="#__codelineno-102-36"></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-102-37" name="__codelineno-102-37" href="#__codelineno-102-37"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-38" name="__codelineno-102-38" href="#__codelineno-102-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-39" name="__codelineno-102-39" href="#__codelineno-102-39"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-102-40" name="__codelineno-102-40" href="#__codelineno-102-40"></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-102-41" name="__codelineno-102-41" href="#__codelineno-102-41"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-102-42" name="__codelineno-102-42" href="#__codelineno-102-42"></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-102-43" name="__codelineno-102-43" href="#__codelineno-102-43"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-102-44" name="__codelineno-102-44" href="#__codelineno-102-44"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
|
||
<a id="__codelineno-102-45" name="__codelineno-102-45" href="#__codelineno-102-45"></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-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="kd">func</span> <span class="nf">remove</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">root</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a>
|
||
<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a><span class="kd">func</span> <span class="nf">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
|
||
<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a> <span class="k">if</span> <span class="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-10" name="__codelineno-103-10" href="#__codelineno-103-10"></a> <span class="k">return</span> <span class="kc">nil</span>
|
||
<a id="__codelineno-103-11" name="__codelineno-103-11" href="#__codelineno-103-11"></a> <span class="p">}</span>
|
||
<a id="__codelineno-103-12" name="__codelineno-103-12" href="#__codelineno-103-12"></a> <span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-103-13" name="__codelineno-103-13" href="#__codelineno-103-13"></a> <span class="k">if</span> <span class="n">val</span> <span class="o"><</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-14" name="__codelineno-103-14" href="#__codelineno-103-14"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-103-15" name="__codelineno-103-15" href="#__codelineno-103-15"></a> <span class="p">}</span> <span class="k">else</span> <span class="k">if</span> <span class="n">val</span> <span class="o">></span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-16" name="__codelineno-103-16" href="#__codelineno-103-16"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-103-17" name="__codelineno-103-17" href="#__codelineno-103-17"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-18" name="__codelineno-103-18" href="#__codelineno-103-18"></a> <span class="k">if</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-19" name="__codelineno-103-19" href="#__codelineno-103-19"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">??</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
|
||
<a id="__codelineno-103-20" name="__codelineno-103-20" href="#__codelineno-103-20"></a> <span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-103-21" name="__codelineno-103-21" href="#__codelineno-103-21"></a> <span class="k">if</span> <span class="n">child</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-22" name="__codelineno-103-22" href="#__codelineno-103-22"></a> <span class="k">return</span> <span class="kc">nil</span>
|
||
<a id="__codelineno-103-23" name="__codelineno-103-23" href="#__codelineno-103-23"></a> <span class="p">}</span>
|
||
<a id="__codelineno-103-24" name="__codelineno-103-24" href="#__codelineno-103-24"></a> <span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-103-25" name="__codelineno-103-25" href="#__codelineno-103-25"></a> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-26" name="__codelineno-103-26" href="#__codelineno-103-26"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">child</span>
|
||
<a id="__codelineno-103-27" name="__codelineno-103-27" href="#__codelineno-103-27"></a> <span class="p">}</span>
|
||
<a id="__codelineno-103-28" name="__codelineno-103-28" href="#__codelineno-103-28"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-29" name="__codelineno-103-29" href="#__codelineno-103-29"></a> <span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-103-30" name="__codelineno-103-30" href="#__codelineno-103-30"></a> <span class="kd">var</span> <span class="nv">temp</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
|
||
<a id="__codelineno-103-31" name="__codelineno-103-31" href="#__codelineno-103-31"></a> <span class="k">while</span> <span class="n">temp</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-32" name="__codelineno-103-32" href="#__codelineno-103-32"></a> <span class="n">temp</span> <span class="p">=</span> <span class="n">temp</span><span class="p">?.</span><span class="kr">left</span>
|
||
<a id="__codelineno-103-33" name="__codelineno-103-33" href="#__codelineno-103-33"></a> <span class="p">}</span>
|
||
<a id="__codelineno-103-34" name="__codelineno-103-34" href="#__codelineno-103-34"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">temp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-103-35" name="__codelineno-103-35" href="#__codelineno-103-35"></a> <span class="n">node</span><span class="p">?.</span><span class="n">val</span> <span class="p">=</span> <span class="n">temp</span><span class="p">!.</span><span class="n">val</span>
|
||
<a id="__codelineno-103-36" name="__codelineno-103-36" href="#__codelineno-103-36"></a> <span class="p">}</span>
|
||
<a id="__codelineno-103-37" name="__codelineno-103-37" href="#__codelineno-103-37"></a> <span class="p">}</span>
|
||
<a id="__codelineno-103-38" name="__codelineno-103-38" href="#__codelineno-103-38"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span> <span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-103-39" name="__codelineno-103-39" href="#__codelineno-103-39"></a> <span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-103-40" name="__codelineno-103-40" href="#__codelineno-103-40"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-103-41" name="__codelineno-103-41" href="#__codelineno-103-41"></a> <span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-103-42" name="__codelineno-103-42" href="#__codelineno-103-42"></a> <span class="k">return</span> <span class="n">node</span>
|
||
<a id="__codelineno-103-43" name="__codelineno-103-43" href="#__codelineno-103-43"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-104-2" name="__codelineno-104-2" href="#__codelineno-104-2"></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-104-3" name="__codelineno-104-3" href="#__codelineno-104-3"></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-104-4" name="__codelineno-104-4" href="#__codelineno-104-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-104-5" name="__codelineno-104-5" href="#__codelineno-104-5"></a>
|
||
<a id="__codelineno-104-6" name="__codelineno-104-6" href="#__codelineno-104-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-104-7" name="__codelineno-104-7" href="#__codelineno-104-7"></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-104-8" name="__codelineno-104-8" href="#__codelineno-104-8"></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-104-9" name="__codelineno-104-9" href="#__codelineno-104-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-104-10" name="__codelineno-104-10" href="#__codelineno-104-10"></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-104-11" name="__codelineno-104-11" href="#__codelineno-104-11"></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-104-12" name="__codelineno-104-12" href="#__codelineno-104-12"></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-104-13" name="__codelineno-104-13" href="#__codelineno-104-13"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-104-14" name="__codelineno-104-14" href="#__codelineno-104-14"></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-104-15" name="__codelineno-104-15" href="#__codelineno-104-15"></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-104-16" name="__codelineno-104-16" href="#__codelineno-104-16"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-104-17" name="__codelineno-104-17" href="#__codelineno-104-17"></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-104-18" name="__codelineno-104-18" href="#__codelineno-104-18"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-104-19" name="__codelineno-104-19" href="#__codelineno-104-19"></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-104-20" name="__codelineno-104-20" href="#__codelineno-104-20"></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-104-21" name="__codelineno-104-21" href="#__codelineno-104-21"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-104-22" name="__codelineno-104-22" href="#__codelineno-104-22"></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-104-23" name="__codelineno-104-23" href="#__codelineno-104-23"></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-104-24" name="__codelineno-104-24" href="#__codelineno-104-24"></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-104-25" name="__codelineno-104-25" href="#__codelineno-104-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-104-26" name="__codelineno-104-26" href="#__codelineno-104-26"></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-104-27" name="__codelineno-104-27" href="#__codelineno-104-27"></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-104-28" name="__codelineno-104-28" href="#__codelineno-104-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-104-29" name="__codelineno-104-29" href="#__codelineno-104-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-104-30" name="__codelineno-104-30" href="#__codelineno-104-30"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-104-31" name="__codelineno-104-31" href="#__codelineno-104-31"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-104-32" name="__codelineno-104-32" href="#__codelineno-104-32"></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-104-33" name="__codelineno-104-33" href="#__codelineno-104-33"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-104-34" name="__codelineno-104-34" href="#__codelineno-104-34"></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-104-35" name="__codelineno-104-35" href="#__codelineno-104-35"></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-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-105-2" name="__codelineno-105-2" href="#__codelineno-105-2"></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-105-3" name="__codelineno-105-3" href="#__codelineno-105-3"></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-105-4" name="__codelineno-105-4" href="#__codelineno-105-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-105-5" name="__codelineno-105-5" href="#__codelineno-105-5"></a>
|
||
<a id="__codelineno-105-6" name="__codelineno-105-6" href="#__codelineno-105-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-105-7" name="__codelineno-105-7" href="#__codelineno-105-7"></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-105-8" name="__codelineno-105-8" href="#__codelineno-105-8"></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-105-9" name="__codelineno-105-9" href="#__codelineno-105-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-105-10" name="__codelineno-105-10" href="#__codelineno-105-10"></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-105-11" name="__codelineno-105-11" href="#__codelineno-105-11"></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-105-12" name="__codelineno-105-12" href="#__codelineno-105-12"></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-105-13" name="__codelineno-105-13" href="#__codelineno-105-13"></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-105-14" name="__codelineno-105-14" href="#__codelineno-105-14"></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-105-15" name="__codelineno-105-15" href="#__codelineno-105-15"></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-105-16" name="__codelineno-105-16" href="#__codelineno-105-16"></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-105-17" name="__codelineno-105-17" href="#__codelineno-105-17"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-105-18" name="__codelineno-105-18" href="#__codelineno-105-18"></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-105-19" name="__codelineno-105-19" href="#__codelineno-105-19"></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-105-20" name="__codelineno-105-20" href="#__codelineno-105-20"></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-105-21" name="__codelineno-105-21" href="#__codelineno-105-21"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-105-22" name="__codelineno-105-22" href="#__codelineno-105-22"></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-105-23" name="__codelineno-105-23" href="#__codelineno-105-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-105-24" name="__codelineno-105-24" href="#__codelineno-105-24"></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-105-25" name="__codelineno-105-25" href="#__codelineno-105-25"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-105-26" name="__codelineno-105-26" href="#__codelineno-105-26"></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-105-27" name="__codelineno-105-27" href="#__codelineno-105-27"></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-105-28" name="__codelineno-105-28" href="#__codelineno-105-28"></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-105-29" name="__codelineno-105-29" href="#__codelineno-105-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-105-30" name="__codelineno-105-30" href="#__codelineno-105-30"></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-105-31" name="__codelineno-105-31" href="#__codelineno-105-31"></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-105-32" name="__codelineno-105-32" href="#__codelineno-105-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-105-33" name="__codelineno-105-33" href="#__codelineno-105-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-105-34" name="__codelineno-105-34" href="#__codelineno-105-34"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-105-35" name="__codelineno-105-35" href="#__codelineno-105-35"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-105-36" name="__codelineno-105-36" href="#__codelineno-105-36"></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-105-37" name="__codelineno-105-37" href="#__codelineno-105-37"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-105-38" name="__codelineno-105-38" href="#__codelineno-105-38"></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-105-39" name="__codelineno-105-39" href="#__codelineno-105-39"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-106-2" name="__codelineno-106-2" href="#__codelineno-106-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-3" name="__codelineno-106-3" href="#__codelineno-106-3"></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-106-4" name="__codelineno-106-4" href="#__codelineno-106-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-106-5" name="__codelineno-106-5" href="#__codelineno-106-5"></a>
|
||
<a id="__codelineno-106-6" name="__codelineno-106-6" href="#__codelineno-106-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-106-7" name="__codelineno-106-7" href="#__codelineno-106-7"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-8" name="__codelineno-106-8" href="#__codelineno-106-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||
<a id="__codelineno-106-9" name="__codelineno-106-9" href="#__codelineno-106-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-106-10" name="__codelineno-106-10" href="#__codelineno-106-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-106-11" name="__codelineno-106-11" href="#__codelineno-106-11"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-106-12" name="__codelineno-106-12" href="#__codelineno-106-12"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-106-13" name="__codelineno-106-13" href="#__codelineno-106-13"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-106-14" name="__codelineno-106-14" href="#__codelineno-106-14"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-15" name="__codelineno-106-15" href="#__codelineno-106-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-16" name="__codelineno-106-16" href="#__codelineno-106-16"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">??</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-106-17" name="__codelineno-106-17" href="#__codelineno-106-17"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-106-18" name="__codelineno-106-18" href="#__codelineno-106-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-106-19" name="__codelineno-106-19" href="#__codelineno-106-19"></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-106-20" name="__codelineno-106-20" href="#__codelineno-106-20"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-106-21" name="__codelineno-106-21" href="#__codelineno-106-21"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-106-22" name="__codelineno-106-22" href="#__codelineno-106-22"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-106-23" name="__codelineno-106-23" href="#__codelineno-106-23"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-24" name="__codelineno-106-24" href="#__codelineno-106-24"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-106-25" name="__codelineno-106-25" href="#__codelineno-106-25"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-106-26" name="__codelineno-106-26" href="#__codelineno-106-26"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">!</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-27" name="__codelineno-106-27" href="#__codelineno-106-27"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-106-28" name="__codelineno-106-28" href="#__codelineno-106-28"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-106-29" name="__codelineno-106-29" href="#__codelineno-106-29"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-106-30" name="__codelineno-106-30" href="#__codelineno-106-30"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-106-31" name="__codelineno-106-31" href="#__codelineno-106-31"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-106-32" name="__codelineno-106-32" href="#__codelineno-106-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-106-33" name="__codelineno-106-33" href="#__codelineno-106-33"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-106-34" name="__codelineno-106-34" href="#__codelineno-106-34"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-106-35" name="__codelineno-106-35" href="#__codelineno-106-35"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-106-36" name="__codelineno-106-36" href="#__codelineno-106-36"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-106-37" name="__codelineno-106-37" href="#__codelineno-106-37"></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-106-38" name="__codelineno-106-38" href="#__codelineno-106-38"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-107-2" name="__codelineno-107-2" href="#__codelineno-107-2"></a><span class="k">fn</span> <span class="nf">remove</span><span class="p">(</span><span class="o">&</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-3" name="__codelineno-107-3" href="#__codelineno-107-3"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">(),</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-107-4" name="__codelineno-107-4" href="#__codelineno-107-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-107-5" name="__codelineno-107-5" href="#__codelineno-107-5"></a>
|
||
<a id="__codelineno-107-6" name="__codelineno-107-6" href="#__codelineno-107-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-107-7" name="__codelineno-107-7" href="#__codelineno-107-7"></a><span class="k">fn</span> <span class="nf">remove_helper</span><span class="p">(</span><span class="n">node</span>: <span class="nc">OptionTreeNodeRc</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="nc">OptionTreeNodeRc</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-8" name="__codelineno-107-8" href="#__codelineno-107-8"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-9" name="__codelineno-107-9" href="#__codelineno-107-9"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-10" name="__codelineno-107-10" href="#__codelineno-107-10"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-107-11" name="__codelineno-107-11" href="#__codelineno-107-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-12" name="__codelineno-107-12" href="#__codelineno-107-12"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-107-13" name="__codelineno-107-13" href="#__codelineno-107-13"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">remove_helper</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-107-14" name="__codelineno-107-14" href="#__codelineno-107-14"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-15" name="__codelineno-107-15" href="#__codelineno-107-15"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-107-16" name="__codelineno-107-16" href="#__codelineno-107-16"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">remove_helper</span><span class="p">(</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-107-17" name="__codelineno-107-17" href="#__codelineno-107-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-18" name="__codelineno-107-18" href="#__codelineno-107-18"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-19" name="__codelineno-107-19" href="#__codelineno-107-19"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span>
|
||
<a id="__codelineno-107-20" name="__codelineno-107-20" href="#__codelineno-107-20"></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-107-21" name="__codelineno-107-21" href="#__codelineno-107-21"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span>
|
||
<a id="__codelineno-107-22" name="__codelineno-107-22" href="#__codelineno-107-22"></a><span class="w"> </span><span class="p">};</span>
|
||
<a id="__codelineno-107-23" name="__codelineno-107-23" href="#__codelineno-107-23"></a><span class="w"> </span><span class="k">match</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-24" name="__codelineno-107-24" href="#__codelineno-107-24"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-107-25" name="__codelineno-107-25" href="#__codelineno-107-25"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-26" name="__codelineno-107-26" href="#__codelineno-107-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
|
||
<a id="__codelineno-107-27" name="__codelineno-107-27" href="#__codelineno-107-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-28" name="__codelineno-107-28" href="#__codelineno-107-28"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-107-29" name="__codelineno-107-29" href="#__codelineno-107-29"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">child</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">,</span>
|
||
<a id="__codelineno-107-30" name="__codelineno-107-30" href="#__codelineno-107-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-31" name="__codelineno-107-31" href="#__codelineno-107-31"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-32" name="__codelineno-107-32" href="#__codelineno-107-32"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-107-33" name="__codelineno-107-33" href="#__codelineno-107-33"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-107-34" name="__codelineno-107-34" href="#__codelineno-107-34"></a><span class="w"> </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-35" name="__codelineno-107-35" href="#__codelineno-107-35"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">temp_left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-107-36" name="__codelineno-107-36" href="#__codelineno-107-36"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">temp_left</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-37" name="__codelineno-107-37" href="#__codelineno-107-37"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-107-38" name="__codelineno-107-38" href="#__codelineno-107-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-39" name="__codelineno-107-39" href="#__codelineno-107-39"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp_left</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-107-40" name="__codelineno-107-40" href="#__codelineno-107-40"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-41" name="__codelineno-107-41" href="#__codelineno-107-41"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
|
||
<a id="__codelineno-107-42" name="__codelineno-107-42" href="#__codelineno-107-42"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">remove_helper</span><span class="p">(</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-107-43" name="__codelineno-107-43" href="#__codelineno-107-43"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-107-44" name="__codelineno-107-44" href="#__codelineno-107-44"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-45" name="__codelineno-107-45" href="#__codelineno-107-45"></a><span class="w"> </span><span class="bp">Self</span>::<span class="n">update_height</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">()));</span><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-107-46" name="__codelineno-107-46" href="#__codelineno-107-46"></a>
|
||
<a id="__codelineno-107-47" name="__codelineno-107-47" href="#__codelineno-107-47"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-107-48" name="__codelineno-107-48" href="#__codelineno-107-48"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">rotate</span><span class="p">(</span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)).</span><span class="n">unwrap</span><span class="p">();</span>
|
||
<a id="__codelineno-107-49" name="__codelineno-107-49" href="#__codelineno-107-49"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-107-50" name="__codelineno-107-50" href="#__codelineno-107-50"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
|
||
<a id="__codelineno-107-51" name="__codelineno-107-51" href="#__codelineno-107-51"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-52" name="__codelineno-107-52" href="#__codelineno-107-52"></a><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
|
||
<a id="__codelineno-107-53" name="__codelineno-107-53" href="#__codelineno-107-53"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-54" name="__codelineno-107-54" href="#__codelineno-107-54"></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-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-108-2" name="__codelineno-108-2" href="#__codelineno-108-2"></a><span class="c1">// 由於引入了 stdio.h ，此處無法使用 remove 關鍵詞</span>
|
||
<a id="__codelineno-108-3" name="__codelineno-108-3" href="#__codelineno-108-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeItem</span><span class="p">(</span><span class="n">AVLTree</span><span class="w"> </span><span class="o">*</span><span class="n">tree</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-4" name="__codelineno-108-4" href="#__codelineno-108-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">tree</span><span class="o">-></span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-108-5" name="__codelineno-108-5" href="#__codelineno-108-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-108-6" name="__codelineno-108-6" href="#__codelineno-108-6"></a>
|
||
<a id="__codelineno-108-7" name="__codelineno-108-7" href="#__codelineno-108-7"></a><span class="cm">/* 遞迴刪除節點（輔助函式） */</span>
|
||
<a id="__codelineno-108-8" name="__codelineno-108-8" href="#__codelineno-108-8"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-9" name="__codelineno-108-9" href="#__codelineno-108-9"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
|
||
<a id="__codelineno-108-10" name="__codelineno-108-10" href="#__codelineno-108-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-11" name="__codelineno-108-11" href="#__codelineno-108-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
|
||
<a id="__codelineno-108-12" name="__codelineno-108-12" href="#__codelineno-108-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-108-13" name="__codelineno-108-13" href="#__codelineno-108-13"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-108-14" name="__codelineno-108-14" href="#__codelineno-108-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-15" name="__codelineno-108-15" href="#__codelineno-108-15"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-108-16" name="__codelineno-108-16" href="#__codelineno-108-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-17" name="__codelineno-108-17" href="#__codelineno-108-17"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-108-18" name="__codelineno-108-18" href="#__codelineno-108-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-19" name="__codelineno-108-19" href="#__codelineno-108-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-20" name="__codelineno-108-20" href="#__codelineno-108-20"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-108-21" name="__codelineno-108-21" href="#__codelineno-108-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-22" name="__codelineno-108-22" href="#__codelineno-108-22"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-108-23" name="__codelineno-108-23" href="#__codelineno-108-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-108-24" name="__codelineno-108-24" href="#__codelineno-108-24"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-108-25" name="__codelineno-108-25" href="#__codelineno-108-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-26" name="__codelineno-108-26" href="#__codelineno-108-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
|
||
<a id="__codelineno-108-27" name="__codelineno-108-27" href="#__codelineno-108-27"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-28" name="__codelineno-108-28" href="#__codelineno-108-28"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-108-29" name="__codelineno-108-29" href="#__codelineno-108-29"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
|
||
<a id="__codelineno-108-30" name="__codelineno-108-30" href="#__codelineno-108-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-108-31" name="__codelineno-108-31" href="#__codelineno-108-31"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-32" name="__codelineno-108-32" href="#__codelineno-108-32"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-108-33" name="__codelineno-108-33" href="#__codelineno-108-33"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">;</span>
|
||
<a id="__codelineno-108-34" name="__codelineno-108-34" href="#__codelineno-108-34"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-35" name="__codelineno-108-35" href="#__codelineno-108-35"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">-></span><span class="n">left</span><span class="p">;</span>
|
||
<a id="__codelineno-108-36" name="__codelineno-108-36" href="#__codelineno-108-36"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-108-37" name="__codelineno-108-37" href="#__codelineno-108-37"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tempVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">-></span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-108-38" name="__codelineno-108-38" href="#__codelineno-108-38"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-></span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="o">-></span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-108-39" name="__codelineno-108-39" href="#__codelineno-108-39"></a><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tempVal</span><span class="p">;</span>
|
||
<a id="__codelineno-108-40" name="__codelineno-108-40" href="#__codelineno-108-40"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-108-41" name="__codelineno-108-41" href="#__codelineno-108-41"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-108-42" name="__codelineno-108-42" href="#__codelineno-108-42"></a><span class="w"> </span><span class="c1">// 更新節點高度</span>
|
||
<a id="__codelineno-108-43" name="__codelineno-108-43" href="#__codelineno-108-43"></a><span class="w"> </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-108-44" name="__codelineno-108-44" href="#__codelineno-108-44"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-108-45" name="__codelineno-108-45" href="#__codelineno-108-45"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-108-46" name="__codelineno-108-46" href="#__codelineno-108-46"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-108-47" name="__codelineno-108-47" href="#__codelineno-108-47"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
|
||
<a id="__codelineno-108-48" name="__codelineno-108-48" href="#__codelineno-108-48"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="cm">/* 刪除節點 */</span>
|
||
<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">_val</span><span class="p">:</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-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></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-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a>
|
||
<a id="__codelineno-109-6" name="__codelineno-109-6" href="#__codelineno-109-6"></a><span class="cm">/* 遞迴刪除節點（輔助方法） */</span>
|
||
<a id="__codelineno-109-7" name="__codelineno-109-7" href="#__codelineno-109-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?,</span><span class="w"> </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </span><span class="p">{</span>
|
||
<a id="__codelineno-109-8" name="__codelineno-109-8" href="#__codelineno-109-8"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">?:</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
|
||
<a id="__codelineno-109-9" name="__codelineno-109-9" href="#__codelineno-109-9"></a><span class="w"> </span><span class="cm">/* 1. 查詢節點並刪除 */</span>
|
||
<a id="__codelineno-109-10" name="__codelineno-109-10" href="#__codelineno-109-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
|
||
<a id="__codelineno-109-11" name="__codelineno-109-11" href="#__codelineno-109-11"></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-109-12" name="__codelineno-109-12" href="#__codelineno-109-12"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_val</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">_val</span><span class="p">)</span>
|
||
<a id="__codelineno-109-13" name="__codelineno-109-13" href="#__codelineno-109-13"></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-109-14" name="__codelineno-109-14" href="#__codelineno-109-14"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-109-15" name="__codelineno-109-15" href="#__codelineno-109-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="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-109-16" name="__codelineno-109-16" href="#__codelineno-109-16"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">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="na">left</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-109-17" name="__codelineno-109-17" href="#__codelineno-109-17"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span>
|
||
<a id="__codelineno-109-18" name="__codelineno-109-18" href="#__codelineno-109-18"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-109-19" name="__codelineno-109-19" href="#__codelineno-109-19"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span>
|
||
<a id="__codelineno-109-20" name="__codelineno-109-20" href="#__codelineno-109-20"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-109-21" name="__codelineno-109-21" href="#__codelineno-109-21"></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-109-22" name="__codelineno-109-22" href="#__codelineno-109-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
|
||
<a id="__codelineno-109-23" name="__codelineno-109-23" href="#__codelineno-109-23"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-109-24" name="__codelineno-109-24" href="#__codelineno-109-24"></a><span class="w"> </span><span class="k">else</span>
|
||
<a id="__codelineno-109-25" name="__codelineno-109-25" href="#__codelineno-109-25"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
|
||
<a id="__codelineno-109-26" name="__codelineno-109-26" href="#__codelineno-109-26"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-109-27" name="__codelineno-109-27" href="#__codelineno-109-27"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-109-28" name="__codelineno-109-28" href="#__codelineno-109-28"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">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>
|
||
<a id="__codelineno-109-29" name="__codelineno-109-29" href="#__codelineno-109-29"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">!!</span><span class="p">.</span><span class="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-109-30" name="__codelineno-109-30" href="#__codelineno-109-30"></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>
|
||
<a id="__codelineno-109-31" name="__codelineno-109-31" href="#__codelineno-109-31"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-109-32" name="__codelineno-109-32" href="#__codelineno-109-32"></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-109-33" name="__codelineno-109-33" href="#__codelineno-109-33"></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>
|
||
<a id="__codelineno-109-34" name="__codelineno-109-34" href="#__codelineno-109-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-109-35" name="__codelineno-109-35" href="#__codelineno-109-35"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-109-36" name="__codelineno-109-36" href="#__codelineno-109-36"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-109-37" name="__codelineno-109-37" href="#__codelineno-109-37"></a><span class="w"> </span><span class="cm">/* 2. 執行旋轉操作，使該子樹重新恢復平衡 */</span>
|
||
<a id="__codelineno-109-38" name="__codelineno-109-38" href="#__codelineno-109-38"></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-109-39" name="__codelineno-109-39" href="#__codelineno-109-39"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-109-40" name="__codelineno-109-40" href="#__codelineno-109-40"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
|
||
<a id="__codelineno-109-41" name="__codelineno-109-41" href="#__codelineno-109-41"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
|
||
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a>
|
||
<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove_helper</span><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-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="c1">// 刪除節點</span>
|
||
<a id="__codelineno-111-2" name="__codelineno-111-2" href="#__codelineno-111-2"></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-111-3" name="__codelineno-111-3" href="#__codelineno-111-3"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">removeHelper</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">).</span><span class="o">?</span><span class="p">;</span>
|
||
<a id="__codelineno-111-4" name="__codelineno-111-4" href="#__codelineno-111-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-111-5" name="__codelineno-111-5" href="#__codelineno-111-5"></a>
|
||
<a id="__codelineno-111-6" name="__codelineno-111-6" href="#__codelineno-111-6"></a><span class="c1">// 遞迴刪除節點（輔助方法）</span>
|
||
<a id="__codelineno-111-7" name="__codelineno-111-7" href="#__codelineno-111-7"></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-111-8" name="__codelineno-111-8" href="#__codelineno-111-8"></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-111-9" name="__codelineno-111-9" href="#__codelineno-111-9"></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-111-10" name="__codelineno-111-10" href="#__codelineno-111-10"></a><span class="w"> </span><span class="c1">// 1. 查詢節點並刪除</span>
|
||
<a id="__codelineno-111-11" name="__codelineno-111-11" href="#__codelineno-111-11"></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-111-12" name="__codelineno-111-12" href="#__codelineno-111-12"></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-111-13" name="__codelineno-111-13" href="#__codelineno-111-13"></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-111-14" name="__codelineno-111-14" href="#__codelineno-111-14"></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-111-15" name="__codelineno-111-15" href="#__codelineno-111-15"></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-111-16" name="__codelineno-111-16" href="#__codelineno-111-16"></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-111-17" name="__codelineno-111-17" href="#__codelineno-111-17"></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-111-18" name="__codelineno-111-18" href="#__codelineno-111-18"></a><span class="w"> </span><span class="c1">// 子節點數量 = 0 ，直接刪除 node 並返回</span>
|
||
<a id="__codelineno-111-19" name="__codelineno-111-19" href="#__codelineno-111-19"></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-111-20" name="__codelineno-111-20" href="#__codelineno-111-20"></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-111-21" name="__codelineno-111-21" href="#__codelineno-111-21"></a><span class="w"> </span><span class="c1">// 子節點數量 = 1 ，直接刪除 node</span>
|
||
<a id="__codelineno-111-22" name="__codelineno-111-22" href="#__codelineno-111-22"></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-111-23" name="__codelineno-111-23" href="#__codelineno-111-23"></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-111-24" name="__codelineno-111-24" href="#__codelineno-111-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-111-25" name="__codelineno-111-25" href="#__codelineno-111-25"></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-111-26" name="__codelineno-111-26" href="#__codelineno-111-26"></a><span class="w"> </span><span class="c1">// 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
|
||
<a id="__codelineno-111-27" name="__codelineno-111-27" href="#__codelineno-111-27"></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-111-28" name="__codelineno-111-28" href="#__codelineno-111-28"></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-111-29" name="__codelineno-111-29" href="#__codelineno-111-29"></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-111-30" name="__codelineno-111-30" href="#__codelineno-111-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-111-31" name="__codelineno-111-31" href="#__codelineno-111-31"></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-111-32" name="__codelineno-111-32" href="#__codelineno-111-32"></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-111-33" name="__codelineno-111-33" href="#__codelineno-111-33"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-111-34" name="__codelineno-111-34" href="#__codelineno-111-34"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-111-35" name="__codelineno-111-35" href="#__codelineno-111-35"></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">// 更新節點高度</span>
|
||
<a id="__codelineno-111-36" name="__codelineno-111-36" href="#__codelineno-111-36"></a><span class="w"> </span><span class="c1">// 2. 執行旋轉操作，使該子樹重新恢復平衡</span>
|
||
<a id="__codelineno-111-37" name="__codelineno-111-37" href="#__codelineno-111-37"></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-111-38" name="__codelineno-111-38" href="#__codelineno-111-38"></a><span class="w"> </span><span class="c1">// 返回子樹的根節點</span>
|
||
<a id="__codelineno-111-39" name="__codelineno-111-39" href="#__codelineno-111-39"></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-111-40" name="__codelineno-111-40" href="#__codelineno-111-40"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="3_1">3. 查詢節點<a class="headerlink" href="#3_1" title="Permanent link">¶</a></h3>
|
||
<p>AVL 樹的節點查詢操作與二元搜尋樹一致，在此不再贅述。</p>
|
||
<h2 id="754-avl">7.5.4 AVL 樹典型應用<a class="headerlink" href="#754-avl" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li>組織和儲存大型資料，適用於高頻查詢、低頻增刪的場景。</li>
|
||
<li>用於構建資料庫中的索引系統。</li>
|
||
<li>紅黑樹也是一種常見的平衡二元搜尋樹。相較於 AVL 樹，紅黑樹的平衡條件更寬鬆，插入與刪除節點所需的旋轉操作更少，節點增刪操作的平均效率更高。</li>
|
||
</ul>
|
||
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