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序
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序
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第 0 章 前言
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第 0 章 前言
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0.1 關於本書
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0.2 如何使用本書
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</a>
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0.3 小結
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第 1 章 初識演算法
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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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1.2 演算法是什麼
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</a>
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1.3 小結
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<span class="md-ellipsis">
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第 2 章 複雜度分析
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第 2 章 複雜度分析
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<a href="../performance_evaluation/" class="md-nav__link">
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2.1 演算法效率評估
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</span>
|
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|
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|
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</a>
|
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</li>
|
||
|
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<li class="md-nav__item">
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<span class="md-ellipsis">
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2.2 迭代與遞迴
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
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|
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<li class="md-nav__item">
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<a href="../time_complexity/" class="md-nav__link">
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2.3 時間複雜度
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
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|
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|
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<span class="md-ellipsis">
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2.4 空間複雜度
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<span class="md-nav__icon md-icon"></span>
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2.4 空間複雜度
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</a>
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<nav class="md-nav md-nav--secondary" aria-label="目錄">
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目錄
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2.4.1 演算法相關空間
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<li class="md-nav__item">
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2.4.2 推算方法
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</a>
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<li class="md-nav__item">
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<span class="md-ellipsis">
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2.4.3 常見型別
|
||
</span>
|
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</a>
|
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|
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<nav class="md-nav" aria-label="2.4.3 常見型別">
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<a href="#1-o1" class="md-nav__link">
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<span class="md-ellipsis">
|
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1. 常數階
|
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|
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</a>
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|
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</li>
|
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|
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<li class="md-nav__item">
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<a href="#2-on" class="md-nav__link">
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<span class="md-ellipsis">
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2. 線性階
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|
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</a>
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|
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#3-on2" class="md-nav__link">
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<span class="md-ellipsis">
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3. 平方階
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|
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|
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<li class="md-nav__item">
|
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<a href="#4-o2n" class="md-nav__link">
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<span class="md-ellipsis">
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4. 指數階
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<li class="md-nav__item">
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5. 對數階
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<li class="md-nav__item">
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<span class="md-ellipsis">
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2.4.4 權衡時間與空間
|
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</a>
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|
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</li>
|
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|
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</ul>
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2.5 小結
|
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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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|
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</nav>
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<span class="md-ellipsis">
|
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第 3 章 資料結構
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第 3 章 資料結構
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3.1 資料結構分類
|
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</span>
|
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|
||
|
||
</a>
|
||
</li>
|
||
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3.2 基本資料型別
|
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</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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3.3 數字編碼 *
|
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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/character_encoding/" class="md-nav__link">
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3.4 字元編碼 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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3.5 小結
|
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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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|
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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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<span class="md-ellipsis">
|
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第 4 章 陣列與鏈結串列
|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
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第 4 章 陣列與鏈結串列
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4.1 陣列
|
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</span>
|
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|
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|
||
</a>
|
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</li>
|
||
|
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
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<span class="md-ellipsis">
|
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4.2 鏈結串列
|
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</span>
|
||
|
||
|
||
</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/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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4.3 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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|
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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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<span class="md-ellipsis">
|
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4.4 記憶體與快取 *
|
||
</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近新增">
|
||
</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/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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4.5 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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</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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|
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<span class="md-ellipsis">
|
||
第 5 章 堆疊與佇列
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第 5 章 堆疊與佇列
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5.1 堆疊
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
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|
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
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5.2 佇列
|
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</span>
|
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|
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|
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</a>
|
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</li>
|
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|
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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">
|
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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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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
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|
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<span class="md-ellipsis">
|
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5.4 小結
|
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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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|
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|
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|
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</nav>
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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<span class="md-ellipsis">
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第 6 章 雜湊表
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</a>
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第 6 章 雜湊表
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6.1 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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</li>
|
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|
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<li class="md-nav__item">
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|
||
<span class="md-ellipsis">
|
||
6.2 雜湊衝突
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.3 雜湊演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
6.4 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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|
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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_9" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_tree/" class="md-nav__link ">
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|
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|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="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>
|
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|
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<span class="md-ellipsis">
|
||
第 7 章 樹
|
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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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<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_9">
|
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<span class="md-nav__icon md-icon"></span>
|
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第 7 章 樹
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
|
||
|
||
|
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<span class="md-ellipsis">
|
||
7.1 二元樹
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
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<a href="../../chapter_tree/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="../../chapter_tree/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="../../chapter_tree/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">
|
||
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.5 AVL *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
7.6 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
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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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|
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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_10" >
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|
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|
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<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">
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
||
</div>
|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_10">
|
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<span class="md-nav__icon md-icon"></span>
|
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第 8 章 堆積
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
<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>
|
||
|
||
|
||
|
||
|
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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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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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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_graph/" 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="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>
|
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|
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<span class="md-ellipsis">
|
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第 9 章 圖
|
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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_11" id="__nav_11_label" tabindex="0">
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
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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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<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">
|
||
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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|
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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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|
||
|
||
<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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|
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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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|
||
|
||
<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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|
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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">
|
||
9.4 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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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>
|
||
|
||
<span class="md-ellipsis">
|
||
第 10 章 搜尋
|
||
</span>
|
||
|
||
|
||
</a>
|
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|
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|
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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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</label>
|
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|
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</div>
|
||
|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_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
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.1 二分搜尋
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.2 二分搜尋插入點
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.3 二分搜尋邊界
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.4 雜湊最佳化策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.5 重識搜尋演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.6 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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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">
|
||
<a href="../../chapter_sorting/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 11 章 排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
|
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<span class="md-nav__icon md-icon"></span>
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</label>
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|
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</div>
|
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|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_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>
|
||
第 11 章 排序
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
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|
||
|
||
|
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|
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|
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|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.1 排序演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.2 選擇排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.3 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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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|
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|
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|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
|
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|
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|
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|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
|
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|
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|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 12 章 分治
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_14">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 12 章 分治
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
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|
||
|
||
|
||
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.1 分治演算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.2 分治搜尋策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.3 構建樹問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.4 河內塔問題
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
12.5 小結
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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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_15" >
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|
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|
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|
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<div class="md-nav__link md-nav__container">
|
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<a href="../../chapter_backtracking/" class="md-nav__link ">
|
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|
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|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
|
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|
||
<span class="md-ellipsis">
|
||
第 13 章 回溯
|
||
</span>
|
||
|
||
|
||
</a>
|
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|
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|
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<label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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|
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</div>
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_15">
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<span class="md-nav__icon md-icon"></span>
|
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第 13 章 回溯
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
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|
||
|
||
<span class="md-ellipsis">
|
||
13.1 回溯演算法
|
||
</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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13.2 全排列問題
|
||
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|
||
|
||
|
||
</a>
|
||
</li>
|
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13.3 子集和問題
|
||
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|
||
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|
||
</a>
|
||
</li>
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13.4 N 皇后問題
|
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</a>
|
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</li>
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13.5 小結
|
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</span>
|
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|
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|
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|
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14.3 DP 解題思路
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|
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14.6 編輯距離問題
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14.7 小結
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第 15 章 貪婪
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15.1 貪婪演算法
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15.4 最大切分乘積問題
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|
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|
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|
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第 16 章 附錄
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|
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<a href="#243" class="md-nav__link">
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2.4.3 常見型別
|
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<nav class="md-nav" aria-label="2.4.3 常見型別">
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1. 常數階
|
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||
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|
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<li class="md-nav__item">
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2. 線性階
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</a>
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</li>
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<li class="md-nav__item">
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3. 平方階
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</a>
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</li>
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<li class="md-nav__item">
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<a href="#4-o2n" class="md-nav__link">
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<span class="md-ellipsis">
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4. 指數階
|
||
</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="#5-olog-n" class="md-nav__link">
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<span class="md-ellipsis">
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5. 對數階
|
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</span>
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</a>
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</li>
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</ul>
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<span class="md-ellipsis">
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2.4.4 權衡時間與空間
|
||
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</a>
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</li>
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<div class="md-content" data-md-component="content">
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href="https://github.com/krahets/hello-algo/tree/main/zh-hant/docs/chapter_computational_complexity/space_complexity.md"
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title="編輯此頁"
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class="md-content__button md-icon"
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<h1 id="24">2.4 空間複雜度<a class="headerlink" href="#24" title="Permanent link">¶</a></h1>
|
||
<p><u>空間複雜度（space complexity）</u>用於衡量演算法佔用記憶體空間隨著資料量變大時的增長趨勢。這個概念與時間複雜度非常類似，只需將“執行時間”替換為“佔用記憶體空間”。</p>
|
||
<h2 id="241">2.4.1 演算法相關空間<a class="headerlink" href="#241" title="Permanent link">¶</a></h2>
|
||
<p>演算法在執行過程中使用的記憶體空間主要包括以下幾種。</p>
|
||
<ul>
|
||
<li><strong>輸入空間</strong>：用於儲存演算法的輸入資料。</li>
|
||
<li><strong>暫存空間</strong>：用於儲存演算法在執行過程中的變數、物件、函式上下文等資料。</li>
|
||
<li><strong>輸出空間</strong>：用於儲存演算法的輸出資料。</li>
|
||
</ul>
|
||
<p>一般情況下，空間複雜度的統計範圍是“暫存空間”加上“輸出空間”。</p>
|
||
<p>暫存空間可以進一步劃分為三個部分。</p>
|
||
<ul>
|
||
<li><strong>暫存資料</strong>：用於儲存演算法執行過程中的各種常數、變數、物件等。</li>
|
||
<li><strong>堆疊幀空間</strong>：用於儲存呼叫函式的上下文資料。系統在每次呼叫函式時都會在堆疊頂部建立一個堆疊幀，函式返回後，堆疊幀空間會被釋放。</li>
|
||
<li><strong>指令空間</strong>：用於儲存編譯後的程式指令，在實際統計中通常忽略不計。</li>
|
||
</ul>
|
||
<p>在分析一段程式的空間複雜度時，<strong>我們通常統計暫存資料、堆疊幀空間和輸出資料三部分</strong>，如圖 2-15 所示。</p>
|
||
<p><a class="glightbox" href="../space_complexity.assets/space_types.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="演算法使用的相關空間" class="animation-figure" src="../space_complexity.assets/space_types.png" /></a></p>
|
||
<p align="center"> 圖 2-15 演算法使用的相關空間 </p>
|
||
|
||
<p>相關程式碼如下：</p>
|
||
<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>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">Node</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">"""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">x</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">x</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">next</span><span class="p">:</span> <span class="n">Node</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向下一節點的引用</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="k">def</span> <span class="nf">function</span><span class="p">()</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="sd">"""函式"""</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="c1"># 執行某些操作...</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="k">def</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span> <span class="c1"># 輸入資料</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="n">A</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 暫存資料（常數，一般用大寫字母表示）</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="n">b</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 暫存資料（變數）</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="n">node</span> <span class="o">=</span> <span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c1"># 暫存資料（物件）</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="n">c</span> <span class="o">=</span> <span class="n">function</span><span class="p">()</span> <span class="c1"># 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="k">return</span> <span class="n">A</span> <span class="o">+</span> <span class="n">b</span> <span class="o">+</span> <span class="n">c</span> <span class="c1"># 輸出資料</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">/* 結構體 */</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">Node</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>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">Node</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><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="p">};</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></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-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</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">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="n">Node</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="k">new</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">func</span><span class="p">();</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></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">/* 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">Node</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="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="n">next</span><span class="p">;</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="n">Node</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-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="p">}</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></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-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</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">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="n">Node</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">new</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></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">/* 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">Node</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="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>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="n">next</span><span class="p">;</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><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-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="p">}</span>
|
||
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a>
|
||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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="c1">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</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="c1">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="n">Node</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">new</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Function</span><span class="p">();</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></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">/* 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">node</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>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">next</span><span class="w"> </span><span class="o">*</span><span class="nx">node</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm">/* 建立 node 結構體 */</span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">&</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">val</span><span class="p">}</span>
|
||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
|
||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</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-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="p">}</span>
|
||
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a>
|
||
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="nx">newNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></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">/* 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">Node</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>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="kd">var</span> <span class="nv">next</span><span class="p">:</span> <span class="n">Node</span><span class="p">?</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></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-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a> <span class="n">val</span> <span class="p">=</span> <span class="n">x</span>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a> <span class="p">}</span>
|
||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>
|
||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="kd">func</span> <span class="nf">function</span><span class="p">()</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a> <span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="p">}</span>
|
||
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>
|
||
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="kd">func</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span> <span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a> <span class="kd">let</span> <span class="nv">a</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a> <span class="kd">var</span> <span class="nv">b</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a> <span class="kd">let</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">Node</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span> <span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a> <span class="kd">let</span> <span class="nv">c</span> <span class="p">=</span> <span class="n">function</span><span class="p">()</span> <span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a> <span class="k">return</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span> <span class="o">+</span> <span class="n">c</span> <span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></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">/* 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">Node</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>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="nx">next</span><span class="p">;</span>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></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="p">{</span>
|
||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></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><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">next</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">// 指向下一節點的引用</span>
|
||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a>
|
||
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><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-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
|
||
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
|
||
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</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="c1">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">b</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="c1">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Node</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></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">/* 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">Node</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>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">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-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></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="p">{</span>
|
||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></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><span class="w"> </span><span class="c1">// 節點值</span>
|
||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">next</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">// 指向下一節點的引用</span>
|
||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
|
||
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a>
|
||
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</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-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><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-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="p">}</span>
|
||
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a>
|
||
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</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="c1">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">b</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="c1">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Node</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></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">/* 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">Node</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>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="n">next</span><span class="p">;</span>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="n">Node</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">next</span><span class="p">]);</span>
|
||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="p">}</span>
|
||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a>
|
||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><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-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a>
|
||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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="c1">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</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="c1">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w"> </span><span class="n">Node</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="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></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">/* 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">Node</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>
|
||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="n">next</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">Node</span><span class="o">>>></span><span class="p">,</span>
|
||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
|
||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* 建立 Node 結構體 */</span>
|
||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="k">impl</span><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></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">Self</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="bp">Self</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span>: <span class="nc">val</span><span class="p">,</span><span class="w"> </span><span class="n">next</span>: <span class="nb">None</span> <span class="p">}</span>
|
||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="p">}</span>
|
||
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
|
||
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="k">fn</span> <span class="nf">function</span><span class="p">()</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span><span class="w"> </span>
|
||
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></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-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="p">}</span>
|
||
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a>
|
||
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="k">fn</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">a</span>: <span class="kt">i32</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">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></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">b</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">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></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="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></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">/* 函式 */</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
|
||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</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">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">func</span><span class="p">();</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></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">/* 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">Node</span><span class="p">(</span><span class="kd">var</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>
|
||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">Node? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span>
|
||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a>
|
||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">function</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-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
|
||
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a>
|
||
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 輸入資料</span>
|
||
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">a</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">// 暫存資料（常數）</span>
|
||
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</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">// 暫存資料（變數）</span>
|
||
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="kd">val</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">Node</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 暫存資料（物件）</span>
|
||
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="c1">// 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="c1">// 輸出資料</span>
|
||
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></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><span class="c1">### 類別 ###</span>
|
||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">Node</span>
|
||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span><span class="w"> </span><span class="c1"># 節點值</span>
|
||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:next</span><span class="w"> </span><span class="c1"># 指向下一節點的引用</span>
|
||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
|
||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span>
|
||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">end</span>
|
||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">end</span>
|
||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a>
|
||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="c1">### 函式 ###</span>
|
||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span>
|
||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 執行某些操作...</span>
|
||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="k">end</span>
|
||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
|
||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="c1">### 演算法 ###</span>
|
||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="c1"># 輸入資料</span>
|
||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 暫存資料（常數）</span>
|
||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># 暫存資料（變數）</span>
|
||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">Node</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1"># 暫存資料（物件）</span>
|
||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="w"> </span><span class="c1"># 堆疊幀空間（呼叫函式）</span>
|
||
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="c1"># 輸出資料</span>
|
||
<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="k">end</span>
|
||
</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>
|
||
<h2 id="242">2.4.2 推算方法<a class="headerlink" href="#242" title="Permanent link">¶</a></h2>
|
||
<p>空間複雜度的推算方法與時間複雜度大致相同，只需將統計物件從“操作數量”轉為“使用空間大小”。</p>
|
||
<p>而與時間複雜度不同的是，<strong>我們通常只關注最差空間複雜度</strong>。這是因為記憶體空間是一項硬性要求，我們必須確保在所有輸入資料下都有足夠的記憶體空間預留。</p>
|
||
<p>觀察以下程式碼，最差空間複雜度中的“最差”有兩層含義。</p>
|
||
<ol>
|
||
<li><strong>以最差輸入資料為準</strong>：當 <span class="arithmatex">\(n < 10\)</span> 時，空間複雜度為 <span class="arithmatex">\(O(1)\)</span> ；但當 <span class="arithmatex">\(n > 10\)</span> 時，初始化的陣列 <code>nums</code> 佔用 <span class="arithmatex">\(O(n)\)</span> 空間，因此最差空間複雜度為 <span class="arithmatex">\(O(n)\)</span> 。</li>
|
||
<li><strong>以演算法執行中的峰值記憶體為準</strong>：例如，程式在執行最後一行之前，佔用 <span class="arithmatex">\(O(1)\)</span> 空間；當初始化陣列 <code>nums</code> 時，程式佔用 <span class="arithmatex">\(O(n)\)</span> 空間，因此最差空間複雜度為 <span class="arithmatex">\(O(n)\)</span> 。</li>
|
||
</ol>
|
||
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|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><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">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</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="n">a</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># O(1)</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a> <span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10000</span> <span class="c1"># O(1)</span>
|
||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">></span> <span class="mi">10</span><span class="p">:</span>
|
||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a> <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="c1"># O(n)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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">// O(1)</span>
|
||
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">b</span><span class="p">(</span><span class="mi">10000</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></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="mi">10</span><span class="p">)</span>
|
||
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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">// O(1)</span>
|
||
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10000</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
|
||
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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="c1">// O(1)</span>
|
||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="m">10000</span><span class="p">];</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></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="m">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</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-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
|
||
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span>
|
||
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="kd">func</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a> <span class="kd">let</span> <span class="nv">a</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// O(1)</span>
|
||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="kd">let</span> <span class="nv">b</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="mi">10000</span><span class="p">)</span> <span class="c1">// O(1)</span>
|
||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">></span> <span class="mi">10</span> <span class="p">{</span>
|
||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="kd">let</span> <span class="nv">nums</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span><span class="p">)</span> <span class="c1">// O(n)</span>
|
||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="p">}</span>
|
||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</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="c1">// O(1)</span>
|
||
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</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-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</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="c1">// O(1)</span>
|
||
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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="c1">// O(1)</span>
|
||
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">10000</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="k">fn</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">a</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">// O(1)</span>
|
||
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">10000</span><span class="p">];</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">10</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="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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">// O(1)</span>
|
||
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="mi">10000</span><span class="p">];</span><span class="w"> </span><span class="c1">// O(1)</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">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">10</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="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">0</span><span class="p">};</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</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-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">a</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">// O(1)</span>
|
||
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="m">10000</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(1)</span>
|
||
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(n)</span>
|
||
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1"># O(1)</span>
|
||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">10000</span><span class="p">)</span><span class="w"> </span><span class="c1"># O(1)</span>
|
||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="c1"># O(n)</span>
|
||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="k">end</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p><strong>在遞迴函式中，需要注意統計堆疊幀空間</strong>。觀察以下程式碼：</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"><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">function</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="c1"># 執行某些操作</span>
|
||
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>
|
||
<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="k">def</span> <span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w"> </span><span class="sd">"""迴圈的空間複雜度為 O(1)"""</span>
|
||
<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a> <span class="n">function</span><span class="p">()</span>
|
||
<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>
|
||
<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="k">def</span> <span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w"> </span><span class="sd">"""遞迴的空間複雜度為 O(n)"""</span>
|
||
<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a> <span class="k">return</span>
|
||
<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a> <span class="k">return</span> <span class="n">recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w"> </span><span class="n">func</span><span class="p">();</span>
|
||
<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></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="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</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-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></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-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w"> </span><span class="n">function</span><span class="p">();</span>
|
||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></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="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><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-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">Loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="n">Function</span><span class="p">();</span>
|
||
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></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="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="n">n</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-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</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-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a>
|
||
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</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-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</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="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w"> </span><span class="nx">function</span><span class="p">()</span>
|
||
<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="p">}</span>
|
||
<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a>
|
||
<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="kd">func</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</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-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</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-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="w"> </span><span class="k">return</span>
|
||
<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</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-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">@</span><span class="n">discardableResult</span>
|
||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">func</span> <span class="nf">function</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">// 執行某些操作</span>
|
||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a>
|
||
<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="kd">func</span> <span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a> <span class="n">function</span><span class="p">()</span>
|
||
<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a> <span class="p">}</span>
|
||
<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a>
|
||
<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="kd">func</span> <span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a> <span class="k">return</span>
|
||
<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a> <span class="p">}</span>
|
||
<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a> <span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><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-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span>
|
||
<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</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="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</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-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><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-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</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-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span>
|
||
<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</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-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</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="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><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-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w"> </span><span class="n">function</span><span class="p">();</span>
|
||
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></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="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</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-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="k">fn</span> <span class="nf">function</span><span class="p">()</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></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-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="k">fn</span> <span class="nf">loop</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</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="n">function</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="p">}</span>
|
||
<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="k">fn</span> <span class="nf">recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</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-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</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-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></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-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w"> </span><span class="n">func</span><span class="p">();</span>
|
||
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></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="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</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-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">function</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-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
|
||
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="cm">/* 迴圈的空間複雜度為 O(1) */</span>
|
||
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</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-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o"><</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a><span class="w"> </span><span class="n">function</span><span class="p">()</span>
|
||
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="cm">/* 遞迴的空間複雜度為 O(n) */</span>
|
||
<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</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-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></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="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span>
|
||
<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</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-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span>
|
||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="w"> </span><span class="c1"># 執行某些操作</span>
|
||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="k">end</span>
|
||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>
|
||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="c1">### 迴圈的空間複雜度為 O(1) ###</span>
|
||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">function</span><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="k">end</span>
|
||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a>
|
||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="c1">### 遞迴的空間複雜度為 O(n) ###</span>
|
||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="k">end</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>函式 <code>loop()</code> 和 <code>recur()</code> 的時間複雜度都為 <span class="arithmatex">\(O(n)\)</span> ，但空間複雜度不同。</p>
|
||
<ul>
|
||
<li>函式 <code>loop()</code> 在迴圈中呼叫了 <span class="arithmatex">\(n\)</span> 次 <code>function()</code> ，每輪中的 <code>function()</code> 都返回並釋放了堆疊幀空間，因此空間複雜度仍為 <span class="arithmatex">\(O(1)\)</span> 。</li>
|
||
<li>遞迴函式 <code>recur()</code> 在執行過程中會同時存在 <span class="arithmatex">\(n\)</span> 個未返回的 <code>recur()</code> ，從而佔用 <span class="arithmatex">\(O(n)\)</span> 的堆疊幀空間。</li>
|
||
</ul>
|
||
<h2 id="243">2.4.3 常見型別<a class="headerlink" href="#243" title="Permanent link">¶</a></h2>
|
||
<p>設輸入資料大小為 <span class="arithmatex">\(n\)</span> ，圖 2-16 展示了常見的空間複雜度型別（從低到高排列）。</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
O(1) < O(\log n) < O(n) < O(n^2) < O(2^n) \newline
|
||
\text{常數階} < \text{對數階} < \text{線性階} < \text{平方階} < \text{指數階}
|
||
\end{aligned}
|
||
\]</div>
|
||
<p><a class="glightbox" href="../space_complexity.assets/space_complexity_common_types.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="常見的空間複雜度型別" class="animation-figure" src="../space_complexity.assets/space_complexity_common_types.png" /></a></p>
|
||
<p align="center"> 圖 2-16 常見的空間複雜度型別 </p>
|
||
|
||
<h3 id="1-o1">1. 常數階 <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">¶</a></h3>
|
||
<p>常數階常見於數量與輸入資料大小 <span class="arithmatex">\(n\)</span> 無關的常數、變數、物件。</p>
|
||
<p>需要注意的是，在迴圈中初始化變數或呼叫函式而佔用的記憶體，在進入下一迴圈後就會被釋放，因此不會累積佔用空間，空間複雜度仍為 <span class="arithmatex">\(O(1)\)</span> ：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.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">function</span><span class="p">()</span> <span class="o">-></span> <span class="nb">int</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">"""函式"""</span>
|
||
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a> <span class="c1"># 執行某些操作</span>
|
||
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>
|
||
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="k">def</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w"> </span><span class="sd">"""常數階"""</span>
|
||
<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a> <span class="c1"># 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a> <span class="n">a</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a> <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10000</span>
|
||
<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a> <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a> <span class="c1"># 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a> <span class="n">c</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a> <span class="c1"># 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a> <span class="n">function</span><span class="p">()</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</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="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></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-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a>
|
||
<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</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-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="mi">10000</span><span class="p">);</span>
|
||
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</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-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w"> </span><span class="n">func</span><span class="p">();</span>
|
||
<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-43-22" name="__codelineno-43-22" href="#__codelineno-43-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</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="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></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-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a>
|
||
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</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-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10000</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w"> </span><span class="n">ListNode</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">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</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-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w"> </span><span class="n">function</span><span class="p">();</span>
|
||
<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</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="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><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-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a>
|
||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="k">void</span><span class="w"> </span><span class="nf">Constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="m">10000</span><span class="p">];</span>
|
||
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w"> </span><span class="n">ListNode</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">new</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w"> </span><span class="n">Function</span><span class="p">();</span>
|
||
<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-22" name="__codelineno-45-22" href="#__codelineno-45-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 函式 */</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="nx">function</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-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="c1">// 執行某些操作...</span>
|
||
<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a>
|
||
<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">spaceConstant</span><span class="p">(</span><span class="nx">n</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-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span>
|
||
<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></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">newNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="kt">int</span>
|
||
<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</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="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</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="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="w"> </span><span class="nx">function</span><span class="p">()</span>
|
||
<a id="__codelineno-46-22" name="__codelineno-46-22" href="#__codelineno-46-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-46-23" name="__codelineno-46-23" href="#__codelineno-46-23"></a><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-46-24" name="__codelineno-46-24" href="#__codelineno-46-24"></a><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-46-25" name="__codelineno-46-25" href="#__codelineno-46-25"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-46-26" name="__codelineno-46-26" href="#__codelineno-46-26"></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="mi">0</span>
|
||
<a id="__codelineno-46-27" name="__codelineno-46-27" href="#__codelineno-46-27"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="p">@</span><span class="n">discardableResult</span>
|
||
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="kd">func</span> <span class="nf">function</span><span class="p">()</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a> <span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="p">}</span>
|
||
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a>
|
||
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="kd">func</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a> <span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a> <span class="kd">let</span> <span class="nv">a</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a> <span class="kd">var</span> <span class="nv">b</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a> <span class="kd">let</span> <span class="nv">nums</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="mi">10000</span><span class="p">)</span>
|
||
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a> <span class="kd">let</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a> <span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a> <span class="kd">let</span> <span class="nv">c</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a> <span class="p">}</span>
|
||
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a> <span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a> <span class="n">function</span><span class="p">()</span>
|
||
<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a> <span class="p">}</span>
|
||
<a id="__codelineno-47-23" name="__codelineno-47-23" href="#__codelineno-47-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</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="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><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-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a>
|
||
<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</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="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span>
|
||
<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span>
|
||
<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-48-22" name="__codelineno-48-22" href="#__codelineno-48-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</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-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><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-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a>
|
||
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</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-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span>
|
||
<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span>
|
||
<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><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-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a>
|
||
<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="kt">void</span><span class="w"> </span><span class="n">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">10000</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w"> </span><span class="n">ListNode</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">ListNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w"> </span><span class="n">function</span><span class="p">();</span>
|
||
<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">fn</span> <span class="nf">function</span><span class="p">()</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></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-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a>
|
||
<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="cp">#[allow(unused)]</span>
|
||
<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="k">fn</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </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">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">A</span>: <span class="kt">i32</span> <span class="o">=</span><span class="w"> </span><span class="mi">0</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="kd">let</span><span class="w"> </span><span class="n">b</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-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">10000</span><span class="p">];</span>
|
||
<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w"> </span><span class="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">ListNode</span>::<span class="n">new</span><span class="p">(</span><span class="mi">0</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="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </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="kd">let</span><span class="w"> </span><span class="n">c</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-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="w"> </span><span class="n">function</span><span class="p">();</span>
|
||
<a id="__codelineno-51-22" name="__codelineno-51-22" href="#__codelineno-51-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-51-23" name="__codelineno-51-23" href="#__codelineno-51-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 函式 */</span>
|
||
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</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="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></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-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>
|
||
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </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">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</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-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">b</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-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1000</span><span class="p">];</span>
|
||
<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
|
||
<a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</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-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a><span class="w"> </span><span class="n">func</span><span class="p">();</span>
|
||
<a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 函式 */</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">function</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-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
|
||
<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a>
|
||
<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="cm">/* 常數階 */</span>
|
||
<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</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-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
|
||
<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
|
||
<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="m">10000</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="w"> </span><span class="kd">val</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">ListNode</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
|
||
<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o"><</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
|
||
<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o"><</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a><span class="w"> </span><span class="n">function</span><span class="p">()</span>
|
||
<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-53-22" name="__codelineno-53-22" href="#__codelineno-53-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 函式 ###</span>
|
||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span>
|
||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="c1"># 執行某些操作</span>
|
||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="k">end</span>
|
||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a>
|
||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="c1">### 常數階 ###</span>
|
||
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="c1"># 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">10000</span>
|
||
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">ListNode</span><span class="o">.</span><span class="n">new</span>
|
||
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a>
|
||
<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w"> </span><span class="c1"># 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">c</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-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w"> </span><span class="c1"># 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">n</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">function</span><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="k">end</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="c1">// 函式</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">function</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-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w"> </span><span class="c1">// 執行某些操作</span>
|
||
<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></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-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="p">}</span>
|
||
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a>
|
||
<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="c1">// 常數階</span>
|
||
<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="k">fn</span><span class="w"> </span><span class="n">constant</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w"> </span><span class="c1">// 常數、變數、物件佔用 O(1) 空間</span>
|
||
<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w"> </span><span class="kr">const</span><span class="w"> </span><span class="n">a</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">b</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="n">_</span><span class="p">]</span><span class="kt">i32</span><span class="p">{</span><span class="mi">0</span><span class="p">}</span><span class="o">**</span><span class="mi">10000</span><span class="p">;</span>
|
||
<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w"> </span><span class="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">inc</span><span class="p">.</span><span class="n">ListNode</span><span class="p">(</span><span class="kt">i32</span><span class="p">){.</span><span class="n">val</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-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="w"> </span><span class="c1">// 迴圈中的變數佔用 O(1) 空間</span>
|
||
<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">c</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">c</span><span class="p">;</span>
|
||
<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a><span class="w"> </span><span class="c1">// 迴圈中的函式佔用 O(1) 空間</span>
|
||
<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="w"> </span><span class="n">i</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-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-23" name="__codelineno-55-23" href="#__codelineno-55-23"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span>
|
||
<a id="__codelineno-55-24" name="__codelineno-55-24" href="#__codelineno-55-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-55-25" name="__codelineno-55-25" href="#__codelineno-55-25"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="p">;</span>
|
||
<a id="__codelineno-55-26" name="__codelineno-55-26" href="#__codelineno-55-26"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
|
||
<a id="__codelineno-55-27" name="__codelineno-55-27" href="#__codelineno-55-27"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-55-28" name="__codelineno-55-28" href="#__codelineno-55-28"></a><span class="w"> </span><span class="n">_</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-55-29" name="__codelineno-55-29" href="#__codelineno-55-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>視覺化執行</summary>
|
||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%8F%88%E7%B5%90%E4%B8%B2%E5%88%97%E7%AF%80%E9%BB%9E%E9%A1%9E%E5%88%A5%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E7%AF%80%E9%BB%9E%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B9%BC%E7%AF%80%E9%BB%9E%E5%BC%95%E7%94%A8%0A%0Adef%20function%28%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%87%BD%E5%BC%8F%22%22%22%0A%20%20%20%20%23%20%E5%9F%B7%E8%A1%8C%E6%9F%90%E4%BA%9B%E6%93%8D%E4%BD%9C%0A%20%20%20%20return%200%0A%0Adef%20constant%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E5%B8%B8%E6%95%B8%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E5%B8%B8%E6%95%B8%E3%80%81%E8%AE%8A%E6%95%B8%E3%80%81%E7%89%A9%E4%BB%B6%E4%BD%94%E7%94%A8%20O%281%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20a%20%3D%200%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%2010%0A%20%20%20%20node%20%3D%20ListNode%280%29%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E4%B8%AD%E7%9A%84%E8%AE%8A%E6%95%B8%E4%BD%94%E7%94%A8%20O%281%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20c%20%3D%200%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E4%B8%AD%E7%9A%84%E5%87%BD%E5%BC%8F%E4%BD%94%E7%94%A8%20O%281%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20function%28%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E5%B8%B8%E6%95%B8%E9%9A%8E%0A%20%20%20%20constant%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%8F%88%E7%B5%90%E4%B8%B2%E5%88%97%E7%AF%80%E9%BB%9E%E9%A1%9E%E5%88%A5%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E7%AF%80%E9%BB%9E%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%BE%8C%E7%B9%BC%E7%AF%80%E9%BB%9E%E5%BC%95%E7%94%A8%0A%0Adef%20function%28%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%87%BD%E5%BC%8F%22%22%22%0A%20%20%20%20%23%20%E5%9F%B7%E8%A1%8C%E6%9F%90%E4%BA%9B%E6%93%8D%E4%BD%9C%0A%20%20%20%20return%200%0A%0Adef%20constant%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E5%B8%B8%E6%95%B8%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E5%B8%B8%E6%95%B8%E3%80%81%E8%AE%8A%E6%95%B8%E3%80%81%E7%89%A9%E4%BB%B6%E4%BD%94%E7%94%A8%20O%281%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20a%20%3D%200%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%2010%0A%20%20%20%20node%20%3D%20ListNode%280%29%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E4%B8%AD%E7%9A%84%E8%AE%8A%E6%95%B8%E4%BD%94%E7%94%A8%20O%281%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20c%20%3D%200%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E4%B8%AD%E7%9A%84%E5%87%BD%E5%BC%8F%E4%BD%94%E7%94%A8%20O%281%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20function%28%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E5%B8%B8%E6%95%B8%E9%9A%8E%0A%20%20%20%20constant%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 ></a></div></p>
|
||
</details>
|
||
<h3 id="2-on">2. 線性階 <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">¶</a></h3>
|
||
<p>線性階常見於元素數量與 <span class="arithmatex">\(n\)</span> 成正比的陣列、鏈結串列、堆疊、佇列等：</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">space_complexity.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">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</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">"""線性階"""</span>
|
||
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a> <span class="c1"># 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a> <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
|
||
<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a> <span class="c1"># 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a> <span class="n">hmap</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">str</span><span class="p">]()</span>
|
||
<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a> <span class="n">hmap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="c1">// 長度為 n 的陣列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</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">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">ListNode</span><span class="o">></span><span class="w"> </span><span class="n">nodes</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </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="n">nodes</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
||
<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w"> </span><span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w"> </span><span class="n">unordered_map</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="o">></span><span class="w"> </span><span class="n">map</span><span class="p">;</span>
|
||
<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">to_string</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="c1">// 長度為 n 的陣列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</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">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">ListNode</span><span class="o">></span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
||
<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w"> </span><span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w"> </span><span class="n">Map</span><span class="o"><</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">></span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="p">.</span><span class="na">valueOf</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
||
<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="c1">// 長度為 n 的陣列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</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">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">ListNode</span><span class="o">></span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
||
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w"> </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="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="n">Dictionary</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">></span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">.</span><span class="n">ToString</span><span class="p">());</span>
|
||
<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 線性階 */</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="nx">spaceLinear</span><span class="p">(</span><span class="nx">n</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-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w"> </span><span class="c1">// 長度為 n 的陣列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w"> </span><span class="nx">_</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w"> </span><span class="c1">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">nodes</span><span class="w"> </span><span class="p">[]</span><span class="o">*</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="k">for</span><span class="w"> </span><span class="nx">i</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="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w"> </span><span class="nx">nodes</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nodes</span><span class="p">,</span><span class="w"> </span><span class="nx">newNode</span><span class="p">(</span><span class="nx">i</span><span class="p">))</span>
|
||
<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w"> </span><span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</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="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="w"> </span><span class="nx">m</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">strconv</span><span class="p">.</span><span class="nx">Itoa</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
|
||
<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="kd">func</span> <span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</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="c1">// 長度為 n 的陣列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a> <span class="kd">let</span> <span class="nv">nums</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a> <span class="c1">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a> <span class="kd">let</span> <span class="nv">nodes</span> <span class="p">=</span> <span class="p">(</span><span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span><span class="p">).</span><span class="bp">map</span> <span class="p">{</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="nv">$0</span><span class="p">)</span> <span class="p">}</span>
|
||
<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a> <span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a> <span class="kd">let</span> <span class="nv">map</span> <span class="p">=</span> <span class="nb">Dictionary</span><span class="p">(</span><span class="n">uniqueKeysWithValues</span><span class="p">:</span> <span class="p">(</span><span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span><span class="p">).</span><span class="bp">map</span> <span class="p">{</span> <span class="p">(</span><span class="nv">$0</span><span class="p">,</span> <span class="s">"</span><span class="si">\(</span><span class="nv">$0</span><span class="si">)</span><span class="s">"</span><span class="p">)</span> <span class="p">})</span>
|
||
<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w"> </span><span class="c1">// 長度為 n 的陣列佔用 O(n) 空間</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">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</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">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w"> </span><span class="nx">nodes</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
|
||
<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w"> </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="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
|
||
<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></a><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">.</span><span class="nx">toString</span><span class="p">());</span>
|
||
<a id="__codelineno-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</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-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w"> </span><span class="c1">// 長度為 n 的陣列佔用 O(n) 空間</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">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</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">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nodes</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w"> </span><span class="nx">nodes</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">i</span><span class="p">));</span>
|
||
<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="w"> </span><span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
|
||
<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">.</span><span class="nx">toString</span><span class="p">());</span>
|
||
<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="c1">// 長度為 n 的陣列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</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">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">ListNode</span><span class="o">></span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
||
<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w"> </span><span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="w"> </span><span class="n">Map</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="o">></span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">();</span>
|
||
<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">putIfAbsent</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="n">i</span><span class="p">.</span><span class="n">toString</span><span class="p">());</span>
|
||
<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="cp">#[allow(unused)]</span>
|
||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="k">fn</span> <span class="nf">linear</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</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="c1">// 長度為 n 的陣列佔用 O(n) 空間</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="k">mut</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</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="c1">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></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">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span>::<span class="n">new</span><span class="p">();</span>
|
||
<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">ListNode</span>::<span class="n">new</span><span class="p">(</span><span class="n">i</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="p">}</span>
|
||
<a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a><span class="w"> </span><span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></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">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span>::<span class="n">new</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="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">.</span><span class="n">to_string</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="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 雜湊表 */</span>
|
||
<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</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="kt">int</span><span class="w"> </span><span class="n">key</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="kt">int</span><span class="w"> </span><span class="n">val</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">UT_hash_handle</span><span class="w"> </span><span class="n">hh</span><span class="p">;</span><span class="w"> </span><span class="c1">// 基於 uthash.h 實現</span>
|
||
<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="p">}</span><span class="w"> </span><span class="n">HashTable</span><span class="p">;</span>
|
||
<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a>
|
||
<a id="__codelineno-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a><span class="cm">/* 線性階 */</span>
|
||
<a id="__codelineno-66-9" name="__codelineno-66-9" href="#__codelineno-66-9"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-66-10" name="__codelineno-66-10" href="#__codelineno-66-10"></a><span class="w"> </span><span class="c1">// 長度為 n 的陣列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</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="n">free</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
|
||
<a id="__codelineno-66-13" name="__codelineno-66-13" href="#__codelineno-66-13"></a>
|
||
<a id="__codelineno-66-14" name="__codelineno-66-14" href="#__codelineno-66-14"></a><span class="w"> </span><span class="c1">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-66-15" name="__codelineno-66-15" href="#__codelineno-66-15"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">**</span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-66-16" name="__codelineno-66-16" href="#__codelineno-66-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-66-17" name="__codelineno-66-17" href="#__codelineno-66-17"></a><span class="w"> </span><span class="n">nodes</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-66-18" name="__codelineno-66-18" href="#__codelineno-66-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-66-19" name="__codelineno-66-19" href="#__codelineno-66-19"></a><span class="w"> </span><span class="c1">// 記憶體釋放</span>
|
||
<a id="__codelineno-66-20" name="__codelineno-66-20" href="#__codelineno-66-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-66-21" name="__codelineno-66-21" href="#__codelineno-66-21"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">nodes</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
|
||
<a id="__codelineno-66-22" name="__codelineno-66-22" href="#__codelineno-66-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-66-23" name="__codelineno-66-23" href="#__codelineno-66-23"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">nodes</span><span class="p">);</span>
|
||
<a id="__codelineno-66-24" name="__codelineno-66-24" href="#__codelineno-66-24"></a>
|
||
<a id="__codelineno-66-25" name="__codelineno-66-25" href="#__codelineno-66-25"></a><span class="w"> </span><span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-66-26" name="__codelineno-66-26" href="#__codelineno-66-26"></a><span class="w"> </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">h</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-66-27" name="__codelineno-66-27" href="#__codelineno-66-27"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-66-28" name="__codelineno-66-28" href="#__codelineno-66-28"></a><span class="w"> </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">HashTable</span><span class="p">));</span>
|
||
<a id="__codelineno-66-29" name="__codelineno-66-29" href="#__codelineno-66-29"></a><span class="w"> </span><span class="n">tmp</span><span class="o">-></span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-66-30" name="__codelineno-66-30" href="#__codelineno-66-30"></a><span class="w"> </span><span class="n">tmp</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">i</span><span class="p">;</span>
|
||
<a id="__codelineno-66-31" name="__codelineno-66-31" href="#__codelineno-66-31"></a><span class="w"> </span><span class="n">HASH_ADD_INT</span><span class="p">(</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">);</span>
|
||
<a id="__codelineno-66-32" name="__codelineno-66-32" href="#__codelineno-66-32"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-66-33" name="__codelineno-66-33" href="#__codelineno-66-33"></a>
|
||
<a id="__codelineno-66-34" name="__codelineno-66-34" href="#__codelineno-66-34"></a><span class="w"> </span><span class="c1">// 記憶體釋放</span>
|
||
<a id="__codelineno-66-35" name="__codelineno-66-35" href="#__codelineno-66-35"></a><span class="w"> </span><span class="n">HashTable</span><span class="w"> </span><span class="o">*</span><span class="n">curr</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-66-36" name="__codelineno-66-36" href="#__codelineno-66-36"></a><span class="w"> </span><span class="n">HASH_ITER</span><span class="p">(</span><span class="n">hh</span><span class="p">,</span><span class="w"> </span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">curr</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-66-37" name="__codelineno-66-37" href="#__codelineno-66-37"></a><span class="w"> </span><span class="n">HASH_DEL</span><span class="p">(</span><span class="n">h</span><span class="p">,</span><span class="w"> </span><span class="n">curr</span><span class="p">);</span>
|
||
<a id="__codelineno-66-38" name="__codelineno-66-38" href="#__codelineno-66-38"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">curr</span><span class="p">);</span>
|
||
<a id="__codelineno-66-39" name="__codelineno-66-39" href="#__codelineno-66-39"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-66-40" name="__codelineno-66-40" href="#__codelineno-66-40"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 線性階 */</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">linear</span><span class="p">(</span><span class="n">n</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-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w"> </span><span class="c1">// 長度為 n 的陣列佔用 O(n) 空間</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">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w"> </span><span class="c1">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o"><</span><span class="n">ListNode</span><span class="o">></span><span class="p">()</span>
|
||
<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o"><</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
|
||
<a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></a><span class="w"> </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="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableMapOf</span><span class="o"><</span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="o">></span><span class="p">()</span>
|
||
<a id="__codelineno-67-12" name="__codelineno-67-12" href="#__codelineno-67-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o"><</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-67-13" name="__codelineno-67-13" href="#__codelineno-67-13"></a><span class="w"> </span><span class="n">map</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">.</span><span class="na">toString</span><span class="p">()</span>
|
||
<a id="__codelineno-67-14" name="__codelineno-67-14" href="#__codelineno-67-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-67-15" name="__codelineno-67-15" href="#__codelineno-67-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="c1">### 線性階 ###</span>
|
||
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="c1"># 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a>
|
||
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="c1"># 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w"> </span><span class="n">hmap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
|
||
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">n</span>
|
||
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w"> </span><span class="n">hmap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="o">.</span><span class="n">to_s</span>
|
||
<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w"> </span><span class="k">end</span>
|
||
<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="k">end</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="c1">// 線性階</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">linear</span><span class="p">(</span><span class="kr">comptime</span><span class="w"> </span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w"> </span><span class="c1">// 長度為 n 的陣列佔用 O(n) 空間</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">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="n">_</span><span class="p">]</span><span class="kt">i32</span><span class="p">{</span><span class="mi">0</span><span class="p">}</span><span class="o">**</span><span class="n">n</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">// 長度為 n 的串列佔用 O(n) 空間</span>
|
||
<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">ArrayList</span><span class="p">(</span><span class="kt">i32</span><span class="p">).</span><span class="n">init</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</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="k">defer</span><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">deinit</span><span class="p">();</span>
|
||
<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-69-12" name="__codelineno-69-12" href="#__codelineno-69-12"></a><span class="w"> </span><span class="c1">// 長度為 n 的雜湊表佔用 O(n) 空間</span>
|
||
<a id="__codelineno-69-13" name="__codelineno-69-13" href="#__codelineno-69-13"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">AutoArrayHashMap</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="p">[]</span><span class="kr">const</span><span class="w"> </span><span class="kt">u8</span><span class="p">).</span><span class="n">init</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</span><span class="p">);</span>
|
||
<a id="__codelineno-69-14" name="__codelineno-69-14" href="#__codelineno-69-14"></a><span class="w"> </span><span class="k">defer</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">deinit</span><span class="p">();</span>
|
||
<a id="__codelineno-69-15" name="__codelineno-69-15" href="#__codelineno-69-15"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">j</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-69-16" name="__codelineno-69-16" href="#__codelineno-69-16"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">j</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-69-17" name="__codelineno-69-17" href="#__codelineno-69-17"></a><span class="w"> </span><span class="kr">const</span><span class="w"> </span><span class="n">string</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">std</span><span class="p">.</span><span class="n">fmt</span><span class="p">.</span><span class="n">allocPrint</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</span><span class="p">,</span><span class="w"> </span><span class="s">"{d}"</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="n">j</span><span class="p">});</span>
|
||
<a id="__codelineno-69-18" name="__codelineno-69-18" href="#__codelineno-69-18"></a><span class="w"> </span><span class="k">defer</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</span><span class="p">.</span><span class="n">free</span><span class="p">(</span><span class="n">string</span><span class="p">);</span>
|
||
<a id="__codelineno-69-19" name="__codelineno-69-19" href="#__codelineno-69-19"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">put</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="p">);</span>
|
||
<a id="__codelineno-69-20" name="__codelineno-69-20" href="#__codelineno-69-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-69-21" name="__codelineno-69-21" href="#__codelineno-69-21"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-69-22" name="__codelineno-69-22" href="#__codelineno-69-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>視覺化執行</summary>
|
||
<p><div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E6%80%A7%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E9%95%B7%E5%BA%A6%E7%82%BA%20n%20%E7%9A%84%E4%B8%B2%E5%88%97%E4%BD%94%E7%94%A8%20O%28n%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20%23%20%E9%95%B7%E5%BA%A6%E7%82%BA%20n%20%E7%9A%84%E9%9B%9C%E6%B9%8A%E8%A1%A8%E4%BD%94%E7%94%A8%20O%28n%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20hmap%20%3D%20dict%5Bint%2C%20str%5D%28%29%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20hmap%5Bi%5D%20%3D%20str%28i%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E7%B7%9A%E6%80%A7%E9%9A%8E%0A%20%20%20%20linear%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=20&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E6%80%A7%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E9%95%B7%E5%BA%A6%E7%82%BA%20n%20%E7%9A%84%E4%B8%B2%E5%88%97%E4%BD%94%E7%94%A8%20O%28n%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20%23%20%E9%95%B7%E5%BA%A6%E7%82%BA%20n%20%E7%9A%84%E9%9B%9C%E6%B9%8A%E8%A1%A8%E4%BD%94%E7%94%A8%20O%28n%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20hmap%20%3D%20dict%5Bint%2C%20str%5D%28%29%0A%20%20%20%20for%20i%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20hmap%5Bi%5D%20%3D%20str%28i%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E7%B7%9A%E6%80%A7%E9%9A%8E%0A%20%20%20%20linear%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=20&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 ></a></div></p>
|
||
</details>
|
||
<p>如圖 2-17 所示，此函式的遞迴深度為 <span class="arithmatex">\(n\)</span> ，即同時存在 <span class="arithmatex">\(n\)</span> 個未返回的 <code>linear_recur()</code> 函式，使用 <span class="arithmatex">\(O(n)\)</span> 大小的堆疊幀空間：</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">space_complexity.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">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</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">"""線性階（遞迴實現）"""</span>
|
||
<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a> <span class="nb">print</span><span class="p">(</span><span class="s2">"遞迴 n ="</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a> <span class="k">return</span>
|
||
<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a> <span class="n">linear_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"遞迴 n = "</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="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w"> </span><span class="k">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="mi">1</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="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w"> </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</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-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">"遞迴 n = "</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></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="mi">1</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="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w"> </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</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-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">LinearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">"遞迴 n = "</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></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="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</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="n">LinearRecur</span><span class="p">(</span><span class="n">n</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-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 線性階（遞迴實現） */</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="nx">spaceLinearRecur</span><span class="p">(</span><span class="nx">n</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-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">"遞迴 n ="</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</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-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w"> </span><span class="k">return</span>
|
||
<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w"> </span><span class="nx">spaceLinearRecur</span><span class="p">(</span><span class="nx">n</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-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kd">func</span> <span class="nf">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</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="bp">print</span><span class="p">(</span><span class="s">"遞迴 n = </span><span class="si">\(</span><span class="n">n</span><span class="si">)</span><span class="s">"</span><span class="p">)</span>
|
||
<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a> <span class="k">return</span>
|
||
<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a> <span class="p">}</span>
|
||
<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a> <span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`遞迴 n = </span><span class="si">${</span><span class="nx">n</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
|
||
<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w"> </span><span class="nx">linearRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`遞迴 n = </span><span class="si">${</span><span class="nx">n</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
|
||
<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</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="k">return</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="nx">linearRecur</span><span class="p">(</span><span class="nx">n</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-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="n">print</span><span class="p">(</span><span class="s1">'遞迴 n = </span><span class="si">$</span><span class="n">n</span><span class="s1">'</span><span class="p">);</span>
|
||
<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></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="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</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="n">linearRecur</span><span class="p">(</span><span class="n">n</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-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">fn</span> <span class="nf">linear_recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">"遞迴 n = {}"</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</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-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><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="n">linear_recur</span><span class="p">(</span><span class="n">n</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-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 線性階（遞迴實現） */</span>
|
||
<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"遞迴 n = %d</span><span class="se">\r\n</span><span class="s">"</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></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="mi">1</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="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w"> </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</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-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 線性階（遞迴實現） */</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">linearRecur</span><span class="p">(</span><span class="n">n</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-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"遞迴 n = </span><span class="si">$</span><span class="n">n</span><span class="s">"</span><span class="p">)</span>
|
||
<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></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="m">1</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="k">return</span>
|
||
<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w"> </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</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-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="c1">### 線性階（遞迴實現）###</span>
|
||
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="nb">puts</span><span class="w"> </span><span class="s2">"遞迴 n = </span><span class="si">#{</span><span class="n">n</span><span class="si">}</span><span class="s2">"</span>
|
||
<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></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="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w"> </span><span class="n">linear_recur</span><span class="p">(</span><span class="n">n</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-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="k">end</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="c1">// 線性階（遞迴實現）</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">linearRecur</span><span class="p">(</span><span class="kr">comptime</span><span class="w"> </span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">"遞迴 n = {}</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="n">n</span><span class="p">});</span>
|
||
<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></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="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</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="n">linearRecur</span><span class="p">(</span><span class="n">n</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-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>視覺化執行</summary>
|
||
<p><div style="height: 441px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear_recur%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E6%80%A7%E9%9A%8E%EF%BC%88%E9%81%9E%E8%BF%B4%E5%AF%A6%E7%8F%BE%EF%BC%89%22%22%22%0A%20%20%20%20print%28%22%E9%81%9E%E8%BF%B4%20n%20%3D%22%2C%20n%29%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20linear_recur%28n%20-%201%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E7%B7%9A%E6%80%A7%E9%9A%8E%0A%20%20%20%20linear_recur%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=25&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear_recur%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E7%B7%9A%E6%80%A7%E9%9A%8E%EF%BC%88%E9%81%9E%E8%BF%B4%E5%AF%A6%E7%8F%BE%EF%BC%89%22%22%22%0A%20%20%20%20print%28%22%E9%81%9E%E8%BF%B4%20n%20%3D%22%2C%20n%29%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20linear_recur%28n%20-%201%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E7%B7%9A%E6%80%A7%E9%9A%8E%0A%20%20%20%20linear_recur%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=25&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 ></a></div></p>
|
||
</details>
|
||
<p><a class="glightbox" href="../space_complexity.assets/space_complexity_recursive_linear.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="遞迴函式產生的線性階空間複雜度" class="animation-figure" src="../space_complexity.assets/space_complexity_recursive_linear.png" /></a></p>
|
||
<p align="center"> 圖 2-17 遞迴函式產生的線性階空間複雜度 </p>
|
||
|
||
<h3 id="3-on2">3. 平方階 <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">¶</a></h3>
|
||
<p>平方階常見於矩陣和圖，元素數量與 <span class="arithmatex">\(n\)</span> 成平方關係：</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">space_complexity.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">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="w"> </span><span class="sd">"""平方階"""</span>
|
||
<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a> <span class="c1"># 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a> <span class="n">num_matrix</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 平方階 */</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">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">numMatrix</span><span class="p">;</span>
|
||
<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</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="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</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="n">tmp</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">0</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="p">}</span>
|
||
<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w"> </span><span class="n">numMatrix</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
|
||
<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 平方階 */</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">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="c1">// 矩陣佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w"> </span><span class="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">>></span><span class="w"> </span><span class="n">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
||
<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</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="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></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">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</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="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </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="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="w"> </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">numList</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">tmp</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="p">}</span>
|
||
<a id="__codelineno-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* 平方階 */</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">Quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="c1">// 矩陣佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w"> </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">];</span>
|
||
<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w"> </span><span class="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</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="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</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="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="m">0</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="p">}</span>
|
||
<a id="__codelineno-87-12" name="__codelineno-87-12" href="#__codelineno-87-12"></a><span class="w"> </span><span class="n">numList</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">tmp</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="p">}</span>
|
||
<a id="__codelineno-87-14" name="__codelineno-87-14" href="#__codelineno-87-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 平方階 */</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="nx">spaceQuadratic</span><span class="p">(</span><span class="nx">n</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="c1">// 矩陣佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w"> </span><span class="nx">numMatrix</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</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="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w"> </span><span class="nx">numMatrix</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 平方階 */</span>
|
||
<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">func</span> <span class="nf">quadratic</span><span class="p">(</span><span class="n">n</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="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a> <span class="kd">let</span> <span class="nv">numList</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span><span class="p">),</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="cm">/* 平方階 */</span>
|
||
<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</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="c1">// 矩陣佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="w"> </span><span class="p">.</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="w"> </span><span class="p">.</span><span class="nx">map</span><span class="p">(()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">));</span>
|
||
<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="w"> </span><span class="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </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">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</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="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </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">tmp</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">0</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="p">}</span>
|
||
<a id="__codelineno-90-14" name="__codelineno-90-14" href="#__codelineno-90-14"></a><span class="w"> </span><span class="nx">numList</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">tmp</span><span class="p">);</span>
|
||
<a id="__codelineno-90-15" name="__codelineno-90-15" href="#__codelineno-90-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-90-16" name="__codelineno-90-16" href="#__codelineno-90-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="cm">/* 平方階 */</span>
|
||
<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</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="c1">// 矩陣佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a><span class="w"> </span><span class="p">.</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">)</span>
|
||
<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a><span class="w"> </span><span class="p">.</span><span class="nx">map</span><span class="p">(()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="kc">null</span><span class="p">));</span>
|
||
<a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></a><span class="w"> </span><span class="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-10" name="__codelineno-91-10" href="#__codelineno-91-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</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="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </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="nx">tmp</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">0</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="p">}</span>
|
||
<a id="__codelineno-91-14" name="__codelineno-91-14" href="#__codelineno-91-14"></a><span class="w"> </span><span class="nx">numList</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">tmp</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="p">}</span>
|
||
<a id="__codelineno-91-16" name="__codelineno-91-16" href="#__codelineno-91-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 平方階 */</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">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="c1">// 矩陣佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">_</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">));</span>
|
||
<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a><span class="w"> </span><span class="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||
<a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</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="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</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="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">0</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="p">}</span>
|
||
<a id="__codelineno-92-12" name="__codelineno-92-12" href="#__codelineno-92-12"></a><span class="w"> </span><span class="n">numList</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">tmp</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="p">}</span>
|
||
<a id="__codelineno-92-14" name="__codelineno-92-14" href="#__codelineno-92-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* 平方階 */</span>
|
||
<a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a><span class="cp">#[allow(unused)]</span>
|
||
<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="k">fn</span> <span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="w"> </span><span class="c1">// 矩陣佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">num_matrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span>
|
||
<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="w"> </span><span class="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></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">num_list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span>::<span class="n">new</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">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</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="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span>::<span class="n">new</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="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">0</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="p">}</span>
|
||
<a id="__codelineno-93-13" name="__codelineno-93-13" href="#__codelineno-93-13"></a><span class="w"> </span><span class="n">num_list</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
|
||
<a id="__codelineno-93-14" name="__codelineno-93-14" href="#__codelineno-93-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-15" name="__codelineno-93-15" href="#__codelineno-93-15"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* 平方階 */</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">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</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="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</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="n">tmp</span><span class="p">[</span><span class="n">j</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>
|
||
<a id="__codelineno-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a><span class="w"> </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="n">numMatrix</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</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="p">}</span>
|
||
<a id="__codelineno-94-12" name="__codelineno-94-12" href="#__codelineno-94-12"></a>
|
||
<a id="__codelineno-94-13" name="__codelineno-94-13" href="#__codelineno-94-13"></a><span class="w"> </span><span class="c1">// 記憶體釋放</span>
|
||
<a id="__codelineno-94-14" name="__codelineno-94-14" href="#__codelineno-94-14"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</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">free</span><span class="p">(</span><span class="n">numMatrix</span><span class="p">[</span><span class="n">i</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>
|
||
<a id="__codelineno-94-17" name="__codelineno-94-17" href="#__codelineno-94-17"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">numMatrix</span><span class="p">);</span>
|
||
<a id="__codelineno-94-18" name="__codelineno-94-18" href="#__codelineno-94-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="cm">/* 平方階 */</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">quadratic</span><span class="p">(</span><span class="n">n</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="c1">// 矩陣佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="o"><</span><span class="n">Array</span><span class="o"><</span><span class="kt">Int</span><span class="o">>?></span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a><span class="w"> </span><span class="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o"><</span><span class="n">MutableList</span><span class="o"><</span><span class="kt">Int</span><span class="o">>></span><span class="p">()</span>
|
||
<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o"><</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="o"><</span><span class="kt">Int</span><span class="o">></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">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">0.</span><span class="p">.</span><span class="o"><</span><span class="n">n</span><span class="p">)</span><span class="w"> </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="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
|
||
<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-95-12" name="__codelineno-95-12" href="#__codelineno-95-12"></a><span class="w"> </span><span class="n">numList</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
|
||
<a id="__codelineno-95-13" name="__codelineno-95-13" href="#__codelineno-95-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-95-14" name="__codelineno-95-14" href="#__codelineno-95-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="c1">### 平方階 ###</span>
|
||
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w"> </span><span class="c1"># 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</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-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a><span class="k">end</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="c1">// 平方階</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">quadratic</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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="c1">// 二維串列佔用 O(n^2) 空間</span>
|
||
<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">ArrayList</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">ArrayList</span><span class="p">(</span><span class="kt">i32</span><span class="p">)).</span><span class="n">init</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</span><span class="p">);</span>
|
||
<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a><span class="w"> </span><span class="k">defer</span><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">deinit</span><span class="p">();</span>
|
||
<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="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">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">ArrayList</span><span class="p">(</span><span class="kt">i32</span><span class="p">).</span><span class="n">init</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</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">defer</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">deinit</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">j</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-97-11" name="__codelineno-97-11" href="#__codelineno-97-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">j</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-97-12" name="__codelineno-97-12" href="#__codelineno-97-12"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</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="k">try</span><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
|
||
<a id="__codelineno-97-15" name="__codelineno-97-15" href="#__codelineno-97-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-97-16" name="__codelineno-97-16" href="#__codelineno-97-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>視覺化執行</summary>
|
||
<p><div style="height: 405px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E4%BA%8C%E7%B6%AD%E4%B8%B2%E5%88%97%E4%BD%94%E7%94%A8%20O%28n%5E2%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20num_matrix%20%3D%20%5B%5B0%5D%20%2A%20n%20for%20_%20in%20range%28n%29%5D%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E5%B9%B3%E6%96%B9%E9%9A%8E%0A%20%20%20%20quadratic%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic%28n%3A%20int%29%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%9A%8E%22%22%22%0A%20%20%20%20%23%20%E4%BA%8C%E7%B6%AD%E4%B8%B2%E5%88%97%E4%BD%94%E7%94%A8%20O%28n%5E2%29%20%E7%A9%BA%E9%96%93%0A%20%20%20%20num_matrix%20%3D%20%5B%5B0%5D%20%2A%20n%20for%20_%20in%20range%28n%29%5D%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E5%B9%B3%E6%96%B9%E9%9A%8E%0A%20%20%20%20quadratic%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=16&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 ></a></div></p>
|
||
</details>
|
||
<p>如圖 2-18 所示，該函式的遞迴深度為 <span class="arithmatex">\(n\)</span> ，在每個遞迴函式中都初始化了一個陣列，長度分別為 <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> ，平均長度為 <span class="arithmatex">\(n / 2\)</span> ，因此總體佔用 <span class="arithmatex">\(O(n^2)\)</span> 空間：</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">space_complexity.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">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="w"> </span><span class="sd">"""平方階（遞迴實現）"""</span>
|
||
<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">0</span><span class="p">:</span>
|
||
<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a> <span class="c1"># 陣列 nums 長度為 n, n-1, ..., 2, 1</span>
|
||
<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a> <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
|
||
<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a> <span class="k">return</span> <span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="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="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></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-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"遞迴 n = "</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="s">" 中的 nums 長度 = "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</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-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="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="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></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-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a><span class="w"> </span><span class="c1">// 陣列 nums 長度為 n, n-1, ..., 2, 1</span>
|
||
<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">"遞迴 n = "</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="s">" 中的 nums 長度 = "</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</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">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</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-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">QuadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="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="m">0</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-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
|
||
<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="s">"遞迴 n = "</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="s">" 中的 nums 長度 = "</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">);</span>
|
||
<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">QuadraticRecur</span><span class="p">(</span><span class="n">n</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-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* 平方階（遞迴實現） */</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="nx">spaceQuadraticRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</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-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">"遞迴 n = %d 中的 nums 長度 = %d \n"</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</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">return</span><span class="w"> </span><span class="nx">spaceQuadraticRecur</span><span class="p">(</span><span class="nx">n</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-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="p">@</span><span class="n">discardableResult</span>
|
||
<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="kd">func</span> <span class="nf">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">0</span> <span class="p">{</span>
|
||
<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a> <span class="p">}</span>
|
||
<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a> <span class="c1">// 陣列 nums 長度為 n, n-1, ..., 2, 1</span>
|
||
<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a> <span class="kd">let</span> <span class="nv">nums</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a> <span class="bp">print</span><span class="p">(</span><span class="s">"遞迴 n = </span><span class="si">\(</span><span class="n">n</span><span class="si">)</span><span class="s"> 中的 nums 長度 = </span><span class="si">\(</span><span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="si">)</span><span class="s">"</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="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-103-11" name="__codelineno-103-11" href="#__codelineno-103-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-104-2" name="__codelineno-104-2" href="#__codelineno-104-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadraticRecur</span><span class="p">(</span><span class="nx">n</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">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</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="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-104-4" name="__codelineno-104-4" href="#__codelineno-104-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
|
||
<a id="__codelineno-104-5" name="__codelineno-104-5" href="#__codelineno-104-5"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`遞迴 n = </span><span class="si">${</span><span class="nx">n</span><span class="si">}</span><span class="sb"> 中的 nums 長度 = </span><span class="si">${</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
|
||
<a id="__codelineno-104-6" name="__codelineno-104-6" href="#__codelineno-104-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">quadraticRecur</span><span class="p">(</span><span class="nx">n</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-104-7" name="__codelineno-104-7" href="#__codelineno-104-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-105-2" name="__codelineno-105-2" href="#__codelineno-105-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadraticRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-105-3" name="__codelineno-105-3" href="#__codelineno-105-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</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="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-105-4" name="__codelineno-105-4" href="#__codelineno-105-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
|
||
<a id="__codelineno-105-5" name="__codelineno-105-5" href="#__codelineno-105-5"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`遞迴 n = </span><span class="si">${</span><span class="nx">n</span><span class="si">}</span><span class="sb"> 中的 nums 長度 = </span><span class="si">${</span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
|
||
<a id="__codelineno-105-6" name="__codelineno-105-6" href="#__codelineno-105-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">quadraticRecur</span><span class="p">(</span><span class="nx">n</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-105-7" name="__codelineno-105-7" href="#__codelineno-105-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-106-2" name="__codelineno-106-2" href="#__codelineno-106-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="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="m">0</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-106-4" name="__codelineno-106-4" href="#__codelineno-106-4"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-106-5" name="__codelineno-106-5" href="#__codelineno-106-5"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="s1">'遞迴 n = </span><span class="si">$</span><span class="n">n</span><span class="s1"> 中的 nums 長度 = </span><span class="si">${</span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="si">}</span><span class="s1">'</span><span class="p">);</span>
|
||
<a id="__codelineno-106-6" name="__codelineno-106-6" href="#__codelineno-106-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</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-106-7" name="__codelineno-106-7" href="#__codelineno-106-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-107-2" name="__codelineno-107-2" href="#__codelineno-107-2"></a><span class="k">fn</span> <span class="nf">quadratic_recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</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="k">if</span><span class="w"> </span><span class="n">n</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-107-4" name="__codelineno-107-4" href="#__codelineno-107-4"></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-107-5" name="__codelineno-107-5" href="#__codelineno-107-5"></a><span class="w"> </span><span class="p">};</span>
|
||
<a id="__codelineno-107-6" name="__codelineno-107-6" href="#__codelineno-107-6"></a><span class="w"> </span><span class="c1">// 陣列 nums 長度為 n, n-1, ..., 2, 1</span>
|
||
<a id="__codelineno-107-7" name="__codelineno-107-7" href="#__codelineno-107-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</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="fm">println!</span><span class="p">(</span><span class="s">"遞迴 n = {} 中的 nums 長度 = {}"</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</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="k">return</span><span class="w"> </span><span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</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-107-10" name="__codelineno-107-10" href="#__codelineno-107-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-108-2" name="__codelineno-108-2" href="#__codelineno-108-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-108-3" name="__codelineno-108-3" href="#__codelineno-108-3"></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="mi">0</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="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-108-5" name="__codelineno-108-5" href="#__codelineno-108-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-108-6" name="__codelineno-108-6" href="#__codelineno-108-6"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"遞迴 n = %d 中的 nums 長度 = %d</span><span class="se">\r\n</span><span class="s">"</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-108-7" name="__codelineno-108-7" href="#__codelineno-108-7"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</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-108-8" name="__codelineno-108-8" href="#__codelineno-108-8"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">nums</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="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-108-10" name="__codelineno-108-10" href="#__codelineno-108-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="cm">/* 平方階（遞迴實現） */</span>
|
||
<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="kd">tailrec</span><span class="w"> </span><span class="kd">fun</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></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="m">0</span><span class="p">)</span>
|
||
<a id="__codelineno-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span>
|
||
<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a><span class="w"> </span><span class="c1">// 陣列 nums 長度為 n, n-1, ..., 2, 1</span>
|
||
<a id="__codelineno-109-6" name="__codelineno-109-6" href="#__codelineno-109-6"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-109-7" name="__codelineno-109-7" href="#__codelineno-109-7"></a><span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"遞迴 n = </span><span class="si">$</span><span class="n">n</span><span class="s"> 中的 nums 長度 = </span><span class="si">${</span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="si">}</span><span class="s">"</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="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</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-109-9" name="__codelineno-109-9" href="#__codelineno-109-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="c1">### 平方階（遞迴實現）###</span>
|
||
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a>
|
||
<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a><span class="w"> </span><span class="c1"># 陣列 nums 長度為 n, n-1, ..., 2, 1</span>
|
||
<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="w"> </span><span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</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-110-8" name="__codelineno-110-8" href="#__codelineno-110-8"></a><span class="k">end</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="c1">// 平方階（遞迴實現）</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">quadraticRecur</span><span class="p">(</span><span class="kr">comptime</span><span class="w"> </span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-111-3" name="__codelineno-111-3" href="#__codelineno-111-3"></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="mi">0</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-111-4" name="__codelineno-111-4" href="#__codelineno-111-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="n">_</span><span class="p">]</span><span class="kt">i32</span><span class="p">{</span><span class="mi">0</span><span class="p">}</span><span class="o">**</span><span class="n">n</span><span class="p">;</span>
|
||
<a id="__codelineno-111-5" name="__codelineno-111-5" href="#__codelineno-111-5"></a><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">"遞迴 n = {} 中的 nums 長度 = {}</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">});</span>
|
||
<a id="__codelineno-111-6" name="__codelineno-111-6" href="#__codelineno-111-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</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-111-7" name="__codelineno-111-7" href="#__codelineno-111-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>視覺化執行</summary>
|
||
<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20quadratic_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%9A%8E%EF%BC%88%E9%81%9E%E8%BF%B4%E5%AF%A6%E7%8F%BE%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%23%20%E9%99%A3%E5%88%97%20nums%20%E9%95%B7%E5%BA%A6%E7%82%BA%20n%2C%20n-1%2C%20...%2C%202%2C%201%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20return%20quadratic_recur%28n%20-%201%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E5%B9%B3%E6%96%B9%E9%9A%8E%0A%20%20%20%20quadratic_recur%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=28&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20quadratic_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%B9%B3%E6%96%B9%E9%9A%8E%EF%BC%88%E9%81%9E%E8%BF%B4%E5%AF%A6%E7%8F%BE%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%23%20%E9%99%A3%E5%88%97%20nums%20%E9%95%B7%E5%BA%A6%E7%82%BA%20n%2C%20n-1%2C%20...%2C%202%2C%201%0A%20%20%20%20nums%20%3D%20%5B0%5D%20%2A%20n%0A%20%20%20%20return%20quadratic_recur%28n%20-%201%29%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E5%B9%B3%E6%96%B9%E9%9A%8E%0A%20%20%20%20quadratic_recur%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=28&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 ></a></div></p>
|
||
</details>
|
||
<p><a class="glightbox" href="../space_complexity.assets/space_complexity_recursive_quadratic.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="遞迴函式產生的平方階空間複雜度" class="animation-figure" src="../space_complexity.assets/space_complexity_recursive_quadratic.png" /></a></p>
|
||
<p align="center"> 圖 2-18 遞迴函式產生的平方階空間複雜度 </p>
|
||
|
||
<h3 id="4-o2n">4. 指數階 <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">¶</a></h3>
|
||
<p>指數階常見於二元樹。觀察圖 2-19 ，層數為 <span class="arithmatex">\(n\)</span> 的“滿二元樹”的節點數量為 <span class="arithmatex">\(2^n - 1\)</span> ，佔用 <span class="arithmatex">\(O(2^n)\)</span> 空間：</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">space_complexity.py</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="k">def</span> <span class="nf">build_tree</span><span class="p">(</span><span class="n">n</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-112-2" name="__codelineno-112-2" href="#__codelineno-112-2"></a><span class="w"> </span><span class="sd">"""指數階（建立滿二元樹）"""</span>
|
||
<a id="__codelineno-112-3" name="__codelineno-112-3" href="#__codelineno-112-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||
<a id="__codelineno-112-4" name="__codelineno-112-4" href="#__codelineno-112-4"></a> <span class="k">return</span> <span class="kc">None</span>
|
||
<a id="__codelineno-112-5" name="__codelineno-112-5" href="#__codelineno-112-5"></a> <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-112-6" name="__codelineno-112-6" href="#__codelineno-112-6"></a> <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">build_tree</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-112-7" name="__codelineno-112-7" href="#__codelineno-112-7"></a> <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">build_tree</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-112-8" name="__codelineno-112-8" href="#__codelineno-112-8"></a> <span class="k">return</span> <span class="n">root</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-113-2" name="__codelineno-113-2" href="#__codelineno-113-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-113-3" name="__codelineno-113-3" href="#__codelineno-113-3"></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="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-113-4" name="__codelineno-113-4" href="#__codelineno-113-4"></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-113-5" name="__codelineno-113-5" href="#__codelineno-113-5"></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="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-113-6" name="__codelineno-113-6" href="#__codelineno-113-6"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-113-7" name="__codelineno-113-7" href="#__codelineno-113-7"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-113-8" name="__codelineno-113-8" href="#__codelineno-113-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||
<a id="__codelineno-113-9" name="__codelineno-113-9" href="#__codelineno-113-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-114-1" name="__codelineno-114-1" href="#__codelineno-114-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-114-2" name="__codelineno-114-2" href="#__codelineno-114-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-114-3" name="__codelineno-114-3" href="#__codelineno-114-3"></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="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-114-4" name="__codelineno-114-4" href="#__codelineno-114-4"></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-114-5" name="__codelineno-114-5" href="#__codelineno-114-5"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-114-6" name="__codelineno-114-6" href="#__codelineno-114-6"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-114-7" name="__codelineno-114-7" href="#__codelineno-114-7"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-114-8" name="__codelineno-114-8" href="#__codelineno-114-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||
<a id="__codelineno-114-9" name="__codelineno-114-9" href="#__codelineno-114-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-115-1" name="__codelineno-115-1" href="#__codelineno-115-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-115-2" name="__codelineno-115-2" href="#__codelineno-115-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-115-3" name="__codelineno-115-3" href="#__codelineno-115-3"></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="m">0</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-115-4" name="__codelineno-115-4" href="#__codelineno-115-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-115-5" name="__codelineno-115-5" href="#__codelineno-115-5"></a><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="n">n</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-115-6" name="__codelineno-115-6" href="#__codelineno-115-6"></a><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="n">n</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-115-7" name="__codelineno-115-7" href="#__codelineno-115-7"></a><span class="w"> </span><span class="p">};</span>
|
||
<a id="__codelineno-115-8" name="__codelineno-115-8" href="#__codelineno-115-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||
<a id="__codelineno-115-9" name="__codelineno-115-9" href="#__codelineno-115-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-116-1" name="__codelineno-116-1" href="#__codelineno-116-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-116-2" name="__codelineno-116-2" href="#__codelineno-116-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</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-116-3" name="__codelineno-116-3" href="#__codelineno-116-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</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-116-4" name="__codelineno-116-4" href="#__codelineno-116-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||
<a id="__codelineno-116-5" name="__codelineno-116-5" href="#__codelineno-116-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-116-6" name="__codelineno-116-6" href="#__codelineno-116-6"></a><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-116-7" name="__codelineno-116-7" href="#__codelineno-116-7"></a><span class="w"> </span><span class="nx">root</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">buildTree</span><span class="p">(</span><span class="nx">n</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-116-8" name="__codelineno-116-8" href="#__codelineno-116-8"></a><span class="w"> </span><span class="nx">root</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">buildTree</span><span class="p">(</span><span class="nx">n</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-116-9" name="__codelineno-116-9" href="#__codelineno-116-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
|
||
<a id="__codelineno-116-10" name="__codelineno-116-10" href="#__codelineno-116-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-117-1" name="__codelineno-117-1" href="#__codelineno-117-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-117-2" name="__codelineno-117-2" href="#__codelineno-117-2"></a><span class="kd">func</span> <span class="nf">buildTree</span><span class="p">(</span><span class="n">n</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-117-3" name="__codelineno-117-3" href="#__codelineno-117-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">{</span>
|
||
<a id="__codelineno-117-4" name="__codelineno-117-4" href="#__codelineno-117-4"></a> <span class="k">return</span> <span class="kc">nil</span>
|
||
<a id="__codelineno-117-5" name="__codelineno-117-5" href="#__codelineno-117-5"></a> <span class="p">}</span>
|
||
<a id="__codelineno-117-6" name="__codelineno-117-6" href="#__codelineno-117-6"></a> <span class="kd">let</span> <span class="nv">root</span> <span class="p">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-117-7" name="__codelineno-117-7" href="#__codelineno-117-7"></a> <span class="n">root</span><span class="p">.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-117-8" name="__codelineno-117-8" href="#__codelineno-117-8"></a> <span class="n">root</span><span class="p">.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-117-9" name="__codelineno-117-9" href="#__codelineno-117-9"></a> <span class="k">return</span> <span class="n">root</span>
|
||
<a id="__codelineno-117-10" name="__codelineno-117-10" href="#__codelineno-117-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-118-1" name="__codelineno-118-1" href="#__codelineno-118-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-118-2" name="__codelineno-118-2" href="#__codelineno-118-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-118-3" name="__codelineno-118-3" href="#__codelineno-118-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</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="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||
<a id="__codelineno-118-4" name="__codelineno-118-4" href="#__codelineno-118-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</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="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-118-5" name="__codelineno-118-5" href="#__codelineno-118-5"></a><span class="w"> </span><span class="nx">root</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">buildTree</span><span class="p">(</span><span class="nx">n</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-118-6" name="__codelineno-118-6" href="#__codelineno-118-6"></a><span class="w"> </span><span class="nx">root</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">buildTree</span><span class="p">(</span><span class="nx">n</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-118-7" name="__codelineno-118-7" href="#__codelineno-118-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
|
||
<a id="__codelineno-118-8" name="__codelineno-118-8" href="#__codelineno-118-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-119-2" name="__codelineno-119-2" href="#__codelineno-119-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">n</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="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-119-3" name="__codelineno-119-3" href="#__codelineno-119-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</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="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||
<a id="__codelineno-119-4" name="__codelineno-119-4" href="#__codelineno-119-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</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="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-119-5" name="__codelineno-119-5" href="#__codelineno-119-5"></a><span class="w"> </span><span class="nx">root</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">buildTree</span><span class="p">(</span><span class="nx">n</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-119-6" name="__codelineno-119-6" href="#__codelineno-119-6"></a><span class="w"> </span><span class="nx">root</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">buildTree</span><span class="p">(</span><span class="nx">n</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-119-7" name="__codelineno-119-7" href="#__codelineno-119-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
|
||
<a id="__codelineno-119-8" name="__codelineno-119-8" href="#__codelineno-119-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-120-1" name="__codelineno-120-1" href="#__codelineno-120-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-120-2" name="__codelineno-120-2" href="#__codelineno-120-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-120-3" name="__codelineno-120-3" href="#__codelineno-120-3"></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="m">0</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-120-4" name="__codelineno-120-4" href="#__codelineno-120-4"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-120-5" name="__codelineno-120-5" href="#__codelineno-120-5"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-120-6" name="__codelineno-120-6" href="#__codelineno-120-6"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-120-7" name="__codelineno-120-7" href="#__codelineno-120-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||
<a id="__codelineno-120-8" name="__codelineno-120-8" href="#__codelineno-120-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-121-1" name="__codelineno-121-1" href="#__codelineno-121-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-121-2" name="__codelineno-121-2" href="#__codelineno-121-2"></a><span class="k">fn</span> <span class="nf">build_tree</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </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="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-121-3" name="__codelineno-121-3" href="#__codelineno-121-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</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-121-4" name="__codelineno-121-4" href="#__codelineno-121-4"></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-121-5" name="__codelineno-121-5" href="#__codelineno-121-5"></a><span class="w"> </span><span class="p">};</span>
|
||
<a id="__codelineno-121-6" name="__codelineno-121-6" href="#__codelineno-121-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span>::<span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-121-7" name="__codelineno-121-7" href="#__codelineno-121-7"></a><span class="w"> </span><span class="n">root</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">build_tree</span><span class="p">(</span><span class="n">n</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-121-8" name="__codelineno-121-8" href="#__codelineno-121-8"></a><span class="w"> </span><span class="n">root</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">build_tree</span><span class="p">(</span><span class="n">n</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-121-9" name="__codelineno-121-9" href="#__codelineno-121-9"></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">root</span><span class="p">);</span>
|
||
<a id="__codelineno-121-10" name="__codelineno-121-10" href="#__codelineno-121-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-122-2" name="__codelineno-122-2" href="#__codelineno-122-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-122-3" name="__codelineno-122-3" href="#__codelineno-122-3"></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="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-122-4" name="__codelineno-122-4" href="#__codelineno-122-4"></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-122-5" name="__codelineno-122-5" href="#__codelineno-122-5"></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">newTreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-122-6" name="__codelineno-122-6" href="#__codelineno-122-6"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-122-7" name="__codelineno-122-7" href="#__codelineno-122-7"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-122-8" name="__codelineno-122-8" href="#__codelineno-122-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||
<a id="__codelineno-122-9" name="__codelineno-122-9" href="#__codelineno-122-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-123-1" name="__codelineno-123-1" href="#__codelineno-123-1"></a><span class="cm">/* 指數階（建立滿二元樹） */</span>
|
||
<a id="__codelineno-123-2" name="__codelineno-123-2" href="#__codelineno-123-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">n</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-123-3" name="__codelineno-123-3" href="#__codelineno-123-3"></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="m">0</span><span class="p">)</span>
|
||
<a id="__codelineno-123-4" name="__codelineno-123-4" href="#__codelineno-123-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
|
||
<a id="__codelineno-123-5" name="__codelineno-123-5" href="#__codelineno-123-5"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
|
||
<a id="__codelineno-123-6" name="__codelineno-123-6" href="#__codelineno-123-6"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-123-7" name="__codelineno-123-7" href="#__codelineno-123-7"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">n</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-123-8" name="__codelineno-123-8" href="#__codelineno-123-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span>
|
||
<a id="__codelineno-123-9" name="__codelineno-123-9" href="#__codelineno-123-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-124-1" name="__codelineno-124-1" href="#__codelineno-124-1"></a><span class="c1">### 指數階（建立滿二元樹）###</span>
|
||
<a id="__codelineno-124-2" name="__codelineno-124-2" href="#__codelineno-124-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-124-3" name="__codelineno-124-3" href="#__codelineno-124-3"></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="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-124-4" name="__codelineno-124-4" href="#__codelineno-124-4"></a>
|
||
<a id="__codelineno-124-5" name="__codelineno-124-5" href="#__codelineno-124-5"></a><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="o">.</span><span class="n">tap</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">root</span><span class="o">|</span>
|
||
<a id="__codelineno-124-6" name="__codelineno-124-6" href="#__codelineno-124-6"></a><span class="w"> </span><span class="n">root</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">build_tree</span><span class="p">(</span><span class="n">n</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-124-7" name="__codelineno-124-7" href="#__codelineno-124-7"></a><span class="w"> </span><span class="n">root</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">build_tree</span><span class="p">(</span><span class="n">n</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-124-8" name="__codelineno-124-8" href="#__codelineno-124-8"></a><span class="w"> </span><span class="k">end</span>
|
||
<a id="__codelineno-124-9" name="__codelineno-124-9" href="#__codelineno-124-9"></a><span class="k">end</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-125-1" name="__codelineno-125-1" href="#__codelineno-125-1"></a><span class="c1">// 指數階（建立滿二元樹）</span>
|
||
<a id="__codelineno-125-2" name="__codelineno-125-2" href="#__codelineno-125-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">mem_allocator</span><span class="o">:</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">mem</span><span class="p">.</span><span class="n">Allocator</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-125-3" name="__codelineno-125-3" href="#__codelineno-125-3"></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="mi">0</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-125-4" name="__codelineno-125-4" href="#__codelineno-125-4"></a><span class="w"> </span><span class="kr">const</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">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="kt">i32</span><span class="p">));</span>
|
||
<a id="__codelineno-125-5" name="__codelineno-125-5" href="#__codelineno-125-5"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">init</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-125-6" name="__codelineno-125-6" href="#__codelineno-125-6"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">mem_allocator</span><span class="p">,</span><span class="w"> </span><span class="n">n</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-125-7" name="__codelineno-125-7" href="#__codelineno-125-7"></a><span class="w"> </span><span class="n">root</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">buildTree</span><span class="p">(</span><span class="n">mem_allocator</span><span class="p">,</span><span class="w"> </span><span class="n">n</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-125-8" name="__codelineno-125-8" href="#__codelineno-125-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||
<a id="__codelineno-125-9" name="__codelineno-125-9" href="#__codelineno-125-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<details class="pythontutor">
|
||
<summary>視覺化執行</summary>
|
||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%85%83%E6%A8%B9%E7%AF%80%E9%BB%9E%E9%A1%9E%E5%88%A5%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E7%AF%80%E9%BB%9E%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E7%AF%80%E9%BB%9E%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E7%AF%80%E9%BB%9E%E5%BC%95%E7%94%A8%0A%0Adef%20build_tree%28n%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%8C%87%E6%95%B8%E9%9A%8E%EF%BC%88%E5%BB%BA%E7%AB%8B%E6%BB%BF%E4%BA%8C%E5%85%83%E6%A8%B9%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20root%20%3D%20TreeNode%280%29%0A%20%20%20%20root.left%20%3D%20build_tree%28n%20-%201%29%0A%20%20%20%20root.right%20%3D%20build_tree%28n%20-%201%29%0A%20%20%20%20return%20root%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E6%8C%87%E6%95%B8%E9%9A%8E%0A%20%20%20%20root%20%3D%20build_tree%28n%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=507&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%85%83%E6%A8%B9%E7%AF%80%E9%BB%9E%E9%A1%9E%E5%88%A5%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E7%AF%80%E9%BB%9E%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E7%AF%80%E9%BB%9E%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E7%AF%80%E9%BB%9E%E5%BC%95%E7%94%A8%0A%0Adef%20build_tree%28n%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%8C%87%E6%95%B8%E9%9A%8E%EF%BC%88%E5%BB%BA%E7%AB%8B%E6%BB%BF%E4%BA%8C%E5%85%83%E6%A8%B9%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20root%20%3D%20TreeNode%280%29%0A%20%20%20%20root.left%20%3D%20build_tree%28n%20-%201%29%0A%20%20%20%20root.right%20%3D%20build_tree%28n%20-%201%29%0A%20%20%20%20return%20root%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%205%0A%20%20%20%20print%28%22%E8%BC%B8%E5%85%A5%E8%B3%87%E6%96%99%E5%A4%A7%E5%B0%8F%20n%20%3D%22%2C%20n%29%0A%0A%20%20%20%20%23%20%E6%8C%87%E6%95%B8%E9%9A%8E%0A%20%20%20%20root%20%3D%20build_tree%28n%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=507&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 ></a></div></p>
|
||
</details>
|
||
<p><a class="glightbox" href="../space_complexity.assets/space_complexity_exponential.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="滿二元樹產生的指數階空間複雜度" class="animation-figure" src="../space_complexity.assets/space_complexity_exponential.png" /></a></p>
|
||
<p align="center"> 圖 2-19 滿二元樹產生的指數階空間複雜度 </p>
|
||
|
||
<h3 id="5-olog-n">5. 對數階 <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">¶</a></h3>
|
||
<p>對數階常見於分治演算法。例如合併排序，輸入長度為 <span class="arithmatex">\(n\)</span> 的陣列，每輪遞迴將陣列從中點處劃分為兩半，形成高度為 <span class="arithmatex">\(\log n\)</span> 的遞迴樹，使用 <span class="arithmatex">\(O(\log n)\)</span> 堆疊幀空間。</p>
|
||
<p>再例如將數字轉化為字串，輸入一個正整數 <span class="arithmatex">\(n\)</span> ，它的位數為 <span class="arithmatex">\(\lfloor \log_{10} n \rfloor + 1\)</span> ，即對應字串長度為 <span class="arithmatex">\(\lfloor \log_{10} n \rfloor + 1\)</span> ，因此空間複雜度為 <span class="arithmatex">\(O(\log_{10} n + 1) = O(\log n)\)</span> 。</p>
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<h2 id="244">2.4.4 權衡時間與空間<a class="headerlink" href="#244" title="Permanent link">¶</a></h2>
|
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<p>理想情況下，我們希望演算法的時間複雜度和空間複雜度都能達到最優。然而在實際情況中，同時最佳化時間複雜度和空間複雜度通常非常困難。</p>
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<p><strong>降低時間複雜度通常需要以提升空間複雜度為代價，反之亦然</strong>。我們將犧牲記憶體空間來提升演算法執行速度的思路稱為“以空間換時間”；反之，則稱為“以時間換空間”。</p>
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<p>選擇哪種思路取決於我們更看重哪個方面。在大多數情況下，時間比空間更寶貴，因此“以空間換時間”通常是更常用的策略。當然，在資料量很大的情況下，控制空間複雜度也非常重要。</p>
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