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krahets/hello-algo
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z" / > < / svg >
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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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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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1.3 小結
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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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2.1 演算法效率評估
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2.2 迭代與遞迴
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2.2 迭代與遞迴
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目錄
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2.2.1 迭代
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1. for 迴圈
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2. while 迴圈
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3. 巢狀迴圈
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2.2.2 遞迴
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1. 呼叫堆疊
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2. 尾遞迴
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3. 遞迴樹
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2.2.3 兩者對比
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2.3 時間複雜度
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2.4 空間複雜度
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2.5 小結
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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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3.2 基本資料型別
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3.3 數字編碼 *
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3.4 字元編碼 *
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3.5 小結
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第 4 章 陣列與鏈結串列
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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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4.2 鏈結串列
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4.3 串列
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4.4 記憶體與快取 *
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4.5 小結
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< a href = "../../chapter_stack_and_queue/" class = "md-nav__link " >
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第 5 章 堆疊與佇列
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第 5 章 堆疊與佇列
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
< span class = "md-ellipsis" >
5.1 堆疊
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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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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
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5.3 雙向佇列
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< / a >
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< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
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5.4 小結
< / span >
< / a >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_hashing/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z" / > < / svg >
< span class = "md-ellipsis" >
第 6 章 雜湊表
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< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
第 6 章 雜湊表
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< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
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6.1 雜湊表
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< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
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6.2 雜湊衝突
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< a href = "../../chapter_hashing/hash_algorithm/" class = "md-nav__link" >
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6.3 雜湊演算法
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< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
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6.4 小結
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_tree/" class = "md-nav__link " >
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< span class = "md-ellipsis" >
第 7 章 樹
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_9_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_9" >
< span class = "md-nav__icon md-icon" > < / span >
第 7 章 樹
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
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7.1 二元樹
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
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7.2 二元樹走訪
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
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7.3 二元樹陣列表示
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< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
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7.4 二元搜尋樹
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
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7.5 AVL *
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.6 小結
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< / a >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_heap/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z" / > < / svg >
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第 8 章 堆積
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
第 8 章 堆積
< / label >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
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8.1 堆積
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
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8.2 建堆積操作
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/top_k/" class = "md-nav__link" >
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8.3 Top-k 問題
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< / a >
< / li >
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< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
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8.4 小結
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_graph/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
< span class = "md-ellipsis" >
第 9 章 圖
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< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
第 9 章 圖
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< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
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9.1 圖
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
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9.2 圖基礎操作
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< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
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9.3 圖的走訪
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9.4 小結
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_searching/" class = "md-nav__link " >
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第 10 章 搜尋
< / span >
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< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_12_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
第 10 章 搜尋
< / label >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.1 二分搜尋
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_insertion/" class = "md-nav__link" >
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10.2 二分搜尋插入點
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
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10.3 二分搜尋邊界
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
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10.4 雜湊最佳化策略
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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10.5 重識搜尋演算法
< / span >
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< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.6 小結
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
< 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 >
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< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
第 11 章 排序
< / label >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
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11.1 排序演算法
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
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11.2 選擇排序
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.3 泡沫排序
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.4 插入排序
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.5 快速排序
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.6 合併排序
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
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11.7 堆積排序
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
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11.8 桶排序
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< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
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11.9 計數排序
< / span >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
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11.10 基數排序
< / span >
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11.11 小結
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第 12 章 分治
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第 12 章 分治
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12.1 分治演算法
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12.2 分治搜尋策略
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12.3 構建樹問題
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12.4 河內塔問題
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12.5 小結
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第 13 章 回溯
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第 13 章 回溯
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13.1 回溯演算法
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13.2 全排列問題
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13.3 子集和問題
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13.4 N 皇后問題
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13.5 小結
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第 14 章 動態規劃
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第 14 章 動態規劃
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14.1 初探動態規劃
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14.2 DP 問題特性
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14.3 DP 解題思路
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14.4 0-1 背包問題
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14.5 完全背包問題
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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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第 15 章 貪婪
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15.1 貪婪演算法
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15.2 分數背包問題
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15.3 最大容量問題
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15.4 最大切分乘積問題
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15.5 小結
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第 16 章 附錄
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第 16 章 附錄
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16.1 程式設計環境安裝
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16.2 一起參與創作
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16.3 術語表
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參考文獻
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2.2.1 迭代
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1. for 迴圈
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2. while 迴圈
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3. 巢狀迴圈
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2.2.2 遞迴
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1. 呼叫堆疊
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2. 尾遞迴
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3. 遞迴樹
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2.2.3 兩者對比
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< h1 id = "22" > 2.2 迭代與遞迴< a class = "headerlink" href = "#22" title = "Permanent link" > ¶ < / a > < / h1 >
< p > 在演算法中，重複執行某個任務是很常見的，它與複雜度分析息息相關。因此，在介紹時間複雜度和空間複雜度之前，我們先來了解如何在程式中實現重複執行任務，即兩種基本的程式控制結構：迭代、遞迴。< / p >
< h2 id = "221" > 2.2.1 迭代< a class = "headerlink" href = "#221" title = "Permanent link" > ¶ < / a > < / h2 >
< p > < u > 迭代（ ） < / u > 是一種重複執行某個任務的控制結構。在迭代中，程式會在滿足一定的條件下重複執行某段程式碼，直到這個條件不再滿足。< / p >
< h3 id = "1-for" > 1. for 迴圈< a class = "headerlink" href = "#1-for" title = "Permanent link" > ¶ < / a > < / h3 >
< p > < code > for< / code > 迴圈是最常見的迭代形式之一，< strong > 適合在預先知道迭代次數時使用< / strong > 。< / p >
< p > 以下函式基於 < code > for< / code > 迴圈實現了求和 < span class = "arithmatex" > \(1 + 2 + \dots + n\)< / span > ，求和結果使用變數 < code > res< / code > 記錄。需要注意的是， < code > range(a, b)< / code > 對應的區間是“左閉右開”的，對應的走訪範圍為 < span class = "arithmatex" > \(a, a + 1, \dots, b-1\)< / span > ： < / 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" > < span class = "filename" > iteration.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > for_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 = "o" > -> < / span > < span class = "nb" > int< / 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" > " " " for 迴圈" " " < / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "c1" > # 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / 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 = "mi" > 1< / 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-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > forLoop< / 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-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" > res< / 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-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / 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" > 1< / 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 = "o" > ++< / span > < span class = "n" > i< / 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 = "w" > < / span > < span class = "n" > res< / 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-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > forLoop< / 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-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" > res< / 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-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / 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" > 1< / 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-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / 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-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > ForLoop< / 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-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" > res< / 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-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / 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 = "m" > 1< / 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-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / 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-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > forLoop< / 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-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / 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" > 1< / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > forLoop< / 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-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "mi" > 1< / span > < span class = "p" > ...< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > forLoop< / 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-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / 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" > 1< / 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-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > forLoop< / 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-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / 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" > 1< / 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-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > forLoop< / 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-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" > res< / 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-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / 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 = "m" > 1< / 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-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / 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-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > for_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 = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / 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" > res< / 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-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / 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" > 1< / span > < span class = "o" > ..=< / span > < span class = "n" > n< / 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" > res< / 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-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* for 迴圈 */< / 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" > forLoop< / 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-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / 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" > 1< / 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-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / 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-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* for 迴圈 */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > forLoop< / 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-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" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / 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" > 1.< / span > < span class = "p" > .< / span > < span class = "na" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span >
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "c1" > ### for 迴圈 ###< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "k" > def< / span > < span class = "w" > < / span > < span class = "nf" > for_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "w" > < / span > < span class = "c1" > # 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / 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" > 1< / span > < span class = "o" > ..< / span > < span class = "n" > n< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / 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 >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "k" > end< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "c1" > // for 迴圈< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > forLoop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > usize< / 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-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / 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-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > i< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nb" > @as< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / 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-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
2024-04-11 01:11:27 +08:00
< p > < div style = "height: 423px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=def%20for_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22for%20%E8%BF%B4%E5%9C%88%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E6%B1%82%E5%92%8C%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20return%20res%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%20res%20%3D%20for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cnfor%20%E8%BF%B4%E5%9C%88%E7%9A%84%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&" > < / iframe > < / div >
< div style = "margin-top: 5px;" > < a href = "https://pythontutor.com/iframe-embed.html#code=def%20for_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22for%20%E8%BF%B4%E5%9C%88%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E6%B1%82%E5%92%8C%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20return%20res%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%20res%20%3D%20for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cnfor%20%E8%BF%B4%E5%9C%88%E7%9A%84%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&" target = "_blank" rel = "noopener noreferrer" > 全螢幕觀看 > < / a > < / div > < / p >
2024-04-06 03:02:26 +08:00
< / details >
< p > 圖 2-1 是該求和函式的流程框圖。< / p >
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/iteration.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "求和函式的流程框圖" class = "animation-figure" src = "../iteration_and_recursion.assets/iteration.png" / > < / a > < / p >
< p align = "center" > 圖 2-1 求和函式的流程框圖 < / p >
< p > 此求和函式的操作數量與輸入資料大小 < span class = "arithmatex" > \(n\)< / span > 成正比，或者說成“線性關係”。實際上，< strong > 時間複雜度描述的就是這個“線性關係”< / strong > 。相關內容將會在下一節中詳細介紹。< / p >
< h3 id = "2-while" > 2. while 迴圈< a class = "headerlink" href = "#2-while" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 與 < code > for< / code > 迴圈類似，< code > while< / code > 迴圈也是一種實現迭代的方法。在 < code > while< / code > 迴圈中，程式每輪都會先檢查條件，如果條件為真，則繼續執行，否則就結束迴圈。< / p >
< p > 下面我們用 < code > while< / code > 迴圈來實現求和 < span class = "arithmatex" > \(1 + 2 + \dots + n\)< / span > ： < / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:14" > < input checked = "checked" id = "__tabbed_2_1" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_2" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_3" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_4" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_5" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_6" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_7" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_8" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_9" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_10" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_11" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_12" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_13" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_14" name = "__tabbed_2" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Python< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Java< / label > < label for = "__tabbed_2_4" > C#< / label > < label for = "__tabbed_2_5" > Go< / label > < label for = "__tabbed_2_6" > Swift< / label > < label for = "__tabbed_2_7" > JS< / label > < label for = "__tabbed_2_8" > TS< / label > < label for = "__tabbed_2_9" > Dart< / label > < label for = "__tabbed_2_10" > Rust< / label > < label for = "__tabbed_2_11" > C< / label > < label for = "__tabbed_2_12" > Kotlin< / label > < label for = "__tabbed_2_13" > Ruby< / label > < label for = "__tabbed_2_14" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > while_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 = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " while 迴圈" " " < / span >
< a id = "__codelineno-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "n" > i< / span > < span class = "o" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 初始化條件變數< / span >
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "c1" > # 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "k" > while< / span > < span class = "n" > i< / span > < span class = "o" > < =< / span > < span class = "n" > n< / span > < span class = "p" > :< / span >
< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 更新條件變數< / span >
< a id = "__codelineno-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoop< / 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-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / 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 = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-15-9" name = "__codelineno-15-9" href = "#__codelineno-15-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / 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-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoop< / 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-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / 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 = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-16-9" name = "__codelineno-16-9" href = "#__codelineno-16-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-10" name = "__codelineno-16-10" href = "#__codelineno-16-10" > < / 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-16-11" name = "__codelineno-16-11" href = "#__codelineno-16-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > WhileLoop< / 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-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / 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 = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-17-4" name = "__codelineno-17-4" href = "#__codelineno-17-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / 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 = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-17-9" name = "__codelineno-17-9" href = "#__codelineno-17-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-17-10" name = "__codelineno-17-10" href = "#__codelineno-17-10" > < / 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-17-11" name = "__codelineno-17-11" href = "#__codelineno-17-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > whileLoop< / 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-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / 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 = "nx" > n< / span > < 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" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > whileLoop< / 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-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > i< / span > < span class = "p" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "k" > while< / span > < span class = "n" > i< / span > < span class = "o" > < =< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > whileLoop< / 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-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "p" > {< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-8" name = "__codelineno-20-8" href = "#__codelineno-20-8" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-20-9" name = "__codelineno-20-9" href = "#__codelineno-20-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-10" name = "__codelineno-20-10" href = "#__codelineno-20-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-11" name = "__codelineno-20-11" href = "#__codelineno-20-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-21-2" name = "__codelineno-21-2" href = "#__codelineno-21-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > whileLoop< / 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-21-3" name = "__codelineno-21-3" href = "#__codelineno-21-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-21-5" name = "__codelineno-21-5" href = "#__codelineno-21-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-21-6" name = "__codelineno-21-6" href = "#__codelineno-21-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "p" > {< / span >
< a id = "__codelineno-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-8" name = "__codelineno-21-8" href = "#__codelineno-21-8" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-21-9" name = "__codelineno-21-9" href = "#__codelineno-21-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-10" name = "__codelineno-21-10" href = "#__codelineno-21-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-11" name = "__codelineno-21-11" href = "#__codelineno-21-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > whileLoop< / 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-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / 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 = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-22-5" name = "__codelineno-22-5" href = "#__codelineno-22-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-22-6" name = "__codelineno-22-6" href = "#__codelineno-22-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-22-7" name = "__codelineno-22-7" href = "#__codelineno-22-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-22-8" name = "__codelineno-22-8" href = "#__codelineno-22-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-22-9" name = "__codelineno-22-9" href = "#__codelineno-22-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-10" name = "__codelineno-22-10" href = "#__codelineno-22-10" > < / 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-22-11" name = "__codelineno-22-11" href = "#__codelineno-22-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > while_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 = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / 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-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / 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" > 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 = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-23-5" name = "__codelineno-23-5" href = "#__codelineno-23-5" > < / a >
< a id = "__codelineno-23-6" name = "__codelineno-23-6" href = "#__codelineno-23-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-23-7" name = "__codelineno-23-7" href = "#__codelineno-23-7" > < / a > < span class = "w" > < / span > < span class = "k" > while< / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-23-8" name = "__codelineno-23-8" href = "#__codelineno-23-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-23-9" name = "__codelineno-23-9" href = "#__codelineno-23-9" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-23-10" name = "__codelineno-23-10" href = "#__codelineno-23-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-23-11" name = "__codelineno-23-11" href = "#__codelineno-23-11" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-23-12" name = "__codelineno-23-12" href = "#__codelineno-23-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoop< / 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-24-3" 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" > res< / 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-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-24-5" name = "__codelineno-24-5" href = "#__codelineno-24-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-24-6" name = "__codelineno-24-6" href = "#__codelineno-24-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-24-7" name = "__codelineno-24-7" href = "#__codelineno-24-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-24-8" name = "__codelineno-24-8" href = "#__codelineno-24-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-24-9" name = "__codelineno-24-9" href = "#__codelineno-24-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-24-10" name = "__codelineno-24-10" href = "#__codelineno-24-10" > < / 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-24-11" name = "__codelineno-24-11" href = "#__codelineno-24-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-25-1" name = "__codelineno-25-1" href = "#__codelineno-25-1" > < / a > < span class = "cm" > /* while 迴圈 */< / span >
< a id = "__codelineno-25-2" name = "__codelineno-25-2" href = "#__codelineno-25-2" > < / a > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > whileLoop< / 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-25-3" name = "__codelineno-25-3" href = "#__codelineno-25-3" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span >
< a id = "__codelineno-25-4" name = "__codelineno-25-4" href = "#__codelineno-25-4" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-25-5" name = "__codelineno-25-5" href = "#__codelineno-25-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-25-6" name = "__codelineno-25-6" href = "#__codelineno-25-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-25-7" name = "__codelineno-25-7" href = "#__codelineno-25-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span >
< a id = "__codelineno-25-8" name = "__codelineno-25-8" href = "#__codelineno-25-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-25-9" name = "__codelineno-25-9" href = "#__codelineno-25-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-10" name = "__codelineno-25-10" href = "#__codelineno-25-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-25-11" name = "__codelineno-25-11" href = "#__codelineno-25-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-26-1" name = "__codelineno-26-1" href = "#__codelineno-26-1" > < / a > < span class = "c1" > ### while 迴圈 ###< / span >
< a id = "__codelineno-26-2" name = "__codelineno-26-2" href = "#__codelineno-26-2" > < / a > < span class = "k" > def< / span > < span class = "w" > < / span > < span class = "nf" > while_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-26-3" name = "__codelineno-26-3" href = "#__codelineno-26-3" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-26-4" name = "__codelineno-26-4" href = "#__codelineno-26-4" > < / 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" > 1< / span > < span class = "w" > < / span > < span class = "c1" > # 初始化條件變數< / span >
< a id = "__codelineno-26-5" name = "__codelineno-26-5" href = "#__codelineno-26-5" > < / a >
< a id = "__codelineno-26-6" name = "__codelineno-26-6" href = "#__codelineno-26-6" > < / a > < span class = "w" > < / span > < span class = "c1" > # 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-26-7" name = "__codelineno-26-7" href = "#__codelineno-26-7" > < / a > < span class = "w" > < / span > < span class = "k" > while< / 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 >
< a id = "__codelineno-26-8" name = "__codelineno-26-8" href = "#__codelineno-26-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span >
< a id = "__codelineno-26-9" name = "__codelineno-26-9" href = "#__codelineno-26-9" > < / 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" > 1< / span > < span class = "w" > < / span > < span class = "c1" > # 更新條件變數< / span >
< a id = "__codelineno-26-10" name = "__codelineno-26-10" href = "#__codelineno-26-10" > < / a > < span class = "w" > < / span > < span class = "k" > end< / span >
< a id = "__codelineno-26-11" name = "__codelineno-26-11" href = "#__codelineno-26-11" > < / a >
< a id = "__codelineno-26-12" name = "__codelineno-26-12" href = "#__codelineno-26-12" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-26-13" name = "__codelineno-26-13" href = "#__codelineno-26-13" > < / a > < span class = "k" > end< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-27-1" name = "__codelineno-27-1" href = "#__codelineno-27-1" > < / a > < span class = "c1" > // while 迴圈< / span >
< a id = "__codelineno-27-2" name = "__codelineno-27-2" href = "#__codelineno-27-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > whileLoop< / 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" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-27-3" name = "__codelineno-27-3" href = "#__codelineno-27-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / 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-27-4" name = "__codelineno-27-4" href = "#__codelineno-27-4" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-27-5" name = "__codelineno-27-5" href = "#__codelineno-27-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-27-6" name = "__codelineno-27-6" href = "#__codelineno-27-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-27-7" name = "__codelineno-27-7" href = "#__codelineno-27-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-27-8" name = "__codelineno-27-8" href = "#__codelineno-27-8" > < / 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" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-9" name = "__codelineno-27-9" href = "#__codelineno-27-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-10" name = "__codelineno-27-10" href = "#__codelineno-27-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-11" name = "__codelineno-27-11" href = "#__codelineno-27-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
2024-04-11 01:11:27 +08:00
< p > < div style = "height: 459px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=def%20while_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22while%20%E8%BF%B4%E5%9C%88%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A2%9D%E4%BB%B6%E8%AE%8A%E6%95%B8%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E6%B1%82%E5%92%8C%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E6%9B%B4%E6%96%B0%E6%A2%9D%E4%BB%B6%E8%AE%8A%E6%95%B8%0A%20%20%20%20return%20res%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%20res%20%3D%20while_loop%28n%29%0A%20%20%20%20print%28f%22%5Cnwhile%20%E8%BF%B4%E5%9C%88%E7%9A%84%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&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%20while_loop%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22while%20%E8%BF%B4%E5%9C%88%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A2%9D%E4%BB%B6%E8%AE%8A%E6%95%B8%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E6%B1%82%E5%92%8C%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%20%20%23%20%E6%9B%B4%E6%96%B0%E6%A2%9D%E4%BB%B6%E8%AE%8A%E6%95%B8%0A%20%20%20%20return%20res%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%20res%20%3D%20while_loop%28n%29%0A%20%20%20%20print%28f%22%5Cnwhile%20%E8%BF%B4%E5%9C%88%E7%9A%84%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&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 >
2024-04-06 03:02:26 +08:00
< / details >
< p > < strong > < code > while< / code > 迴圈比 < code > for< / code > 迴圈的自由度更高< / strong > 。在 < code > while< / code > 迴圈中，我們可以自由地設計條件變數的初始化和更新步驟。< / p >
< p > 例如在以下程式碼中，條件變數 < span class = "arithmatex" > \(i\)< / span > 每輪進行兩次更新，這種情況就不太方便用 < code > for< / code > 迴圈實現：< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:14" > < input checked = "checked" id = "__tabbed_3_1" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_2" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_3" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_4" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_5" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_6" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_7" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_8" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_9" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_10" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_11" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_12" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_13" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_14" name = "__tabbed_3" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Python< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Java< / label > < label for = "__tabbed_3_4" > C#< / label > < label for = "__tabbed_3_5" > Go< / label > < label for = "__tabbed_3_6" > Swift< / label > < label for = "__tabbed_3_7" > JS< / label > < label for = "__tabbed_3_8" > TS< / label > < label for = "__tabbed_3_9" > Dart< / label > < label for = "__tabbed_3_10" > Rust< / label > < label for = "__tabbed_3_11" > C< / label > < label for = "__tabbed_3_12" > Kotlin< / label > < label for = "__tabbed_3_13" > Ruby< / label > < label for = "__tabbed_3_14" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-28-1" name = "__codelineno-28-1" href = "#__codelineno-28-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > while_loop_ii< / 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-28-2" name = "__codelineno-28-2" href = "#__codelineno-28-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " while 迴圈（兩次更新）" " " < / span >
< a id = "__codelineno-28-3" name = "__codelineno-28-3" href = "#__codelineno-28-3" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-28-4" name = "__codelineno-28-4" href = "#__codelineno-28-4" > < / a > < span class = "n" > i< / span > < span class = "o" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 初始化條件變數< / span >
< a id = "__codelineno-28-5" name = "__codelineno-28-5" href = "#__codelineno-28-5" > < / a > < span class = "c1" > # 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-28-6" name = "__codelineno-28-6" href = "#__codelineno-28-6" > < / a > < span class = "k" > while< / span > < span class = "n" > i< / span > < span class = "o" > < =< / span > < span class = "n" > n< / span > < span class = "p" > :< / span >
< a id = "__codelineno-28-7" name = "__codelineno-28-7" href = "#__codelineno-28-7" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-28-8" name = "__codelineno-28-8" href = "#__codelineno-28-8" > < / a > < span class = "c1" > # 更新條件變數< / span >
< a id = "__codelineno-28-9" name = "__codelineno-28-9" href = "#__codelineno-28-9" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-28-10" name = "__codelineno-28-10" href = "#__codelineno-28-10" > < / a > < span class = "n" > i< / span > < span class = "o" > *=< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-28-11" name = "__codelineno-28-11" href = "#__codelineno-28-11" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-29-1" name = "__codelineno-29-1" href = "#__codelineno-29-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-29-2" name = "__codelineno-29-2" href = "#__codelineno-29-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoopII< / 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-29-3" name = "__codelineno-29-3" href = "#__codelineno-29-3" > < / 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 = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-29-4" name = "__codelineno-29-4" href = "#__codelineno-29-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-29-5" name = "__codelineno-29-5" href = "#__codelineno-29-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-29-6" name = "__codelineno-29-6" href = "#__codelineno-29-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-29-7" name = "__codelineno-29-7" href = "#__codelineno-29-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-29-8" name = "__codelineno-29-8" href = "#__codelineno-29-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-29-9" name = "__codelineno-29-9" href = "#__codelineno-29-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-29-10" name = "__codelineno-29-10" href = "#__codelineno-29-10" > < / 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" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-29-11" name = "__codelineno-29-11" href = "#__codelineno-29-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-29-12" name = "__codelineno-29-12" href = "#__codelineno-29-12" > < / 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-29-13" name = "__codelineno-29-13" href = "#__codelineno-29-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-30-1" name = "__codelineno-30-1" href = "#__codelineno-30-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-30-2" name = "__codelineno-30-2" href = "#__codelineno-30-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoopII< / 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-30-3" name = "__codelineno-30-3" href = "#__codelineno-30-3" > < / 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 = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-4" name = "__codelineno-30-4" href = "#__codelineno-30-4" > < / a > < span class = "w" > < / span > < span class = "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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-30-5" name = "__codelineno-30-5" href = "#__codelineno-30-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-30-6" name = "__codelineno-30-6" href = "#__codelineno-30-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-30-7" name = "__codelineno-30-7" href = "#__codelineno-30-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-30-8" name = "__codelineno-30-8" href = "#__codelineno-30-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-30-9" name = "__codelineno-30-9" href = "#__codelineno-30-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-10" name = "__codelineno-30-10" href = "#__codelineno-30-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-11" name = "__codelineno-30-11" href = "#__codelineno-30-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-12" name = "__codelineno-30-12" href = "#__codelineno-30-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-13" name = "__codelineno-30-13" href = "#__codelineno-30-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-31-1" name = "__codelineno-31-1" href = "#__codelineno-31-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-31-2" name = "__codelineno-31-2" href = "#__codelineno-31-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > WhileLoopII< / 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-31-3" name = "__codelineno-31-3" href = "#__codelineno-31-3" > < / 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 = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-4" name = "__codelineno-31-4" href = "#__codelineno-31-4" > < / a > < span class = "w" > < / span > < span class = "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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-31-5" name = "__codelineno-31-5" href = "#__codelineno-31-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-31-6" name = "__codelineno-31-6" href = "#__codelineno-31-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-31-7" name = "__codelineno-31-7" href = "#__codelineno-31-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-31-8" name = "__codelineno-31-8" href = "#__codelineno-31-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-31-9" name = "__codelineno-31-9" href = "#__codelineno-31-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / 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 >
< a id = "__codelineno-31-10" name = "__codelineno-31-10" href = "#__codelineno-31-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-11" name = "__codelineno-31-11" href = "#__codelineno-31-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-12" name = "__codelineno-31-12" href = "#__codelineno-31-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-13" name = "__codelineno-31-13" href = "#__codelineno-31-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-32-1" name = "__codelineno-32-1" href = "#__codelineno-32-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-32-2" name = "__codelineno-32-2" href = "#__codelineno-32-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > whileLoopII< / 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-32-3" name = "__codelineno-32-3" href = "#__codelineno-32-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / 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 = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-32-5" name = "__codelineno-32-5" href = "#__codelineno-32-5" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-32-6" name = "__codelineno-32-6" href = "#__codelineno-32-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-32-7" name = "__codelineno-32-7" href = "#__codelineno-32-7" > < / 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 = "nx" > n< / 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 = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-32-9" name = "__codelineno-32-9" href = "#__codelineno-32-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-32-10" name = "__codelineno-32-10" href = "#__codelineno-32-10" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-32-11" name = "__codelineno-32-11" href = "#__codelineno-32-11" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-32-12" name = "__codelineno-32-12" href = "#__codelineno-32-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-32-13" name = "__codelineno-32-13" href = "#__codelineno-32-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-32-14" name = "__codelineno-32-14" href = "#__codelineno-32-14" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-33-1" name = "__codelineno-33-1" href = "#__codelineno-33-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-33-2" name = "__codelineno-33-2" href = "#__codelineno-33-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > whileLoopII< / 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-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > i< / span > < span class = "p" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-33-5" name = "__codelineno-33-5" href = "#__codelineno-33-5" > < / a > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / a > < span class = "k" > while< / span > < span class = "n" > i< / span > < span class = "o" > < =< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-7" name = "__codelineno-33-7" href = "#__codelineno-33-7" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-33-8" name = "__codelineno-33-8" href = "#__codelineno-33-8" > < / a > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / a > < span class = "n" > i< / span > < span class = "o" > *=< / span > < span class = "mi" > 2< / 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 = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-34-1" name = "__codelineno-34-1" href = "#__codelineno-34-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-34-2" name = "__codelineno-34-2" href = "#__codelineno-34-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > whileLoopII< / 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-34-3" name = "__codelineno-34-3" href = "#__codelineno-34-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-34-5" name = "__codelineno-34-5" href = "#__codelineno-34-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "p" > {< / span >
< a id = "__codelineno-34-7" name = "__codelineno-34-7" href = "#__codelineno-34-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-8" name = "__codelineno-34-8" href = "#__codelineno-34-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-11" name = "__codelineno-34-11" href = "#__codelineno-34-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-35-1" name = "__codelineno-35-1" href = "#__codelineno-35-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > whileLoopII< / 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-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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-35-4" name = "__codelineno-35-4" href = "#__codelineno-35-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-35-5" name = "__codelineno-35-5" href = "#__codelineno-35-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-35-6" name = "__codelineno-35-6" href = "#__codelineno-35-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "p" > {< / span >
< a id = "__codelineno-35-7" name = "__codelineno-35-7" href = "#__codelineno-35-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-8" name = "__codelineno-35-8" href = "#__codelineno-35-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-35-9" name = "__codelineno-35-9" href = "#__codelineno-35-9" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-10" name = "__codelineno-35-10" href = "#__codelineno-35-10" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-11" name = "__codelineno-35-11" href = "#__codelineno-35-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-35-12" name = "__codelineno-35-12" href = "#__codelineno-35-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-13" name = "__codelineno-35-13" href = "#__codelineno-35-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-36-1" name = "__codelineno-36-1" href = "#__codelineno-36-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-36-2" name = "__codelineno-36-2" href = "#__codelineno-36-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > whileLoopII< / 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-36-3" name = "__codelineno-36-3" href = "#__codelineno-36-3" > < / 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 = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-36-4" name = "__codelineno-36-4" href = "#__codelineno-36-4" > < / a > < span class = "w" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-36-5" name = "__codelineno-36-5" href = "#__codelineno-36-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-36-6" name = "__codelineno-36-6" href = "#__codelineno-36-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-36-7" name = "__codelineno-36-7" href = "#__codelineno-36-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-36-8" name = "__codelineno-36-8" href = "#__codelineno-36-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-36-9" name = "__codelineno-36-9" href = "#__codelineno-36-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-36-10" name = "__codelineno-36-10" href = "#__codelineno-36-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-36-11" name = "__codelineno-36-11" href = "#__codelineno-36-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-12" name = "__codelineno-36-12" href = "#__codelineno-36-12" > < / 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-36-13" name = "__codelineno-36-13" href = "#__codelineno-36-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-37-1" name = "__codelineno-37-1" href = "#__codelineno-37-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-37-2" name = "__codelineno-37-2" href = "#__codelineno-37-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > while_loop_ii< / 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-37-3" name = "__codelineno-37-3" href = "#__codelineno-37-3" > < / 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" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-4" name = "__codelineno-37-4" href = "#__codelineno-37-4" > < / 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" > 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 = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-37-5" name = "__codelineno-37-5" href = "#__codelineno-37-5" > < / a >
< a id = "__codelineno-37-6" name = "__codelineno-37-6" href = "#__codelineno-37-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-37-7" name = "__codelineno-37-7" href = "#__codelineno-37-7" > < / a > < span class = "w" > < / span > < span class = "k" > while< / 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 = "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" > res< / 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-37-9" name = "__codelineno-37-9" href = "#__codelineno-37-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-37-10" name = "__codelineno-37-10" href = "#__codelineno-37-10" > < / 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" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-11" name = "__codelineno-37-11" href = "#__codelineno-37-11" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-12" name = "__codelineno-37-12" href = "#__codelineno-37-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-13" name = "__codelineno-37-13" href = "#__codelineno-37-13" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-37-14" name = "__codelineno-37-14" href = "#__codelineno-37-14" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-38-1" name = "__codelineno-38-1" href = "#__codelineno-38-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-38-2" name = "__codelineno-38-2" href = "#__codelineno-38-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoopII< / 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-38-3" name = "__codelineno-38-3" href = "#__codelineno-38-3" > < / 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 = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-38-4" name = "__codelineno-38-4" href = "#__codelineno-38-4" > < / a > < span class = "w" > < / span > < span class = "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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-38-5" name = "__codelineno-38-5" href = "#__codelineno-38-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-38-6" name = "__codelineno-38-6" href = "#__codelineno-38-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-38-7" name = "__codelineno-38-7" href = "#__codelineno-38-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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-38-8" name = "__codelineno-38-8" href = "#__codelineno-38-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-38-9" name = "__codelineno-38-9" href = "#__codelineno-38-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-38-10" name = "__codelineno-38-10" href = "#__codelineno-38-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-38-11" name = "__codelineno-38-11" href = "#__codelineno-38-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-38-12" name = "__codelineno-38-12" href = "#__codelineno-38-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-38-13" name = "__codelineno-38-13" href = "#__codelineno-38-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-39-1" name = "__codelineno-39-1" href = "#__codelineno-39-1" > < / a > < span class = "cm" > /* while 迴圈（兩次更新） */< / span >
< a id = "__codelineno-39-2" name = "__codelineno-39-2" href = "#__codelineno-39-2" > < / a > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > whileLoopII< / 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-39-3" name = "__codelineno-39-3" href = "#__codelineno-39-3" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / 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 = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-39-5" name = "__codelineno-39-5" href = "#__codelineno-39-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-39-6" name = "__codelineno-39-6" href = "#__codelineno-39-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-39-7" name = "__codelineno-39-7" href = "#__codelineno-39-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span >
< a id = "__codelineno-39-8" name = "__codelineno-39-8" href = "#__codelineno-39-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-39-9" name = "__codelineno-39-9" href = "#__codelineno-39-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-39-10" name = "__codelineno-39-10" href = "#__codelineno-39-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "m" > 2< / span >
< a id = "__codelineno-39-11" name = "__codelineno-39-11" href = "#__codelineno-39-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-12" name = "__codelineno-39-12" href = "#__codelineno-39-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-39-13" name = "__codelineno-39-13" href = "#__codelineno-39-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-40-1" name = "__codelineno-40-1" href = "#__codelineno-40-1" > < / a > < span class = "c1" > ### while 迴圈（兩次更新）###< / span >
< a id = "__codelineno-40-2" name = "__codelineno-40-2" href = "#__codelineno-40-2" > < / a > < span class = "k" > def< / span > < span class = "w" > < / span > < span class = "nf" > while_loop_ii< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-40-3" name = "__codelineno-40-3" href = "#__codelineno-40-3" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < 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 = "w" > < / 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 = "w" > < / span > < span class = "c1" > # 初始化條件變數< / 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 = "w" > < / span > < span class = "c1" > # 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-40-7" name = "__codelineno-40-7" href = "#__codelineno-40-7" > < / a > < span class = "w" > < / span > < span class = "k" > while< / 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 >
< a id = "__codelineno-40-8" name = "__codelineno-40-8" href = "#__codelineno-40-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span >
< a id = "__codelineno-40-9" name = "__codelineno-40-9" href = "#__codelineno-40-9" > < / a > < span class = "w" > < / span > < span class = "c1" > # 更新條件變數< / span >
< a id = "__codelineno-40-10" name = "__codelineno-40-10" href = "#__codelineno-40-10" > < / 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" > 1< / span >
< a id = "__codelineno-40-11" name = "__codelineno-40-11" href = "#__codelineno-40-11" > < / 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" > 2< / span >
< a id = "__codelineno-40-12" name = "__codelineno-40-12" href = "#__codelineno-40-12" > < / a > < span class = "w" > < / span > < span class = "k" > end< / span >
< a id = "__codelineno-40-13" name = "__codelineno-40-13" href = "#__codelineno-40-13" > < / a >
< a id = "__codelineno-40-14" name = "__codelineno-40-14" href = "#__codelineno-40-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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" > < span class = "filename" > iteration.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-41-1" name = "__codelineno-41-1" href = "#__codelineno-41-1" > < / a > < span class = "c1" > // while 迴圈（兩次更新）< / span >
< a id = "__codelineno-41-2" name = "__codelineno-41-2" href = "#__codelineno-41-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > whileLoopII< / 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" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-3" name = "__codelineno-41-3" href = "#__codelineno-41-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / 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-41-4" name = "__codelineno-41-4" href = "#__codelineno-41-4" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化條件變數< / span >
< a id = "__codelineno-41-5" name = "__codelineno-41-5" href = "#__codelineno-41-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈求和 1, 4, 10, ...< / span >
< a id = "__codelineno-41-6" name = "__codelineno-41-6" href = "#__codelineno-41-6" > < / 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 = "p" > {< / span >
< a id = "__codelineno-41-7" name = "__codelineno-41-7" href = "#__codelineno-41-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-41-8" name = "__codelineno-41-8" href = "#__codelineno-41-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新條件變數< / span >
< a id = "__codelineno-41-9" name = "__codelineno-41-9" href = "#__codelineno-41-9" > < / 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" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-10" name = "__codelineno-41-10" href = "#__codelineno-41-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-11" name = "__codelineno-41-11" href = "#__codelineno-41-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-41-12" name = "__codelineno-41-12" href = "#__codelineno-41-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-13" name = "__codelineno-41-13" href = "#__codelineno-41-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
2024-04-11 01:11:27 +08:00
< p > < div style = "height: 495px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=def%20while_loop_ii%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22while%20%E8%BF%B4%E5%9C%88%EF%BC%88%E5%85%A9%E6%AC%A1%E6%9B%B4%E6%96%B0%EF%BC%89%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A2%9D%E4%BB%B6%E8%AE%8A%E6%95%B8%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E6%B1%82%E5%92%8C%201%2C%204%2C%2010%2C%20...%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20%23%20%E6%9B%B4%E6%96%B0%E6%A2%9D%E4%BB%B6%E8%AE%8A%E6%95%B8%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20i%20%2A%3D%202%0A%20%20%20%20return%20res%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%20res%20%3D%20while_loop_ii%28n%29%0A%20%20%20%20print%28f%22%5Cnwhile%20%E8%BF%B4%E5%9C%88%EF%BC%88%E5%85%A9%E6%AC%A1%E6%9B%B4%E6%96%B0%EF%BC%89%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&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%20while_loop_ii%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22while%20%E8%BF%B4%E5%9C%88%EF%BC%88%E5%85%A9%E6%AC%A1%E6%9B%B4%E6%96%B0%EF%BC%89%22%22%22%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20i%20%3D%201%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A2%9D%E4%BB%B6%E8%AE%8A%E6%95%B8%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E6%B1%82%E5%92%8C%201%2C%204%2C%2010%2C%20...%0A%20%20%20%20while%20i%20%3C%3D%20n%3A%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20i%0A%20%20%20%20%20%20%20%20%23%20%E6%9B%B4%E6%96%B0%E6%A2%9D%E4%BB%B6%E8%AE%8A%E6%95%B8%0A%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20i%20%2A%3D%202%0A%20%20%20%20return%20res%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%20res%20%3D%20while_loop_ii%28n%29%0A%20%20%20%20print%28f%22%5Cnwhile%20%E8%BF%B4%E5%9C%88%EF%BC%88%E5%85%A9%E6%AC%A1%E6%9B%B4%E6%96%B0%EF%BC%89%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&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 >
2024-04-06 03:02:26 +08:00
< / details >
< p > 總的來說，< strong > < code > for< / code > 迴圈的程式碼更加緊湊，< code > while< / code > 迴圈更加靈活< / strong > ，兩者都可以實現迭代結構。選擇使用哪一個應該根據特定問題的需求來決定。< / p >
< h3 id = "3" > 3. 巢狀迴圈< a class = "headerlink" href = "#3" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 我們可以在一個迴圈結構內巢狀另一個迴圈結構，下面以 < code > for< / code > 迴圈為例：< / 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" > iteration.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" > nested_for_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 = "o" > -> < / span > < span class = "nb" > str< / 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" > " " " 雙層 for 迴圈" " " < / span >
< a id = "__codelineno-42-3" name = "__codelineno-42-3" href = "#__codelineno-42-3" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "s2" > " " < / span >
< a id = "__codelineno-42-4" name = "__codelineno-42-4" href = "#__codelineno-42-4" > < / a > < span class = "c1" > # 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-42-5" name = "__codelineno-42-5" href = "#__codelineno-42-5" > < / 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 = "mi" > 1< / 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-42-6" name = "__codelineno-42-6" href = "#__codelineno-42-6" > < / a > < span class = "c1" > # 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-42-7" name = "__codelineno-42-7" href = "#__codelineno-42-7" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / 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-42-8" name = "__codelineno-42-8" href = "#__codelineno-42-8" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "sa" > f< / span > < span class = "s2" > " (< / span > < span class = "si" > {< / span > < span class = "n" > i< / span > < span class = "si" > }< / span > < span class = "s2" > , < / span > < span class = "si" > {< / span > < span class = "n" > j< / span > < span class = "si" > }< / span > < span class = "s2" > ), " < / span >
< a id = "__codelineno-42-9" name = "__codelineno-42-9" href = "#__codelineno-42-9" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-43-1" name = "__codelineno-43-1" href = "#__codelineno-43-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / span >
< a id = "__codelineno-43-2" name = "__codelineno-43-2" href = "#__codelineno-43-2" > < / a > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "nf" > nestedForLoop< / 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-43-3" name = "__codelineno-43-3" href = "#__codelineno-43-3" > < / a > < span class = "w" > < / span > < span class = "n" > ostringstream< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-43-4" name = "__codelineno-43-4" href = "#__codelineno-43-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-43-5" name = "__codelineno-43-5" href = "#__codelineno-43-5" > < / 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" > 1< / 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 = "o" > ++< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-43-6" name = "__codelineno-43-6" href = "#__codelineno-43-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-43-7" name = "__codelineno-43-7" href = "#__codelineno-43-7" > < / 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" > 1< / 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 = "o" > ++< / span > < span class = "n" > j< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-43-8" name = "__codelineno-43-8" href = "#__codelineno-43-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "s" > " (" < / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "s" > " , " < / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "s" > " ), " < / 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 = "p" > }< / span >
< a id = "__codelineno-43-10" name = "__codelineno-43-10" href = "#__codelineno-43-10" > < / a > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > str< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-43-12" name = "__codelineno-43-12" href = "#__codelineno-43-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-44-1" name = "__codelineno-44-1" href = "#__codelineno-44-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / span >
< a id = "__codelineno-44-2" name = "__codelineno-44-2" href = "#__codelineno-44-2" > < / a > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "nf" > nestedForLoop< / 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-44-3" name = "__codelineno-44-3" href = "#__codelineno-44-3" > < / a > < span class = "w" > < / span > < span class = "n" > StringBuilder< / span > < span class = "w" > < / span > < span class = "n" > res< / 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" > StringBuilder< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-44-4" name = "__codelineno-44-4" href = "#__codelineno-44-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-44-5" name = "__codelineno-44-5" href = "#__codelineno-44-5" > < / 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" > 1< / 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-44-6" name = "__codelineno-44-6" href = "#__codelineno-44-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-44-7" name = "__codelineno-44-7" href = "#__codelineno-44-7" > < / 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" > 1< / 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-44-8" name = "__codelineno-44-8" href = "#__codelineno-44-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > append< / span > < span class = "p" > (< / span > < span class = "s" > " (" < / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "s" > " , " < / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "s" > " ), " < / 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 = "p" > }< / span >
< a id = "__codelineno-44-10" name = "__codelineno-44-10" href = "#__codelineno-44-10" > < / a > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > toString< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-44-12" name = "__codelineno-44-12" href = "#__codelineno-44-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-45-1" name = "__codelineno-45-1" href = "#__codelineno-45-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / span >
< a id = "__codelineno-45-2" name = "__codelineno-45-2" href = "#__codelineno-45-2" > < / a > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "nf" > NestedForLoop< / 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-45-3" name = "__codelineno-45-3" href = "#__codelineno-45-3" > < / a > < span class = "w" > < / span > < span class = "n" > StringBuilder< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-45-4" name = "__codelineno-45-4" href = "#__codelineno-45-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-45-5" name = "__codelineno-45-5" href = "#__codelineno-45-5" > < / 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 = "m" > 1< / 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-45-6" name = "__codelineno-45-6" href = "#__codelineno-45-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-45-7" name = "__codelineno-45-7" href = "#__codelineno-45-7" > < / 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 = "m" > 1< / 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-45-8" name = "__codelineno-45-8" href = "#__codelineno-45-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > Append< / span > < span class = "p" > (< / span > < span class = "s" > $" ({i}, {j}), " < / 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 = "p" > }< / span >
< a id = "__codelineno-45-10" name = "__codelineno-45-10" href = "#__codelineno-45-10" > < / a > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > ToString< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-45-12" name = "__codelineno-45-12" href = "#__codelineno-45-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-46-1" name = "__codelineno-46-1" href = "#__codelineno-46-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / 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" > nestedForLoop< / 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" > string< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-3" name = "__codelineno-46-3" href = "#__codelineno-46-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "s" > " " < / span >
< a id = "__codelineno-46-4" name = "__codelineno-46-4" href = "#__codelineno-46-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-46-5" name = "__codelineno-46-5" href = "#__codelineno-46-5" > < / 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" > 1< / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-6" name = "__codelineno-46-6" href = "#__codelineno-46-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > 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 = "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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-7" name = "__codelineno-46-7" href = "#__codelineno-46-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-46-8" name = "__codelineno-46-8" href = "#__codelineno-46-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > fmt< / span > < span class = "p" > .< / span > < span class = "nx" > Sprintf< / span > < span class = "p" > (< / span > < span class = "s" > " (%d, %d), " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > j< / 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 = "p" > }< / span >
< a id = "__codelineno-46-10" name = "__codelineno-46-10" href = "#__codelineno-46-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-46-11" name = "__codelineno-46-11" href = "#__codelineno-46-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-46-12" name = "__codelineno-46-12" href = "#__codelineno-46-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-47-1" name = "__codelineno-47-1" href = "#__codelineno-47-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / span >
< a id = "__codelineno-47-2" name = "__codelineno-47-2" href = "#__codelineno-47-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > nestedForLoop< / 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" > String< / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-3" name = "__codelineno-47-3" href = "#__codelineno-47-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "s" > " " < / span >
< a id = "__codelineno-47-4" name = "__codelineno-47-4" href = "#__codelineno-47-4" > < / a > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-47-5" name = "__codelineno-47-5" href = "#__codelineno-47-5" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "mi" > 1< / span > < span class = "p" > ...< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-6" name = "__codelineno-47-6" href = "#__codelineno-47-6" > < / a > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-47-7" name = "__codelineno-47-7" href = "#__codelineno-47-7" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "k" > in< / span > < span class = "mi" > 1< / span > < span class = "p" > ...< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-8" name = "__codelineno-47-8" href = "#__codelineno-47-8" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "s" > " (< / span > < span class = "si" > \(< / span > < span class = "n" > i< / span > < span class = "si" > )< / span > < span class = "s" > , < / span > < span class = "si" > \(< / span > < span class = "n" > j< / span > < span class = "si" > )< / span > < span class = "s" > ), " < / span > < span class = "p" > )< / span >
< a id = "__codelineno-47-9" name = "__codelineno-47-9" href = "#__codelineno-47-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-10" name = "__codelineno-47-10" href = "#__codelineno-47-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-11" name = "__codelineno-47-11" href = "#__codelineno-47-11" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-47-12" name = "__codelineno-47-12" href = "#__codelineno-47-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-48-1" name = "__codelineno-48-1" href = "#__codelineno-48-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / 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" > nestedForLoop< / 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-48-3" name = "__codelineno-48-3" href = "#__codelineno-48-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' ' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-48-4" name = "__codelineno-48-4" href = "#__codelineno-48-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-48-5" name = "__codelineno-48-5" href = "#__codelineno-48-5" > < / 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" > 1< / 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-48-6" name = "__codelineno-48-6" href = "#__codelineno-48-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-48-7" name = "__codelineno-48-7" href = "#__codelineno-48-7" > < / 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" > j< / 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 = "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-48-8" name = "__codelineno-48-8" href = "#__codelineno-48-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "sb" > `(< / span > < span class = "si" > ${< / span > < span class = "nx" > i< / span > < span class = "si" > }< / span > < span class = "sb" > , < / span > < span class = "si" > ${< / span > < span class = "nx" > j< / span > < span class = "si" > }< / span > < span class = "sb" > ), `< / 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 = "p" > }< / span >
< a id = "__codelineno-48-10" name = "__codelineno-48-10" href = "#__codelineno-48-10" > < / a > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-48-12" name = "__codelineno-48-12" href = "#__codelineno-48-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-49-1" name = "__codelineno-49-1" href = "#__codelineno-49-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / 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" > nestedForLoop< / 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" > string< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-3" name = "__codelineno-49-3" href = "#__codelineno-49-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' ' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-4" name = "__codelineno-49-4" href = "#__codelineno-49-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-49-5" name = "__codelineno-49-5" href = "#__codelineno-49-5" > < / 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" > 1< / 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-49-6" name = "__codelineno-49-6" href = "#__codelineno-49-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-49-7" name = "__codelineno-49-7" href = "#__codelineno-49-7" > < / 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" > j< / 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 = "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-49-8" name = "__codelineno-49-8" href = "#__codelineno-49-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "sb" > `(< / span > < span class = "si" > ${< / span > < span class = "nx" > i< / span > < span class = "si" > }< / span > < span class = "sb" > , < / span > < span class = "si" > ${< / span > < span class = "nx" > j< / span > < span class = "si" > }< / span > < span class = "sb" > ), `< / 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 = "p" > }< / span >
< a id = "__codelineno-49-10" name = "__codelineno-49-10" href = "#__codelineno-49-10" > < / a > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-12" name = "__codelineno-49-12" href = "#__codelineno-49-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-50-1" name = "__codelineno-50-1" href = "#__codelineno-50-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / span >
< a id = "__codelineno-50-2" name = "__codelineno-50-2" href = "#__codelineno-50-2" > < / a > < span class = "kt" > String< / span > < span class = "w" > < / span > < span class = "n" > nestedForLoop< / 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-50-3" name = "__codelineno-50-3" href = "#__codelineno-50-3" > < / a > < span class = "w" > < / span > < span class = "kt" > String< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s2" > " " < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-4" name = "__codelineno-50-4" href = "#__codelineno-50-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-50-5" name = "__codelineno-50-5" href = "#__codelineno-50-5" > < / 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 = "m" > 1< / 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-50-6" name = "__codelineno-50-6" href = "#__codelineno-50-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-50-7" name = "__codelineno-50-7" href = "#__codelineno-50-7" > < / 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 = "m" > 1< / 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-50-8" name = "__codelineno-50-8" href = "#__codelineno-50-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "s2" > " (< / span > < span class = "si" > $< / span > < span class = "n" > i< / span > < span class = "s2" > , < / span > < span class = "si" > $< / span > < span class = "n" > j< / span > < span class = "s2" > ), " < / 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 = "p" > }< / span >
< a id = "__codelineno-50-10" name = "__codelineno-50-10" href = "#__codelineno-50-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-11" name = "__codelineno-50-11" href = "#__codelineno-50-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-12" name = "__codelineno-50-12" href = "#__codelineno-50-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-51-1" name = "__codelineno-51-1" href = "#__codelineno-51-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / span >
< a id = "__codelineno-51-2" name = "__codelineno-51-2" href = "#__codelineno-51-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > nested_for_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 = "nb" > String< / 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 = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "fm" > vec!< / span > < span class = "p" > [];< / span >
< a id = "__codelineno-51-4" name = "__codelineno-51-4" href = "#__codelineno-51-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-51-5" name = "__codelineno-51-5" href = "#__codelineno-51-5" > < / 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" > 1< / span > < span class = "o" > ..=< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-6" name = "__codelineno-51-6" href = "#__codelineno-51-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-51-7" name = "__codelineno-51-7" href = "#__codelineno-51-7" > < / 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" > 1< / span > < span class = "o" > ..=< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-8" name = "__codelineno-51-8" href = "#__codelineno-51-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "fm" > format!< / span > < span class = "p" > (< / span > < span class = "s" > " ({}, {}), " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-51-9" name = "__codelineno-51-9" href = "#__codelineno-51-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-10" name = "__codelineno-51-10" href = "#__codelineno-51-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-11" name = "__codelineno-51-11" href = "#__codelineno-51-11" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > join< / span > < span class = "p" > (< / span > < span class = "s" > " " < / span > < span class = "p" > )< / span >
< a id = "__codelineno-51-12" name = "__codelineno-51-12" href = "#__codelineno-51-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-52-1" name = "__codelineno-52-1" href = "#__codelineno-52-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / span >
< a id = "__codelineno-52-2" name = "__codelineno-52-2" href = "#__codelineno-52-2" > < / a > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > nestedForLoop< / 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-52-3" name = "__codelineno-52-3" href = "#__codelineno-52-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // n * n 為對應點數量，" (i, j), " 對應字串長最大為 6+10*2， < / span >
< a id = "__codelineno-52-4" name = "__codelineno-52-4" href = "#__codelineno-52-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > size< / 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" > n< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "mi" > 26< / 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-52-5" name = "__codelineno-52-5" href = "#__codelineno-52-5" > < / a > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-52-6" name = "__codelineno-52-6" href = "#__codelineno-52-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-52-7" name = "__codelineno-52-7" href = "#__codelineno-52-7" > < / 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" > 1< / 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-52-8" name = "__codelineno-52-8" href = "#__codelineno-52-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-52-9" name = "__codelineno-52-9" href = "#__codelineno-52-9" > < / 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" > 1< / 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-52-10" name = "__codelineno-52-10" href = "#__codelineno-52-10" > < / a > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "mi" > 26< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-52-11" name = "__codelineno-52-11" href = "#__codelineno-52-11" > < / a > < span class = "w" > < / span > < span class = "n" > snprintf< / span > < span class = "p" > (< / span > < span class = "n" > tmp< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > tmp< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "s" > " (%d, %d), " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / 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 = "n" > strncat< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > strlen< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-52-13" name = "__codelineno-52-13" href = "#__codelineno-52-13" > < / a > < span class = "w" > < / 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 = "p" > }< / span >
< a id = "__codelineno-52-15" name = "__codelineno-52-15" href = "#__codelineno-52-15" > < / 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-52-16" name = "__codelineno-52-16" href = "#__codelineno-52-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-53-1" name = "__codelineno-53-1" href = "#__codelineno-53-1" > < / a > < span class = "cm" > /* 雙層 for 迴圈 */< / 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" > nestedForLoop< / 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" > String< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-53-3" name = "__codelineno-53-3" href = "#__codelineno-53-3" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > StringBuilder< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-53-4" name = "__codelineno-53-4" href = "#__codelineno-53-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-53-5" name = "__codelineno-53-5" href = "#__codelineno-53-5" > < / 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" > 1.< / span > < span class = "p" > .< / span > < span class = "na" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-53-6" name = "__codelineno-53-6" href = "#__codelineno-53-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-53-7" name = "__codelineno-53-7" href = "#__codelineno-53-7" > < / 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" > 1.< / span > < span class = "p" > .< / span > < span class = "na" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-53-8" name = "__codelineno-53-8" href = "#__codelineno-53-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > append< / span > < span class = "p" > (< / span > < span class = "s" > " (< / span > < span class = "si" > $< / span > < span class = "n" > i< / span > < span class = "s" > , < / span > < span class = "si" > $< / span > < span class = "n" > j< / span > < span class = "s" > ), " < / 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 = "p" > }< / span >
< a id = "__codelineno-53-10" name = "__codelineno-53-10" href = "#__codelineno-53-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-11" name = "__codelineno-53-11" href = "#__codelineno-53-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > toString< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-53-12" name = "__codelineno-53-12" href = "#__codelineno-53-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-54-1" name = "__codelineno-54-1" href = "#__codelineno-54-1" > < / a > < span class = "c1" > ### 雙層 for 迴圈 ###< / 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" > nested_for_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-54-3" name = "__codelineno-54-3" href = "#__codelineno-54-3" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s2" > " " < / span >
< a id = "__codelineno-54-4" name = "__codelineno-54-4" href = "#__codelineno-54-4" > < / a >
< a id = "__codelineno-54-5" name = "__codelineno-54-5" href = "#__codelineno-54-5" > < / a > < span class = "w" > < / span > < span class = "c1" > # 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-54-6" name = "__codelineno-54-6" href = "#__codelineno-54-6" > < / 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" > 1< / span > < span class = "o" > ..< / span > < span class = "n" > n< / span >
< a id = "__codelineno-54-7" name = "__codelineno-54-7" href = "#__codelineno-54-7" > < / a > < span class = "w" > < / span > < span class = "c1" > # 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-54-8" name = "__codelineno-54-8" href = "#__codelineno-54-8" > < / 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" > 1< / span > < span class = "o" > ..< / span > < span class = "n" > n< / span >
< a id = "__codelineno-54-9" name = "__codelineno-54-9" href = "#__codelineno-54-9" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "s2" > " (< / span > < span class = "si" > #{< / span > < span class = "n" > i< / span > < span class = "si" > }< / span > < span class = "s2" > , < / span > < span class = "si" > #{< / span > < span class = "n" > j< / span > < span class = "si" > }< / span > < span class = "s2" > ), " < / span >
< a id = "__codelineno-54-10" name = "__codelineno-54-10" href = "#__codelineno-54-10" > < / a > < span class = "w" > < / span > < span class = "k" > end< / span >
< a id = "__codelineno-54-11" name = "__codelineno-54-11" href = "#__codelineno-54-11" > < / a > < span class = "w" > < / span > < span class = "k" > end< / span >
< a id = "__codelineno-54-12" name = "__codelineno-54-12" href = "#__codelineno-54-12" > < / a >
< a id = "__codelineno-54-13" name = "__codelineno-54-13" href = "#__codelineno-54-13" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-54-14" name = "__codelineno-54-14" href = "#__codelineno-54-14" > < / a > < span class = "k" > end< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > iteration.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-55-1" name = "__codelineno-55-1" href = "#__codelineno-55-1" > < / a > < span class = "c1" > // 雙層 for 迴圈< / 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" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "n" > allocator< / span > < span class = "o" > :< / span > < span class = "w" > < / 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" > usize< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "p" > []< / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "kt" > u8< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-3" name = "__codelineno-55-3" href = "#__codelineno-55-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / 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" > u8< / span > < span class = "p" > ).< / span > < span class = "n" > init< / span > < span class = "p" > (< / span > < span class = "n" > allocator< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-4" name = "__codelineno-55-4" href = "#__codelineno-55-4" > < / a > < span class = "w" > < / span > < span class = "k" > defer< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > deinit< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-55-5" name = "__codelineno-55-5" href = "#__codelineno-55-5" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > buffer< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "mi" > 20< / span > < span class = "p" > ]< / span > < span class = "kt" > u8< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-55-6" name = "__codelineno-55-6" href = "#__codelineno-55-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-55-7" name = "__codelineno-55-7" href = "#__codelineno-55-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > i< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-8" name = "__codelineno-55-8" href = "#__codelineno-55-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-55-9" name = "__codelineno-55-9" href = "#__codelineno-55-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > j< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-10" name = "__codelineno-55-10" href = "#__codelineno-55-10" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > _str< / 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" > bufPrint< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > buffer< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " ({d}, {d}), " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > .{< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / 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 = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > appendSlice< / span > < span class = "p" > (< / span > < span class = "n" > _str< / 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 = "p" > }< / span >
< a id = "__codelineno-55-13" name = "__codelineno-55-13" href = "#__codelineno-55-13" > < / a > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > toOwnedSlice< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-55-15" name = "__codelineno-55-15" href = "#__codelineno-55-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
2024-04-11 01:11:27 +08:00
< p > < div style = "height: 459px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=def%20nested_for_loop%28n%3A%20int%29%20-%3E%20str%3A%0A%20%20%20%20%22%22%22%E9%9B%99%E5%B1%A4%20for%20%E8%BF%B4%E5%9C%88%22%22%22%0A%20%20%20%20res%20%3D%20%22%22%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%20i%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%20j%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20f%22%28%7Bi%7D%2C%20%7Bj%7D%29%2C%20%22%0A%20%20%20%20return%20res%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%20res%20%3D%20nested_for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cn%E9%9B%99%E5%B1%A4%20for%20%E8%BF%B4%E5%9C%88%E7%9A%84%E8%B5%B0%E8%A8%AA%E7%B5%90%E6%9E%9C%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&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%20nested_for_loop%28n%3A%20int%29%20-%3E%20str%3A%0A%20%20%20%20%22%22%22%E9%9B%99%E5%B1%A4%20for%20%E8%BF%B4%E5%9C%88%22%22%22%0A%20%20%20%20res%20%3D%20%22%22%0A%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%20i%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20for%20i%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%20j%20%3D%201%2C%202%2C%20...%2C%20n-1%2C%20n%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281%2C%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20res%20%2B%3D%20f%22%28%7Bi%7D%2C%20%7Bj%7D%29%2C%20%22%0A%20%20%20%20return%20res%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%20res%20%3D%20nested_for_loop%28n%29%0A%20%20%20%20print%28f%22%5Cn%E9%9B%99%E5%B1%A4%20for%20%E8%BF%B4%E5%9C%88%E7%9A%84%E8%B5%B0%E8%A8%AA%E7%B5%90%E6%9E%9C%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&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 >
2024-04-06 03:02:26 +08:00
< / details >
< p > 圖 2-2 是該巢狀迴圈的流程框圖。< / p >
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/nested_iteration.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "巢狀迴圈的流程框圖" class = "animation-figure" src = "../iteration_and_recursion.assets/nested_iteration.png" / > < / a > < / p >
< p align = "center" > 圖 2-2 巢狀迴圈的流程框圖 < / p >
< p > 在這種情況下，函式的操作數量與 < span class = "arithmatex" > \(n^2\)< / span > 成正比，或者說演算法執行時間和輸入資料大小 < span class = "arithmatex" > \(n\)< / span > 成“平方關係”。< / p >
< p > 我們可以繼續新增巢狀迴圈，每一次巢狀都是一次“升維”，將會使時間複雜度提高至“立方關係”“四次方關係”，以此類推。< / p >
< h2 id = "222" > 2.2.2 遞迴< a class = "headerlink" href = "#222" title = "Permanent link" > ¶ < / a > < / h2 >
< p > < u > 遞迴（ ） < / u > 是一種演算法策略，透過函式呼叫自身來解決問題。它主要包含兩個階段。< / p >
< ol >
< li > < strong > 遞< / strong > ：程式不斷深入地呼叫自身，通常傳入更小或更簡化的參數，直到達到“終止條件”。< / li >
< li > < strong > 迴< / strong > ：觸發“終止條件”後，程式從最深層的遞迴函式開始逐層返回，匯聚每一層的結果。< / li >
< / ol >
< p > 而從實現的角度看，遞迴程式碼主要包含三個要素。< / p >
< ol >
< li > < strong > 終止條件< / strong > ：用於決定什麼時候由“遞”轉“迴”。< / li >
< li > < strong > 遞迴呼叫< / strong > ：對應“遞”，函式呼叫自身，通常輸入更小或更簡化的參數。< / li >
< li > < strong > 返回結果< / strong > ：對應“迴”，將當前遞迴層級的結果返回至上一層。< / li >
< / ol >
< p > 觀察以下程式碼，我們只需呼叫函式 < code > recur(n)< / code > ，就可以完成 < span class = "arithmatex" > \(1 + 2 + \dots + n\)< / span > 的計算：< / 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" > recursion.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" > 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-56-2" name = "__codelineno-56-2" href = "#__codelineno-56-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 遞迴" " " < / span >
< a id = "__codelineno-56-3" name = "__codelineno-56-3" href = "#__codelineno-56-3" > < / a > < span class = "c1" > # 終止條件< / span >
< a id = "__codelineno-56-4" name = "__codelineno-56-4" href = "#__codelineno-56-4" > < / 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-56-5" name = "__codelineno-56-5" href = "#__codelineno-56-5" > < / a > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-56-6" name = "__codelineno-56-6" href = "#__codelineno-56-6" > < / a > < span class = "c1" > # 遞：遞迴呼叫< / span >
< a id = "__codelineno-56-7" name = "__codelineno-56-7" href = "#__codelineno-56-7" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / 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 >
< a id = "__codelineno-56-8" name = "__codelineno-56-8" href = "#__codelineno-56-8" > < / a > < span class = "c1" > # 迴：返回結果< / span >
< a id = "__codelineno-56-9" name = "__codelineno-56-9" href = "#__codelineno-56-9" > < / a > < span class = "k" > return< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-57-1" name = "__codelineno-57-1" href = "#__codelineno-57-1" > < / a > < span class = "cm" > /* 遞迴 */< / span >
< a id = "__codelineno-57-2" name = "__codelineno-57-2" href = "#__codelineno-57-2" > < / 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-57-3" name = "__codelineno-57-3" href = "#__codelineno-57-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-57-4" name = "__codelineno-57-4" href = "#__codelineno-57-4" > < / 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-57-5" name = "__codelineno-57-5" href = "#__codelineno-57-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-57-6" name = "__codelineno-57-6" href = "#__codelineno-57-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-57-7" name = "__codelineno-57-7" href = "#__codelineno-57-7" > < / 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" > 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-57-8" name = "__codelineno-57-8" href = "#__codelineno-57-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-57-9" name = "__codelineno-57-9" href = "#__codelineno-57-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-57-10" name = "__codelineno-57-10" href = "#__codelineno-57-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-58-1" name = "__codelineno-58-1" href = "#__codelineno-58-1" > < / a > < span class = "cm" > /* 遞迴 */< / span >
< a id = "__codelineno-58-2" name = "__codelineno-58-2" href = "#__codelineno-58-2" > < / 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-58-3" name = "__codelineno-58-3" href = "#__codelineno-58-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-58-4" name = "__codelineno-58-4" href = "#__codelineno-58-4" > < / 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-58-5" name = "__codelineno-58-5" href = "#__codelineno-58-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-58-6" name = "__codelineno-58-6" href = "#__codelineno-58-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-58-7" name = "__codelineno-58-7" href = "#__codelineno-58-7" > < / 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" > 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-58-8" name = "__codelineno-58-8" href = "#__codelineno-58-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-58-9" name = "__codelineno-58-9" href = "#__codelineno-58-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-58-10" name = "__codelineno-58-10" href = "#__codelineno-58-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-59-1" name = "__codelineno-59-1" href = "#__codelineno-59-1" > < / a > < span class = "cm" > /* 遞迴 */< / span >
< a id = "__codelineno-59-2" name = "__codelineno-59-2" href = "#__codelineno-59-2" > < / 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-59-3" name = "__codelineno-59-3" href = "#__codelineno-59-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-59-4" name = "__codelineno-59-4" href = "#__codelineno-59-4" > < / 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-59-5" name = "__codelineno-59-5" href = "#__codelineno-59-5" > < / a > < 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-59-6" name = "__codelineno-59-6" href = "#__codelineno-59-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-59-7" name = "__codelineno-59-7" href = "#__codelineno-59-7" > < / 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" > 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-59-8" name = "__codelineno-59-8" href = "#__codelineno-59-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-59-9" name = "__codelineno-59-9" href = "#__codelineno-59-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-59-10" name = "__codelineno-59-10" href = "#__codelineno-59-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-60-1" name = "__codelineno-60-1" href = "#__codelineno-60-1" > < / a > < span class = "cm" > /* 遞迴 */< / 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" > 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 = "kt" > int< / 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" > // 終止條件< / span >
< a id = "__codelineno-60-4" name = "__codelineno-60-4" href = "#__codelineno-60-4" > < / 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-60-5" name = "__codelineno-60-5" href = "#__codelineno-60-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-60-6" name = "__codelineno-60-6" href = "#__codelineno-60-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-60-7" name = "__codelineno-60-7" href = "#__codelineno-60-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-60-8" name = "__codelineno-60-8" href = "#__codelineno-60-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / 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 = "mi" > 1< / 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 = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-60-10" name = "__codelineno-60-10" href = "#__codelineno-60-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-60-11" name = "__codelineno-60-11" href = "#__codelineno-60-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-61-1" name = "__codelineno-61-1" href = "#__codelineno-61-1" > < / a > < span class = "cm" > /* 遞迴 */< / span >
< a id = "__codelineno-61-2" name = "__codelineno-61-2" href = "#__codelineno-61-2" > < / 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 > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-61-3" name = "__codelineno-61-3" href = "#__codelineno-61-3" > < / a > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-61-4" name = "__codelineno-61-4" href = "#__codelineno-61-4" > < / 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-61-5" name = "__codelineno-61-5" href = "#__codelineno-61-5" > < / a > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-61-6" name = "__codelineno-61-6" href = "#__codelineno-61-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-61-7" name = "__codelineno-61-7" href = "#__codelineno-61-7" > < / a > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-61-8" name = "__codelineno-61-8" href = "#__codelineno-61-8" > < / a > < span class = "kd" > let< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < 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-61-9" name = "__codelineno-61-9" href = "#__codelineno-61-9" > < / a > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-61-10" name = "__codelineno-61-10" href = "#__codelineno-61-10" > < / a > < span class = "k" > return< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "n" > res< / span >
< a id = "__codelineno-61-11" name = "__codelineno-61-11" href = "#__codelineno-61-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-62-1" name = "__codelineno-62-1" href = "#__codelineno-62-1" > < / a > < span class = "cm" > /* 遞迴 */< / 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" > 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-62-3" name = "__codelineno-62-3" href = "#__codelineno-62-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-62-4" name = "__codelineno-62-4" href = "#__codelineno-62-4" > < / 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 = "w" > < / span > < span class = "mf" > 1< / 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" > // 遞：遞迴呼叫< / 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" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / 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-62-7" name = "__codelineno-62-7" href = "#__codelineno-62-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-62-8" name = "__codelineno-62-8" href = "#__codelineno-62-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-62-9" name = "__codelineno-62-9" href = "#__codelineno-62-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-63-1" name = "__codelineno-63-1" href = "#__codelineno-63-1" > < / a > < span class = "cm" > /* 遞迴 */< / 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" > 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 = "kt" > number< / 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" > // 終止條件< / span >
< a id = "__codelineno-63-4" name = "__codelineno-63-4" href = "#__codelineno-63-4" > < / 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 = "w" > < / span > < span class = "mf" > 1< / 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" > // 遞：遞迴呼叫< / 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" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / 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-63-7" name = "__codelineno-63-7" href = "#__codelineno-63-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-63-8" name = "__codelineno-63-8" href = "#__codelineno-63-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-63-9" name = "__codelineno-63-9" href = "#__codelineno-63-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-64-1" name = "__codelineno-64-1" href = "#__codelineno-64-1" > < / a > < span class = "cm" > /* 遞迴 */< / span >
< a id = "__codelineno-64-2" name = "__codelineno-64-2" href = "#__codelineno-64-2" > < / a > < span class = "kt" > int< / 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-64-3" name = "__codelineno-64-3" href = "#__codelineno-64-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-64-4" name = "__codelineno-64-4" href = "#__codelineno-64-4" > < / 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 = "w" > < / span > < span class = "m" > 1< / 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" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-64-6" name = "__codelineno-64-6" href = "#__codelineno-64-6" > < / 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" > 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-64-7" name = "__codelineno-64-7" href = "#__codelineno-64-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-64-8" name = "__codelineno-64-8" href = "#__codelineno-64-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-64-9" name = "__codelineno-64-9" href = "#__codelineno-64-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-65-1" name = "__codelineno-65-1" href = "#__codelineno-65-1" > < / a > < span class = "cm" > /* 遞迴 */< / span >
< a id = "__codelineno-65-2" name = "__codelineno-65-2" href = "#__codelineno-65-2" > < / 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 = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-65-3" name = "__codelineno-65-3" href = "#__codelineno-65-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-65-4" name = "__codelineno-65-4" href = "#__codelineno-65-4" > < / 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-65-5" name = "__codelineno-65-5" href = "#__codelineno-65-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-65-6" name = "__codelineno-65-6" href = "#__codelineno-65-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-65-7" name = "__codelineno-65-7" href = "#__codelineno-65-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-65-8" name = "__codelineno-65-8" href = "#__codelineno-65-8" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / 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" > 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-65-9" name = "__codelineno-65-9" href = "#__codelineno-65-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-65-10" name = "__codelineno-65-10" href = "#__codelineno-65-10" > < / a > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-65-11" name = "__codelineno-65-11" href = "#__codelineno-65-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-66-1" name = "__codelineno-66-1" href = "#__codelineno-66-1" > < / a > < span class = "cm" > /* 遞迴 */< / span >
< a id = "__codelineno-66-2" name = "__codelineno-66-2" href = "#__codelineno-66-2" > < / 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-66-3" name = "__codelineno-66-3" href = "#__codelineno-66-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-66-4" name = "__codelineno-66-4" href = "#__codelineno-66-4" > < / 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-66-5" name = "__codelineno-66-5" href = "#__codelineno-66-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-66-6" name = "__codelineno-66-6" href = "#__codelineno-66-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-66-7" name = "__codelineno-66-7" href = "#__codelineno-66-7" > < / 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" > 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-66-8" name = "__codelineno-66-8" href = "#__codelineno-66-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-66-9" name = "__codelineno-66-9" href = "#__codelineno-66-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-66-10" name = "__codelineno-66-10" href = "#__codelineno-66-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-67-1" name = "__codelineno-67-1" href = "#__codelineno-67-1" > < / a > < span class = "cm" > /* 遞迴 */< / 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" > 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 = "kt" > Int< / 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" > // 終止條件< / span >
< a id = "__codelineno-67-4" name = "__codelineno-67-4" href = "#__codelineno-67-4" > < / 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-67-5" name = "__codelineno-67-5" href = "#__codelineno-67-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 1< / span >
< a id = "__codelineno-67-6" name = "__codelineno-67-6" href = "#__codelineno-67-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞: 遞迴呼叫< / span >
< a id = "__codelineno-67-7" name = "__codelineno-67-7" href = "#__codelineno-67-7" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / 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-67-8" name = "__codelineno-67-8" href = "#__codelineno-67-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴: 返回結果< / span >
< a id = "__codelineno-67-9" name = "__codelineno-67-9" href = "#__codelineno-67-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-67-10" name = "__codelineno-67-10" href = "#__codelineno-67-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-68-1" name = "__codelineno-68-1" href = "#__codelineno-68-1" > < / a > < span class = "c1" > ### 遞迴 ###< / 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" > recur< / 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" > # 終止條件< / span >
< a id = "__codelineno-68-4" name = "__codelineno-68-4" href = "#__codelineno-68-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / 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-68-5" name = "__codelineno-68-5" href = "#__codelineno-68-5" > < / a > < span class = "w" > < / span > < span class = "c1" > # 遞：遞迴呼叫< / span >
< a id = "__codelineno-68-6" name = "__codelineno-68-6" href = "#__codelineno-68-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / 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-68-7" name = "__codelineno-68-7" href = "#__codelineno-68-7" > < / a > < span class = "w" > < / span > < span class = "c1" > # 迴：返回結果< / span >
< a id = "__codelineno-68-8" name = "__codelineno-68-8" href = "#__codelineno-68-8" > < / a > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-68-9" name = "__codelineno-68-9" href = "#__codelineno-68-9" > < / a > < span class = "k" > end< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-69-1" name = "__codelineno-69-1" href = "#__codelineno-69-1" > < / a > < span class = "c1" > // 遞迴函式< / 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" > recur< / 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" > i32< / 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" > // 終止條件< / span >
< a id = "__codelineno-69-4" name = "__codelineno-69-4" href = "#__codelineno-69-4" > < / 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 = "p" > {< / span >
< a id = "__codelineno-69-5" name = "__codelineno-69-5" href = "#__codelineno-69-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-69-6" name = "__codelineno-69-6" href = "#__codelineno-69-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-69-7" name = "__codelineno-69-7" href = "#__codelineno-69-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / 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" > res< / 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 = "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-69-9" name = "__codelineno-69-9" href = "#__codelineno-69-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-69-10" name = "__codelineno-69-10" href = "#__codelineno-69-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-69-11" name = "__codelineno-69-11" href = "#__codelineno-69-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
2024-04-11 01:11:27 +08:00
< p > < div style = "height: 459px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=def%20recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%81%9E%E8%BF%B4%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E6%AD%A2%E6%A2%9D%E4%BB%B6%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20%23%20%E9%81%9E%EF%BC%9A%E9%81%9E%E8%BF%B4%E5%91%BC%E5%8F%AB%0A%20%20%20%20res%20%3D%20recur%28n%20-%201%29%0A%20%20%20%20%23%20%E8%BF%B4%EF%BC%9A%E8%BF%94%E5%9B%9E%E7%B5%90%E6%9E%9C%0A%20%20%20%20return%20n%20%2B%20res%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%20res%20%3D%20recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%E9%81%9E%E8%BF%B4%E5%87%BD%E5%BC%8F%E7%9A%84%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&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%20recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E9%81%9E%E8%BF%B4%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E6%AD%A2%E6%A2%9D%E4%BB%B6%0A%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20%23%20%E9%81%9E%EF%BC%9A%E9%81%9E%E8%BF%B4%E5%91%BC%E5%8F%AB%0A%20%20%20%20res%20%3D%20recur%28n%20-%201%29%0A%20%20%20%20%23%20%E8%BF%B4%EF%BC%9A%E8%BF%94%E5%9B%9E%E7%B5%90%E6%9E%9C%0A%20%20%20%20return%20n%20%2B%20res%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%20res%20%3D%20recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%E9%81%9E%E8%BF%B4%E5%87%BD%E5%BC%8F%E7%9A%84%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&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 >
2024-04-06 03:02:26 +08:00
< / details >
< p > 圖 2-3 展示了該函式的遞迴過程。< / p >
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/recursion_sum.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "求和函式的遞迴過程" class = "animation-figure" src = "../iteration_and_recursion.assets/recursion_sum.png" / > < / a > < / p >
< p align = "center" > 圖 2-3 求和函式的遞迴過程 < / p >
< p > 雖然從計算角度看，迭代與遞迴可以得到相同的結果，< strong > 但它們代表了兩種完全不同的思考和解決問題的範式< / strong > 。< / p >
< ul >
< li > < strong > 迭代< / strong > ：“自下而上”地解決問題。從最基礎的步驟開始，然後不斷重複或累加這些步驟，直到任務完成。< / li >
< li > < strong > 遞迴< / strong > ：“自上而下”地解決問題。將原問題分解為更小的子問題，這些子問題和原問題具有相同的形式。接下來將子問題繼續分解為更小的子問題，直到基本情況時停止（基本情況的解是已知的）。< / li >
< / ul >
< p > 以上述求和函式為例，設問題 < span class = "arithmatex" > \(f(n) = 1 + 2 + \dots + n\)< / span > 。< / p >
< ul >
< li > < strong > 迭代< / strong > ：在迴圈中模擬求和過程，從 < span class = "arithmatex" > \(1\)< / span > 走訪到 < span class = "arithmatex" > \(n\)< / span > ，每輪執行求和操作，即可求得 < span class = "arithmatex" > \(f(n)\)< / span > 。< / li >
< li > < strong > 遞迴< / strong > ：將問題分解為子問題 < span class = "arithmatex" > \(f(n) = n + f(n-1)\)< / span > ，不斷（遞迴地）分解下去，直至基本情況 < span class = "arithmatex" > \(f(1) = 1\)< / span > 時終止。< / li >
< / ul >
< h3 id = "1" > 1. 呼叫堆疊< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 遞迴函式每次呼叫自身時，系統都會為新開啟的函式分配記憶體，以儲存區域性變數、呼叫位址和其他資訊等。這將導致兩方面的結果。< / p >
< ul >
< li > 函式的上下文資料都儲存在稱為“堆疊幀空間”的記憶體區域中，直至函式返回後才會被釋放。因此，< strong > 遞迴通常比迭代更加耗費記憶體空間< / strong > 。< / li >
< li > 遞迴呼叫函式會產生額外的開銷。< strong > 因此遞迴通常比迴圈的時間效率更低< / strong > 。< / li >
< / ul >
< p > 如圖 2-4 所示，在觸發終止條件前，同時存在 < span class = "arithmatex" > \(n\)< / span > 個未返回的遞迴函式，< strong > 遞迴深度為 < span class = "arithmatex" > \(n\)< / span > < / strong > 。< / p >
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/recursion_sum_depth.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "遞迴呼叫深度" class = "animation-figure" src = "../iteration_and_recursion.assets/recursion_sum_depth.png" / > < / a > < / p >
< p align = "center" > 圖 2-4 遞迴呼叫深度 < / p >
< p > 在實際中，程式語言允許的遞迴深度通常是有限的，過深的遞迴可能導致堆疊溢位錯誤。< / p >
< h3 id = "2" > 2. 尾遞迴< a class = "headerlink" href = "#2" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 有趣的是，< strong > 如果函式在返回前的最後一步才進行遞迴呼叫< / strong > ，則該函式可以被編譯器或直譯器最佳化，使其在空間效率上與迭代相當。這種情況被稱為< u > 尾遞迴（ ） < / u > 。< / p >
< ul >
< li > < strong > 普通遞迴< / strong > ：當函式返回到上一層級的函式後，需要繼續執行程式碼，因此系統需要儲存上一層呼叫的上下文。< / li >
< li > < strong > 尾遞迴< / strong > ：遞迴呼叫是函式返回前的最後一個操作，這意味著函式返回到上一層級後，無須繼續執行其他操作，因此系統無須儲存上一層函式的上下文。< / li >
< / ul >
< p > 以計算 < span class = "arithmatex" > \(1 + 2 + \dots + n\)< / span > 為例，我們可以將結果變數 < code > res< / code > 設為函式參數，從而實現尾遞迴：< / 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" > recursion.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" > tail_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > res< / 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" > " " " 尾遞迴" " " < / span >
< a id = "__codelineno-70-3" name = "__codelineno-70-3" href = "#__codelineno-70-3" > < / a > < span class = "c1" > # 終止條件< / 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" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-70-5" name = "__codelineno-70-5" href = "#__codelineno-70-5" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-70-6" name = "__codelineno-70-6" href = "#__codelineno-70-6" > < / a > < span class = "c1" > # 尾遞迴呼叫< / span >
< a id = "__codelineno-70-7" name = "__codelineno-70-7" href = "#__codelineno-70-7" > < / a > < span class = "k" > return< / span > < span class = "n" > tail_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "o" > +< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< / code > < / pre > < / div >
< / div >
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< div class = "highlight" > < span class = "filename" > recursion.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-71-1" name = "__codelineno-71-1" href = "#__codelineno-71-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / span >
< a id = "__codelineno-71-2" name = "__codelineno-71-2" href = "#__codelineno-71-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > tailRecur< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-3" name = "__codelineno-71-3" href = "#__codelineno-71-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / 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 = "w" > < / span > < span class = "n" > res< / 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 = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-71-7" name = "__codelineno-71-7" href = "#__codelineno-71-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / 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 = "n" > res< / 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-71-8" name = "__codelineno-71-8" href = "#__codelineno-71-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
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< div class = "highlight" > < span class = "filename" > recursion.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-72-1" name = "__codelineno-72-1" href = "#__codelineno-72-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / span >
< a id = "__codelineno-72-2" name = "__codelineno-72-2" href = "#__codelineno-72-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > tailRecur< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-72-3" name = "__codelineno-72-3" href = "#__codelineno-72-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / 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 = "w" > < / span > < span class = "n" > res< / 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 = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-72-7" name = "__codelineno-72-7" href = "#__codelineno-72-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / 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 = "n" > res< / 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-72-8" name = "__codelineno-72-8" href = "#__codelineno-72-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
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< div class = "highlight" > < span class = "filename" > recursion.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-73-1" name = "__codelineno-73-1" href = "#__codelineno-73-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / span >
< a id = "__codelineno-73-2" name = "__codelineno-73-2" href = "#__codelineno-73-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > TailRecur< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-3" name = "__codelineno-73-3" href = "#__codelineno-73-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-73-6" name = "__codelineno-73-6" href = "#__codelineno-73-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-73-7" name = "__codelineno-73-7" href = "#__codelineno-73-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > TailRecur< / 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 = "n" > res< / 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-73-8" name = "__codelineno-73-8" href = "#__codelineno-73-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
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< div class = "highlight" > < span class = "filename" > recursion.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-74-1" name = "__codelineno-74-1" href = "#__codelineno-74-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / 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" > tailRecur< / 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 = "nx" > res< / 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-74-3" name = "__codelineno-74-3" href = "#__codelineno-74-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / 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 > < span class = "w" > < / span > < span class = "nx" > res< / 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 = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-74-8" name = "__codelineno-74-8" href = "#__codelineno-74-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > +< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-74-9" name = "__codelineno-74-9" href = "#__codelineno-74-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-75-1" name = "__codelineno-75-1" href = "#__codelineno-75-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / span >
< a id = "__codelineno-75-2" name = "__codelineno-75-2" href = "#__codelineno-75-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > tailRecur< / 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 = "n" > res< / 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-75-3" name = "__codelineno-75-3" href = "#__codelineno-75-3" > < / a > < span class = "c1" > // 終止條件< / 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" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-75-5" name = "__codelineno-75-5" href = "#__codelineno-75-5" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / 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 = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-75-8" name = "__codelineno-75-8" href = "#__codelineno-75-8" > < / a > < span class = "k" > return< / span > < span class = "n" > tailRecur< / 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 > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "n" > res< / span > < span class = "o" > +< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-75-9" name = "__codelineno-75-9" href = "#__codelineno-75-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-76-1" name = "__codelineno-76-1" href = "#__codelineno-76-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / 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" > tailRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-76-3" name = "__codelineno-76-3" href = "#__codelineno-76-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-76-5" name = "__codelineno-76-5" href = "#__codelineno-76-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-76-6" name = "__codelineno-76-6" href = "#__codelineno-76-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / 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 = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-76-7" name = "__codelineno-76-7" href = "#__codelineno-76-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-77-1" name = "__codelineno-77-1" href = "#__codelineno-77-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / 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" > tailRecur< / 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 = "w" > < / span > < span class = "nx" > res< / 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-77-3" name = "__codelineno-77-3" href = "#__codelineno-77-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-5" name = "__codelineno-77-5" href = "#__codelineno-77-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-77-6" name = "__codelineno-77-6" href = "#__codelineno-77-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / 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 = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-7" name = "__codelineno-77-7" href = "#__codelineno-77-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-78-1" name = "__codelineno-78-1" href = "#__codelineno-78-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / span >
< a id = "__codelineno-78-2" name = "__codelineno-78-2" href = "#__codelineno-78-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-3" name = "__codelineno-78-3" href = "#__codelineno-78-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / span > < span class = "p" > )< / span > < 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-78-5" name = "__codelineno-78-5" href = "#__codelineno-78-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-78-6" name = "__codelineno-78-6" href = "#__codelineno-78-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / 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 = "n" > res< / 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-78-7" name = "__codelineno-78-7" href = "#__codelineno-78-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-79-1" name = "__codelineno-79-1" href = "#__codelineno-79-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / span >
< a id = "__codelineno-79-2" name = "__codelineno-79-2" href = "#__codelineno-79-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > tail_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 = "n" > res< / 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-79-3" name = "__codelineno-79-3" href = "#__codelineno-79-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / 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 = "w" > < / span > < span class = "n" > res< / 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 = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-79-8" name = "__codelineno-79-8" href = "#__codelineno-79-8" > < / a > < span class = "w" > < / span > < span class = "n" > tail_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 > < span class = "w" > < / span > < span class = "n" > res< / 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-79-9" name = "__codelineno-79-9" href = "#__codelineno-79-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-80-1" name = "__codelineno-80-1" href = "#__codelineno-80-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / span >
< a id = "__codelineno-80-2" name = "__codelineno-80-2" href = "#__codelineno-80-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > tailRecur< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-80-3" name = "__codelineno-80-3" href = "#__codelineno-80-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / 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 = "w" > < / span > < span class = "n" > res< / 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 = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-80-7" name = "__codelineno-80-7" href = "#__codelineno-80-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / 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 = "n" > res< / 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-80-8" name = "__codelineno-80-8" href = "#__codelineno-80-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-81-1" name = "__codelineno-81-1" href = "#__codelineno-81-1" > < / a > < span class = "cm" > /* 尾遞迴 */< / span >
< a id = "__codelineno-81-2" name = "__codelineno-81-2" href = "#__codelineno-81-2" > < / a > < span class = "kd" > tailrec< / span > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > tailRecur< / 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" > res< / 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-81-3" name = "__codelineno-81-3" href = "#__codelineno-81-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 新增 tailrec 關鍵詞，以開啟尾遞迴最佳化< / span >
< a id = "__codelineno-81-4" name = "__codelineno-81-4" href = "#__codelineno-81-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / span >
< a id = "__codelineno-81-5" name = "__codelineno-81-5" href = "#__codelineno-81-5" > < / 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-81-6" name = "__codelineno-81-6" href = "#__codelineno-81-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-81-7" name = "__codelineno-81-7" href = "#__codelineno-81-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-81-8" name = "__codelineno-81-8" href = "#__codelineno-81-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / 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 = "n" > res< / 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-81-9" name = "__codelineno-81-9" href = "#__codelineno-81-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-82-1" name = "__codelineno-82-1" href = "#__codelineno-82-1" > < / a > < span class = "c1" > ### 尾遞迴 ###< / 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" > tail_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / 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 = "c1" > # 終止條件< / 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 = "n" > res< / 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-82-5" name = "__codelineno-82-5" href = "#__codelineno-82-5" > < / a > < span class = "w" > < / span > < span class = "c1" > # 尾遞迴呼叫< / span >
< a id = "__codelineno-82-6" name = "__codelineno-82-6" href = "#__codelineno-82-6" > < / a > < span class = "w" > < / span > < span class = "n" > tail_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 > < span class = "w" > < / span > < span class = "n" > res< / 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-82-7" name = "__codelineno-82-7" href = "#__codelineno-82-7" > < / a > < span class = "k" > end< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-83-1" name = "__codelineno-83-1" href = "#__codelineno-83-1" > < / a > < span class = "c1" > // 尾遞迴函式< / 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" > tailRecur< / 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 = "n" > res< / 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-83-3" name = "__codelineno-83-3" href = "#__codelineno-83-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件< / 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" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-83-6" name = "__codelineno-83-6" href = "#__codelineno-83-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-83-7" name = "__codelineno-83-7" href = "#__codelineno-83-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾遞迴呼叫< / span >
< a id = "__codelineno-83-8" name = "__codelineno-83-8" href = "#__codelineno-83-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / 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 = "n" > res< / 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-83-9" name = "__codelineno-83-9" href = "#__codelineno-83-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
2024-04-11 01:11:27 +08:00
< p > < div style = "height: 423px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=def%20tail_recur%28n%2C%20res%29%3A%0A%20%20%20%20%22%22%22%E5%B0%BE%E9%81%9E%E8%BF%B4%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E6%AD%A2%E6%A2%9D%E4%BB%B6%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20res%0A%20%20%20%20%23%20%E5%B0%BE%E9%81%9E%E8%BF%B4%E5%91%BC%E5%8F%AB%0A%20%20%20%20return%20tail_recur%28n%20-%201%2C%20res%20%2B%20n%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%20res%20%3D%20tail_recur%28n%2C%200%29%0A%20%20%20%20print%28f%22%5Cn%E5%B0%BE%E9%81%9E%E8%BF%B4%E5%87%BD%E5%BC%8F%E7%9A%84%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&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%20tail_recur%28n%2C%20res%29%3A%0A%20%20%20%20%22%22%22%E5%B0%BE%E9%81%9E%E8%BF%B4%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E6%AD%A2%E6%A2%9D%E4%BB%B6%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%20res%0A%20%20%20%20%23%20%E5%B0%BE%E9%81%9E%E8%BF%B4%E5%91%BC%E5%8F%AB%0A%20%20%20%20return%20tail_recur%28n%20-%201%2C%20res%20%2B%20n%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%20res%20%3D%20tail_recur%28n%2C%200%29%0A%20%20%20%20print%28f%22%5Cn%E5%B0%BE%E9%81%9E%E8%BF%B4%E5%87%BD%E5%BC%8F%E7%9A%84%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&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 >
2024-04-06 03:02:26 +08:00
< / details >
< p > 尾遞迴的執行過程如圖 2-5 所示。對比普通遞迴和尾遞迴，兩者的求和操作的執行點是不同的。< / p >
< ul >
< li > < strong > 普通遞迴< / strong > ：求和操作是在“迴”的過程中執行的，每層返回後都要再執行一次求和操作。< / li >
< li > < strong > 尾遞迴< / strong > ：求和操作是在“遞”的過程中執行的，“迴”的過程只需層層返回。< / li >
< / ul >
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/tail_recursion_sum.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "尾遞迴過程" class = "animation-figure" src = "../iteration_and_recursion.assets/tail_recursion_sum.png" / > < / a > < / p >
< p align = "center" > 圖 2-5 尾遞迴過程 < / p >
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > 請注意， ， < / p >
< / div >
< h3 id = "3_1" > 3. 遞迴樹< a class = "headerlink" href = "#3_1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 當處理與“分治”相關的演算法問題時，遞迴往往比迭代的思路更加直觀、程式碼更加易讀。以“費波那契數列”為例。< / p >
< div class = "admonition question" >
< p class = "admonition-title" > Question< / p >
< p > 給定一個費波那契數列 < span class = "arithmatex" > \(0, 1, 1, 2, 3, 5, 8, 13, \dots\)< / span > ，求該數列的第 < span class = "arithmatex" > \(n\)< / span > 個數字。< / p >
< / div >
< p > 設費波那契數列的第 < span class = "arithmatex" > \(n\)< / span > 個數字為 < span class = "arithmatex" > \(f(n)\)< / span > ，易得兩個結論。< / p >
< ul >
< li > 數列的前兩個數字為 < span class = "arithmatex" > \(f(1) = 0\)< / span > 和 < span class = "arithmatex" > \(f(2) = 1\)< / span > 。< / li >
< li > 數列中的每個數字是前兩個數字的和，即 < span class = "arithmatex" > \(f(n) = f(n - 1) + f(n - 2)\)< / span > 。< / li >
< / ul >
< p > 按照遞推關係進行遞迴呼叫，將前兩個數字作為終止條件，便可寫出遞迴程式碼。呼叫 < code > fib(n)< / code > 即可得到費波那契數列的第 < span class = "arithmatex" > \(n\)< / span > 個數字：< / 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" > recursion.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" > fib< / 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-84-2" name = "__codelineno-84-2" href = "#__codelineno-84-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 費波那契數列：遞迴" " " < / span >
< a id = "__codelineno-84-3" name = "__codelineno-84-3" href = "#__codelineno-84-3" > < / a > < span class = "c1" > # 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-84-4" name = "__codelineno-84-4" href = "#__codelineno-84-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 1< / span > < span class = "ow" > or< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 2< / span > < span class = "p" > :< / span >
< a id = "__codelineno-84-5" name = "__codelineno-84-5" href = "#__codelineno-84-5" > < / a > < span class = "k" > return< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-84-6" name = "__codelineno-84-6" href = "#__codelineno-84-6" > < / a > < span class = "c1" > # 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-84-7" name = "__codelineno-84-7" href = "#__codelineno-84-7" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "o" > +< / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-84-8" name = "__codelineno-84-8" href = "#__codelineno-84-8" > < / a > < span class = "c1" > # 返回結果 f(n)< / span >
< a id = "__codelineno-84-9" name = "__codelineno-84-9" href = "#__codelineno-84-9" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-85-1" name = "__codelineno-85-1" href = "#__codelineno-85-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / span >
< a id = "__codelineno-85-2" name = "__codelineno-85-2" href = "#__codelineno-85-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > fib< / 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" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-85-4" name = "__codelineno-85-4" href = "#__codelineno-85-4" > < / 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 = "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 = "mi" > 2< / 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" > return< / 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-85-6" name = "__codelineno-85-6" href = "#__codelineno-85-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-85-7" name = "__codelineno-85-7" href = "#__codelineno-85-7" > < / 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" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > 2< / 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 = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-85-9" name = "__codelineno-85-9" href = "#__codelineno-85-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-85-10" name = "__codelineno-85-10" href = "#__codelineno-85-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-86-1" name = "__codelineno-86-1" href = "#__codelineno-86-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / span >
< a id = "__codelineno-86-2" name = "__codelineno-86-2" href = "#__codelineno-86-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > fib< / 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" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-86-4" name = "__codelineno-86-4" href = "#__codelineno-86-4" > < / 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 = "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 = "mi" > 2< / 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 = "k" > return< / 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-86-6" name = "__codelineno-86-6" href = "#__codelineno-86-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-86-7" name = "__codelineno-86-7" href = "#__codelineno-86-7" > < / 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" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > 2< / 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 = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-86-9" name = "__codelineno-86-9" href = "#__codelineno-86-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-86-10" name = "__codelineno-86-10" href = "#__codelineno-86-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-87-1" name = "__codelineno-87-1" href = "#__codelineno-87-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / span >
< a id = "__codelineno-87-2" name = "__codelineno-87-2" href = "#__codelineno-87-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > Fib< / 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" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-87-4" name = "__codelineno-87-4" href = "#__codelineno-87-4" > < / 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 = "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 = "m" > 2< / 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 = "k" > return< / span > < span class = "w" > < / 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-87-6" name = "__codelineno-87-6" href = "#__codelineno-87-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-87-7" name = "__codelineno-87-7" href = "#__codelineno-87-7" > < / 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" > Fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > Fib< / 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" > 2< / 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 = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-87-9" name = "__codelineno-87-9" href = "#__codelineno-87-9" > < / 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-87-10" name = "__codelineno-87-10" href = "#__codelineno-87-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-88-1" name = "__codelineno-88-1" href = "#__codelineno-88-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / 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" > fib< / 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-88-3" name = "__codelineno-88-3" href = "#__codelineno-88-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-88-4" name = "__codelineno-88-4" href = "#__codelineno-88-4" > < / 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 = "o" > ||< / 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" > 2< / span > < span class = "w" > < / 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" > return< / 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 >
< a id = "__codelineno-88-6" name = "__codelineno-88-6" href = "#__codelineno-88-6" > < / a > < span class = "w" > < / 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 = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-88-8" name = "__codelineno-88-8" href = "#__codelineno-88-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-88-9" name = "__codelineno-88-9" href = "#__codelineno-88-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-88-10" name = "__codelineno-88-10" href = "#__codelineno-88-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-88-11" name = "__codelineno-88-11" href = "#__codelineno-88-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-89-1" name = "__codelineno-89-1" href = "#__codelineno-89-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / span >
< a id = "__codelineno-89-2" name = "__codelineno-89-2" href = "#__codelineno-89-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > fib< / 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-89-3" name = "__codelineno-89-3" href = "#__codelineno-89-3" > < / a > < span class = "c1" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-89-4" name = "__codelineno-89-4" href = "#__codelineno-89-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 1< / span > < span class = "o" > ||< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 2< / span > < span class = "p" > {< / span >
< a id = "__codelineno-89-5" name = "__codelineno-89-5" href = "#__codelineno-89-5" > < / a > < span class = "k" > return< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-89-6" name = "__codelineno-89-6" href = "#__codelineno-89-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-89-7" name = "__codelineno-89-7" href = "#__codelineno-89-7" > < / a > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-89-8" name = "__codelineno-89-8" href = "#__codelineno-89-8" > < / a > < span class = "kd" > let< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "n" > fib< / 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 > < span class = "o" > +< / span > < span class = "n" > fib< / 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" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-89-9" name = "__codelineno-89-9" href = "#__codelineno-89-9" > < / a > < span class = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-89-10" name = "__codelineno-89-10" href = "#__codelineno-89-10" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-89-11" name = "__codelineno-89-11" href = "#__codelineno-89-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-90-1" name = "__codelineno-90-1" href = "#__codelineno-90-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / 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" > fib< / 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" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-90-4" name = "__codelineno-90-4" href = "#__codelineno-90-4" > < / 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 = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / 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-90-5" name = "__codelineno-90-5" href = "#__codelineno-90-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-90-6" name = "__codelineno-90-6" href = "#__codelineno-90-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > fib< / 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" > 2< / 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" > // 返回結果 f(n)< / span >
< a id = "__codelineno-90-8" name = "__codelineno-90-8" href = "#__codelineno-90-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-90-9" name = "__codelineno-90-9" href = "#__codelineno-90-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-91-1" name = "__codelineno-91-1" href = "#__codelineno-91-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / 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" > fib< / 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-91-3" name = "__codelineno-91-3" href = "#__codelineno-91-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-91-4" name = "__codelineno-91-4" href = "#__codelineno-91-4" > < / 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 = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / 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-91-5" name = "__codelineno-91-5" href = "#__codelineno-91-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-91-6" name = "__codelineno-91-6" href = "#__codelineno-91-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > fib< / 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" > 2< / 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" > // 返回結果 f(n)< / span >
< a id = "__codelineno-91-8" name = "__codelineno-91-8" href = "#__codelineno-91-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-91-9" name = "__codelineno-91-9" href = "#__codelineno-91-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-92-1" name = "__codelineno-92-1" href = "#__codelineno-92-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / span >
< a id = "__codelineno-92-2" name = "__codelineno-92-2" href = "#__codelineno-92-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-92-4" name = "__codelineno-92-4" href = "#__codelineno-92-4" > < / 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 = "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 = "m" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / 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-92-5" name = "__codelineno-92-5" href = "#__codelineno-92-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-92-6" name = "__codelineno-92-6" href = "#__codelineno-92-6" > < / 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" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > 2< / 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 = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-92-8" name = "__codelineno-92-8" href = "#__codelineno-92-8" > < / 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-92-9" name = "__codelineno-92-9" href = "#__codelineno-92-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-93-1" name = "__codelineno-93-1" href = "#__codelineno-93-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / span >
< a id = "__codelineno-93-2" name = "__codelineno-93-2" href = "#__codelineno-93-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > fib< / 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-93-3" name = "__codelineno-93-3" href = "#__codelineno-93-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-93-4" name = "__codelineno-93-4" href = "#__codelineno-93-4" > < / 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 = "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 = "mi" > 2< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-93-5" name = "__codelineno-93-5" href = "#__codelineno-93-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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-93-6" name = "__codelineno-93-6" href = "#__codelineno-93-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-93-7" name = "__codelineno-93-7" href = "#__codelineno-93-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-93-8" name = "__codelineno-93-8" href = "#__codelineno-93-8" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / 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" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > 2< / 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 = "c1" > // 返回結果< / span >
< a id = "__codelineno-93-10" name = "__codelineno-93-10" href = "#__codelineno-93-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-93-11" name = "__codelineno-93-11" href = "#__codelineno-93-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-94-1" name = "__codelineno-94-1" href = "#__codelineno-94-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / span >
< a id = "__codelineno-94-2" name = "__codelineno-94-2" href = "#__codelineno-94-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > fib< / 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" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-94-4" name = "__codelineno-94-4" href = "#__codelineno-94-4" > < / 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 = "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 = "mi" > 2< / 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" > return< / 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-94-6" name = "__codelineno-94-6" href = "#__codelineno-94-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-94-7" name = "__codelineno-94-7" href = "#__codelineno-94-7" > < / 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" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > 2< / 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 = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-94-9" name = "__codelineno-94-9" href = "#__codelineno-94-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-94-10" name = "__codelineno-94-10" href = "#__codelineno-94-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-95-1" name = "__codelineno-95-1" href = "#__codelineno-95-1" > < / a > < span class = "cm" > /* 費波那契數列：遞迴 */< / 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" > fib< / 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-95-3" name = "__codelineno-95-3" href = "#__codelineno-95-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-95-4" name = "__codelineno-95-4" href = "#__codelineno-95-4" > < / 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 = "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 = "m" > 2< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span >
< a id = "__codelineno-95-6" name = "__codelineno-95-6" href = "#__codelineno-95-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-95-7" name = "__codelineno-95-7" href = "#__codelineno-95-7" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > 2< / 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 = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-95-9" name = "__codelineno-95-9" href = "#__codelineno-95-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-95-10" name = "__codelineno-95-10" href = "#__codelineno-95-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-96-1" name = "__codelineno-96-1" href = "#__codelineno-96-1" > < / a > < span class = "c1" > ### 費波那契數列：遞迴 ###< / 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" > fib< / 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" > # 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-96-4" name = "__codelineno-96-4" href = "#__codelineno-96-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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 = "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 = "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 = "mi" > 2< / span >
< a id = "__codelineno-96-5" name = "__codelineno-96-5" href = "#__codelineno-96-5" > < / a > < span class = "w" > < / span > < span class = "c1" > # 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-96-6" name = "__codelineno-96-6" href = "#__codelineno-96-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-96-7" name = "__codelineno-96-7" href = "#__codelineno-96-7" > < / a > < span class = "w" > < / span > < span class = "c1" > # 返回結果 f(n)< / span >
< a id = "__codelineno-96-8" name = "__codelineno-96-8" href = "#__codelineno-96-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-96-9" name = "__codelineno-96-9" href = "#__codelineno-96-9" > < / a > < span class = "k" > end< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-97-1" name = "__codelineno-97-1" href = "#__codelineno-97-1" > < / a > < span class = "c1" > // 費波那契數列< / 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" > fib< / 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" > i32< / 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" > // 終止條件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-97-4" name = "__codelineno-97-4" href = "#__codelineno-97-4" > < / 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 = "w" > < / span > < span class = "k" > or< / 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" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / 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" > return< / 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-97-6" name = "__codelineno-97-6" href = "#__codelineno-97-6" > < / a > < span class = "w" > < / 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 = "c1" > // 遞迴呼叫 f(n) = f(n-1) + f(n-2)< / 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" > res< / 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 = "n" > fib< / 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 = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / 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" > 2< / 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 = "c1" > // 返回結果 f(n)< / span >
< a id = "__codelineno-97-10" name = "__codelineno-97-10" href = "#__codelineno-97-10" > < / 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-97-11" name = "__codelineno-97-11" href = "#__codelineno-97-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
2024-04-11 01:11:27 +08:00
< p > < div style = "height: 459px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=def%20fib%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E8%B2%BB%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8%E5%88%97%EF%BC%9A%E9%81%9E%E8%BF%B4%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E6%AD%A2%E6%A2%9D%E4%BB%B6%20f%281%29%20%3D%200%2C%20f%282%29%20%3D%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%20-%201%0A%20%20%20%20%23%20%E9%81%9E%E8%BF%B4%E5%91%BC%E5%8F%AB%20f%28n%29%20%3D%20f%28n-1%29%20%2B%20f%28n-2%29%0A%20%20%20%20res%20%3D%20fib%28n%20-%201%29%20%2B%20fib%28n%20-%202%29%0A%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E7%B5%90%E6%9E%9C%20f%28n%29%0A%20%20%20%20return%20res%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%20res%20%3D%20fib%28n%29%0A%20%20%20%20print%28f%22%5Cn%E8%B2%BB%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8%E5%88%97%E7%9A%84%E7%AC%AC%20%7Bn%7D%20%E9%A0%85%E7%82%BA%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&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%20fib%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E8%B2%BB%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8%E5%88%97%EF%BC%9A%E9%81%9E%E8%BF%B4%22%22%22%0A%20%20%20%20%23%20%E7%B5%82%E6%AD%A2%E6%A2%9D%E4%BB%B6%20f%281%29%20%3D%200%2C%20f%282%29%20%3D%201%0A%20%20%20%20if%20n%20%3D%3D%201%20or%20n%20%3D%3D%202%3A%0A%20%20%20%20%20%20%20%20return%20n%20-%201%0A%20%20%20%20%23%20%E9%81%9E%E8%BF%B4%E5%91%BC%E5%8F%AB%20f%28n%29%20%3D%20f%28n-1%29%20%2B%20f%28n-2%29%0A%20%20%20%20res%20%3D%20fib%28n%20-%201%29%20%2B%20fib%28n%20-%202%29%0A%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E7%B5%90%E6%9E%9C%20f%28n%29%0A%20%20%20%20return%20res%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%20res%20%3D%20fib%28n%29%0A%20%20%20%20print%28f%22%5Cn%E8%B2%BB%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B8%E5%88%97%E7%9A%84%E7%AC%AC%20%7Bn%7D%20%E9%A0%85%E7%82%BA%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&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 >
2024-04-06 03:02:26 +08:00
< / details >
< p > 觀察以上程式碼，我們在函式內遞迴呼叫了兩個函式，< strong > 這意味著從一個呼叫產生了兩個呼叫分支< / strong > 。如圖 2-6 所示，這樣不斷遞迴呼叫下去，最終將產生一棵層數為 < span class = "arithmatex" > \(n\)< / span > 的< u > 遞迴樹（ ） < / u > 。< / p >
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/recursion_tree.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "費波那契數列的遞迴樹" class = "animation-figure" src = "../iteration_and_recursion.assets/recursion_tree.png" / > < / a > < / p >
< p align = "center" > 圖 2-6 費波那契數列的遞迴樹 < / p >
< p > 從本質上看，遞迴體現了“將問題分解為更小子問題”的思維範式，這種分治策略至關重要。< / p >
< ul >
< li > 從演算法角度看，搜尋、排序、回溯、分治、動態規劃等許多重要演算法策略直接或間接地應用了這種思維方式。< / li >
< li > 從資料結構角度看，遞迴天然適合處理鏈結串列、樹和圖的相關問題，因為它們非常適合用分治思想進行分析。< / li >
< / ul >
< h2 id = "223" > 2.2.3 兩者對比< a class = "headerlink" href = "#223" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 總結以上內容，如表 2-1 所示，迭代和遞迴在實現、效能和適用性上有所不同。< / p >
< p align = "center" > 表 2-1 迭代與遞迴特點對比 < / p >
< div class = "center-table" >
< table >
< thead >
< tr >
< th > < / th >
< th > 迭代< / th >
< th > 遞迴< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > 實現方式< / td >
< td > 迴圈結構< / td >
< td > 函式呼叫自身< / td >
< / tr >
< tr >
< td > 時間效率< / td >
< td > 效率通常較高，無函式呼叫開銷< / td >
< td > 每次函式呼叫都會產生開銷< / td >
< / tr >
< tr >
< td > 記憶體使用< / td >
< td > 通常使用固定大小的記憶體空間< / td >
< td > 累積函式呼叫可能使用大量的堆疊幀空間< / td >
< / tr >
< tr >
< td > 適用問題< / td >
< td > 適用於簡單迴圈任務，程式碼直觀、可讀性好< / td >
< td > 適用於子問題分解，如樹、圖、分治、回溯等，程式碼結構簡潔、清晰< / td >
< / tr >
< / tbody >
< / table >
< / div >
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > 如果感覺以下內容理解困難，可以在讀完“堆疊”章節後再來複習。< / p >
< / div >
< p > 那麼，迭代和遞迴具有什麼內在關聯呢？以上述遞迴函式為例，求和操作在遞迴的“迴”階段進行。這意味著最初被呼叫的函式實際上是最後完成其求和操作的，< strong > 這種工作機制與堆疊的“先入後出”原則異曲同工< / strong > 。< / p >
< p > 事實上，“呼叫堆疊”和“堆疊幀空間”這類遞迴術語已經暗示了遞迴與堆疊之間的密切關係。< / p >
< ol >
< li > < strong > 遞< / strong > ：當函式被呼叫時，系統會在“呼叫堆疊”上為該函式分配新的堆疊幀，用於儲存函式的區域性變數、參數、返回位址等資料。< / li >
< li > < strong > 迴< / strong > ：當函式完成執行並返回時，對應的堆疊幀會被從“呼叫堆疊”上移除，恢復之前函式的執行環境。< / li >
< / ol >
< p > 因此，< strong > 我們可以使用一個顯式的堆疊來模擬呼叫堆疊的行為< / strong > ，從而將遞迴轉化為迭代形式：< / 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" > recursion.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" > for_loop_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" > " " " 使用迭代模擬遞迴" " " < / span >
< a id = "__codelineno-98-3" name = "__codelineno-98-3" href = "#__codelineno-98-3" > < / a > < span class = "c1" > # 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-98-4" name = "__codelineno-98-4" href = "#__codelineno-98-4" > < / a > < span class = "n" > stack< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-98-5" name = "__codelineno-98-5" href = "#__codelineno-98-5" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-98-6" name = "__codelineno-98-6" href = "#__codelineno-98-6" > < / a > < span class = "c1" > # 遞：遞迴呼叫< / span >
< a id = "__codelineno-98-7" name = "__codelineno-98-7" href = "#__codelineno-98-7" > < / 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 > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-98-8" name = "__codelineno-98-8" href = "#__codelineno-98-8" > < / a > < span class = "c1" > # 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-98-9" name = "__codelineno-98-9" href = "#__codelineno-98-9" > < / a > < span class = "n" > stack< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-98-10" name = "__codelineno-98-10" href = "#__codelineno-98-10" > < / a > < span class = "c1" > # 迴：返回結果< / span >
< a id = "__codelineno-98-11" name = "__codelineno-98-11" href = "#__codelineno-98-11" > < / a > < span class = "k" > while< / span > < span class = "n" > stack< / span > < span class = "p" > :< / span >
< a id = "__codelineno-98-12" name = "__codelineno-98-12" href = "#__codelineno-98-12" > < / a > < span class = "c1" > # 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-98-13" name = "__codelineno-98-13" href = "#__codelineno-98-13" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > stack< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-98-14" name = "__codelineno-98-14" href = "#__codelineno-98-14" > < / a > < span class = "c1" > # res = 1+2+3+...+n< / span >
< a id = "__codelineno-98-15" name = "__codelineno-98-15" href = "#__codelineno-98-15" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-99-1" name = "__codelineno-99-1" href = "#__codelineno-99-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / 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" > forLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-99-4" name = "__codelineno-99-4" href = "#__codelineno-99-4" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > stack< / 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 = "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 = "mi" > 0< / 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 = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-99-7" name = "__codelineno-99-7" href = "#__codelineno-99-7" > < / 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 = "n" > n< / 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 = "mi" > 0< / 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-99-8" name = "__codelineno-99-8" href = "#__codelineno-99-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-99-9" name = "__codelineno-99-9" href = "#__codelineno-99-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-99-10" name = "__codelineno-99-10" href = "#__codelineno-99-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-99-11" name = "__codelineno-99-11" href = "#__codelineno-99-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-99-12" name = "__codelineno-99-12" href = "#__codelineno-99-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > empty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-99-13" name = "__codelineno-99-13" href = "#__codelineno-99-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-99-14" name = "__codelineno-99-14" href = "#__codelineno-99-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > top< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-99-15" name = "__codelineno-99-15" href = "#__codelineno-99-15" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-99-16" name = "__codelineno-99-16" href = "#__codelineno-99-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-99-17" name = "__codelineno-99-17" href = "#__codelineno-99-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-99-18" name = "__codelineno-99-18" href = "#__codelineno-99-18" > < / 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-99-19" name = "__codelineno-99-19" href = "#__codelineno-99-19" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-100-1" name = "__codelineno-100-1" href = "#__codelineno-100-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / 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" > forLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-100-4" name = "__codelineno-100-4" href = "#__codelineno-100-4" > < / a > < span class = "w" > < / span > < span class = "n" > Stack< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > stack< / 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" > Stack< / span > < span class = "o" > < > < / 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 = "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 = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-100-6" name = "__codelineno-100-6" href = "#__codelineno-100-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-100-7" name = "__codelineno-100-7" href = "#__codelineno-100-7" > < / 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 = "n" > n< / 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 = "mi" > 0< / 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-100-8" name = "__codelineno-100-8" href = "#__codelineno-100-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-100-9" name = "__codelineno-100-9" href = "#__codelineno-100-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-100-10" name = "__codelineno-100-10" href = "#__codelineno-100-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-100-11" name = "__codelineno-100-11" href = "#__codelineno-100-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-100-12" name = "__codelineno-100-12" href = "#__codelineno-100-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > isEmpty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-100-13" name = "__codelineno-100-13" href = "#__codelineno-100-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-100-14" name = "__codelineno-100-14" href = "#__codelineno-100-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-100-15" name = "__codelineno-100-15" href = "#__codelineno-100-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-100-16" name = "__codelineno-100-16" href = "#__codelineno-100-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-100-17" name = "__codelineno-100-17" href = "#__codelineno-100-17" > < / 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-100-18" name = "__codelineno-100-18" href = "#__codelineno-100-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-101-1" name = "__codelineno-101-1" href = "#__codelineno-101-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / 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" > ForLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-101-4" name = "__codelineno-101-4" href = "#__codelineno-101-4" > < / a > < span class = "w" > < / span > < span class = "n" > Stack< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / 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 = "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 = "m" > 0< / 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 = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-101-7" name = "__codelineno-101-7" href = "#__codelineno-101-7" > < / 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 = "n" > n< / 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 = "m" > 0< / 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-101-8" name = "__codelineno-101-8" href = "#__codelineno-101-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-101-9" name = "__codelineno-101-9" href = "#__codelineno-101-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > Push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-101-10" name = "__codelineno-101-10" href = "#__codelineno-101-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-101-11" name = "__codelineno-101-11" href = "#__codelineno-101-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-101-12" name = "__codelineno-101-12" href = "#__codelineno-101-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-101-13" name = "__codelineno-101-13" href = "#__codelineno-101-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-101-14" name = "__codelineno-101-14" href = "#__codelineno-101-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > Pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-101-15" name = "__codelineno-101-15" href = "#__codelineno-101-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-101-16" name = "__codelineno-101-16" href = "#__codelineno-101-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-101-17" name = "__codelineno-101-17" href = "#__codelineno-101-17" > < / 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-101-18" name = "__codelineno-101-18" href = "#__codelineno-101-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-102-1" name = "__codelineno-102-1" href = "#__codelineno-102-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / 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" > forLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-102-4" name = "__codelineno-102-4" href = "#__codelineno-102-4" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > list< / span > < span class = "p" > .< / span > < span class = "nx" > New< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-102-5" name = "__codelineno-102-5" href = "#__codelineno-102-5" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-102-6" name = "__codelineno-102-6" href = "#__codelineno-102-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-102-7" name = "__codelineno-102-7" href = "#__codelineno-102-7" > < / 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 = "nx" > n< / 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 = "mi" > 0< / 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-102-8" name = "__codelineno-102-8" href = "#__codelineno-102-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-102-9" name = "__codelineno-102-9" href = "#__codelineno-102-9" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > PushBack< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-102-10" name = "__codelineno-102-10" href = "#__codelineno-102-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-102-11" name = "__codelineno-102-11" href = "#__codelineno-102-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-102-12" name = "__codelineno-102-12" href = "#__codelineno-102-12" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > Len< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-102-13" name = "__codelineno-102-13" href = "#__codelineno-102-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-102-14" name = "__codelineno-102-14" href = "#__codelineno-102-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > Back< / span > < span class = "p" > ().< / span > < span class = "nx" > Value< / span > < span class = "p" > .(< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span >
< a id = "__codelineno-102-15" name = "__codelineno-102-15" href = "#__codelineno-102-15" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > Remove< / span > < span class = "p" > (< / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > Back< / span > < span class = "p" > ())< / span >
< a id = "__codelineno-102-16" name = "__codelineno-102-16" href = "#__codelineno-102-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-102-17" name = "__codelineno-102-17" href = "#__codelineno-102-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-102-18" name = "__codelineno-102-18" href = "#__codelineno-102-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-102-19" name = "__codelineno-102-19" href = "#__codelineno-102-19" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-103-1" name = "__codelineno-103-1" href = "#__codelineno-103-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / span >
< a id = "__codelineno-103-2" name = "__codelineno-103-2" href = "#__codelineno-103-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > forLoopRecur< / 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-103-3" name = "__codelineno-103-3" href = "#__codelineno-103-3" > < / a > < span class = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-103-4" name = "__codelineno-103-4" href = "#__codelineno-103-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > stack< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-103-5" name = "__codelineno-103-5" href = "#__codelineno-103-5" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-103-6" name = "__codelineno-103-6" href = "#__codelineno-103-6" > < / a > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-103-7" name = "__codelineno-103-7" href = "#__codelineno-103-7" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ...< / span > < span class = "n" > n< / span > < span class = "p" > ).< / span > < span class = "n" > reversed< / span > < span class = "p" > ()< / span > < span class = "p" > {< / span >
< a id = "__codelineno-103-8" name = "__codelineno-103-8" href = "#__codelineno-103-8" > < / a > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-103-9" name = "__codelineno-103-9" href = "#__codelineno-103-9" > < / a > < span class = "n" > stack< / 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-103-10" name = "__codelineno-103-10" href = "#__codelineno-103-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-103-11" name = "__codelineno-103-11" href = "#__codelineno-103-11" > < / a > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-103-12" name = "__codelineno-103-12" href = "#__codelineno-103-12" > < / a > < span class = "k" > while< / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "bp" > isEmpty< / span > < span class = "p" > {< / span >
< a id = "__codelineno-103-13" name = "__codelineno-103-13" href = "#__codelineno-103-13" > < / a > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-103-14" name = "__codelineno-103-14" href = "#__codelineno-103-14" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-103-15" name = "__codelineno-103-15" href = "#__codelineno-103-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-103-16" name = "__codelineno-103-16" href = "#__codelineno-103-16" > < / a > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-103-17" name = "__codelineno-103-17" href = "#__codelineno-103-17" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-103-18" name = "__codelineno-103-18" href = "#__codelineno-103-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-104-1" name = "__codelineno-104-1" href = "#__codelineno-104-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / 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" > forLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / 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" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / 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 = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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-104-6" name = "__codelineno-104-6" href = "#__codelineno-104-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-104-7" name = "__codelineno-104-7" href = "#__codelineno-104-7" > < / 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 = "nx" > n< / 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 = "mf" > 0< / 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-104-8" name = "__codelineno-104-8" href = "#__codelineno-104-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-104-9" name = "__codelineno-104-9" href = "#__codelineno-104-9" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-104-10" name = "__codelineno-104-10" href = "#__codelineno-104-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-104-11" name = "__codelineno-104-11" href = "#__codelineno-104-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-104-12" name = "__codelineno-104-12" href = "#__codelineno-104-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-104-13" name = "__codelineno-104-13" href = "#__codelineno-104-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-104-14" name = "__codelineno-104-14" href = "#__codelineno-104-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-104-15" name = "__codelineno-104-15" href = "#__codelineno-104-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-104-16" name = "__codelineno-104-16" href = "#__codelineno-104-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-104-17" name = "__codelineno-104-17" href = "#__codelineno-104-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-104-18" name = "__codelineno-104-18" href = "#__codelineno-104-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-105-1" name = "__codelineno-105-1" href = "#__codelineno-105-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / 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" > forLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊 < / 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" > stack< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / 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 = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / 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-105-6" name = "__codelineno-105-6" href = "#__codelineno-105-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-105-7" name = "__codelineno-105-7" href = "#__codelineno-105-7" > < / 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 = "nx" > n< / 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 = "mf" > 0< / 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-105-8" name = "__codelineno-105-8" href = "#__codelineno-105-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-105-9" name = "__codelineno-105-9" href = "#__codelineno-105-9" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-105-10" name = "__codelineno-105-10" href = "#__codelineno-105-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-105-11" name = "__codelineno-105-11" href = "#__codelineno-105-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-105-12" name = "__codelineno-105-12" href = "#__codelineno-105-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-105-13" name = "__codelineno-105-13" href = "#__codelineno-105-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-105-14" name = "__codelineno-105-14" href = "#__codelineno-105-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-105-15" name = "__codelineno-105-15" href = "#__codelineno-105-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-105-16" name = "__codelineno-105-16" href = "#__codelineno-105-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-105-17" name = "__codelineno-105-17" href = "#__codelineno-105-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-105-18" name = "__codelineno-105-18" href = "#__codelineno-105-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-106-1" name = "__codelineno-106-1" href = "#__codelineno-106-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / 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" > forLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / 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" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / 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 = "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 = "m" > 0< / 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 = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-106-7" name = "__codelineno-106-7" href = "#__codelineno-106-7" > < / 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 = "n" > n< / 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 = "m" > 0< / 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-106-8" name = "__codelineno-106-8" href = "#__codelineno-106-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-106-9" name = "__codelineno-106-9" href = "#__codelineno-106-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-106-10" name = "__codelineno-106-10" href = "#__codelineno-106-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-106-11" name = "__codelineno-106-11" href = "#__codelineno-106-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-106-12" name = "__codelineno-106-12" href = "#__codelineno-106-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > isEmpty< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-106-13" name = "__codelineno-106-13" href = "#__codelineno-106-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-106-14" name = "__codelineno-106-14" href = "#__codelineno-106-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > removeLast< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-106-15" name = "__codelineno-106-15" href = "#__codelineno-106-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-106-16" name = "__codelineno-106-16" href = "#__codelineno-106-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-106-17" name = "__codelineno-106-17" href = "#__codelineno-106-17" > < / 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-106-18" name = "__codelineno-106-18" href = "#__codelineno-106-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-107-1" name = "__codelineno-107-1" href = "#__codelineno-107-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / span >
< a id = "__codelineno-107-2" name = "__codelineno-107-2" href = "#__codelineno-107-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > for_loop_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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-107-4" name = "__codelineno-107-4" href = "#__codelineno-107-4" > < / 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" > stack< / 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-107-5" name = "__codelineno-107-5" href = "#__codelineno-107-5" > < / 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" > res< / 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-107-6" name = "__codelineno-107-6" href = "#__codelineno-107-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-107-7" name = "__codelineno-107-7" href = "#__codelineno-107-7" > < / 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 = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "o" > ..=< / span > < span class = "n" > n< / span > < span class = "p" > ).< / span > < span class = "n" > rev< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-107-8" name = "__codelineno-107-8" href = "#__codelineno-107-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-107-9" name = "__codelineno-107-9" href = "#__codelineno-107-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-107-10" name = "__codelineno-107-10" href = "#__codelineno-107-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-107-11" name = "__codelineno-107-11" href = "#__codelineno-107-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-107-12" name = "__codelineno-107-12" href = "#__codelineno-107-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > is_empty< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-107-13" name = "__codelineno-107-13" href = "#__codelineno-107-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-107-14" name = "__codelineno-107-14" href = "#__codelineno-107-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ().< / span > < span class = "n" > unwrap< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-107-15" name = "__codelineno-107-15" href = "#__codelineno-107-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-107-16" name = "__codelineno-107-16" href = "#__codelineno-107-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-107-17" name = "__codelineno-107-17" href = "#__codelineno-107-17" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-107-18" name = "__codelineno-107-18" href = "#__codelineno-107-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-108-1" name = "__codelineno-108-1" href = "#__codelineno-108-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / 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" > forLoopRecur< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "mi" > 1000< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 藉助一個大陣列來模擬堆疊< / span >
< a id = "__codelineno-108-4" name = "__codelineno-108-4" href = "#__codelineno-108-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > top< / 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 = "c1" > // 堆疊頂索引< / 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 = "n" > res< / 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-108-6" name = "__codelineno-108-6" href = "#__codelineno-108-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-108-7" name = "__codelineno-108-7" href = "#__codelineno-108-7" > < / 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 = "n" > n< / 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 = "mi" > 0< / 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-108-8" name = "__codelineno-108-8" href = "#__codelineno-108-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-108-9" name = "__codelineno-108-9" href = "#__codelineno-108-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > top< / span > < span class = "o" > ++< / 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 >
< a id = "__codelineno-108-10" name = "__codelineno-108-10" href = "#__codelineno-108-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-108-11" name = "__codelineno-108-11" href = "#__codelineno-108-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-108-12" name = "__codelineno-108-12" href = "#__codelineno-108-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > top< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-108-13" name = "__codelineno-108-13" href = "#__codelineno-108-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-108-14" name = "__codelineno-108-14" href = "#__codelineno-108-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "n" > top< / span > < span class = "o" > --< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-108-15" name = "__codelineno-108-15" href = "#__codelineno-108-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-108-16" name = "__codelineno-108-16" href = "#__codelineno-108-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-108-17" name = "__codelineno-108-17" href = "#__codelineno-108-17" > < / 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-108-18" name = "__codelineno-108-18" href = "#__codelineno-108-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-109-1" name = "__codelineno-109-1" href = "#__codelineno-109-1" > < / a > < span class = "cm" > /* 使用迭代模擬遞迴 */< / span >
< a id = "__codelineno-109-2" name = "__codelineno-109-2" href = "#__codelineno-109-2" > < / a > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > forLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-109-4" name = "__codelineno-109-4" href = "#__codelineno-109-4" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Stack< / span > < span class = "o" > < < / span > < span class = "kt" > Int< / span > < span class = "o" > > < / span > < span class = "p" > ()< / span >
< a id = "__codelineno-109-5" name = "__codelineno-109-5" href = "#__codelineno-109-5" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span >
< a id = "__codelineno-109-6" name = "__codelineno-109-6" href = "#__codelineno-109-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞: 遞迴呼叫< / span >
< a id = "__codelineno-109-7" name = "__codelineno-109-7" href = "#__codelineno-109-7" > < / 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 = "n" > n< / span > < span class = "w" > < / span > < span class = "n" > downTo< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2024-04-13 21:17:50 +08:00
< a id = "__codelineno-109-8" name = "__codelineno-109-8" href = "#__codelineno-109-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-109-9" name = "__codelineno-109-9" href = "#__codelineno-109-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-109-10" name = "__codelineno-109-10" href = "#__codelineno-109-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-109-11" name = "__codelineno-109-11" href = "#__codelineno-109-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴: 返回結果< / span >
< a id = "__codelineno-109-12" name = "__codelineno-109-12" href = "#__codelineno-109-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > isNotEmpty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-109-13" name = "__codelineno-109-13" href = "#__codelineno-109-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 透過“出堆疊操作”模擬“迴”< / span >
< a id = "__codelineno-109-14" name = "__codelineno-109-14" href = "#__codelineno-109-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-109-15" name = "__codelineno-109-15" href = "#__codelineno-109-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-109-16" name = "__codelineno-109-16" href = "#__codelineno-109-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-109-17" name = "__codelineno-109-17" href = "#__codelineno-109-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-109-18" name = "__codelineno-109-18" href = "#__codelineno-109-18" > < / a > < span class = "p" > }< / span >
2024-04-06 03:02:26 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-110-1" name = "__codelineno-110-1" href = "#__codelineno-110-1" > < / a > < span class = "c1" > ### 使用迭代模擬遞迴 ###< / 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" > for_loop_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 = "c1" > # 使用一個顯式的堆疊來模擬系統呼叫堆疊< / span >
< a id = "__codelineno-110-4" name = "__codelineno-110-4" href = "#__codelineno-110-4" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "o" > []< / span >
< a id = "__codelineno-110-5" name = "__codelineno-110-5" href = "#__codelineno-110-5" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-110-6" name = "__codelineno-110-6" href = "#__codelineno-110-6" > < / a >
< a id = "__codelineno-110-7" name = "__codelineno-110-7" href = "#__codelineno-110-7" > < / a > < span class = "w" > < / span > < span class = "c1" > # 遞：遞迴呼叫< / span >
< a id = "__codelineno-110-8" name = "__codelineno-110-8" href = "#__codelineno-110-8" > < / 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 = "n" > n< / span > < span class = "o" > .< / span > < span class = "n" > downto< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-110-9" name = "__codelineno-110-9" href = "#__codelineno-110-9" > < / a > < span class = "w" > < / span > < span class = "c1" > # 透過“入堆疊操作”模擬“遞”< / span >
< a id = "__codelineno-110-10" name = "__codelineno-110-10" href = "#__codelineno-110-10" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "n" > i< / span >
< a id = "__codelineno-110-11" name = "__codelineno-110-11" href = "#__codelineno-110-11" > < / a > < span class = "w" > < / span > < span class = "k" > end< / span >
< a id = "__codelineno-110-12" name = "__codelineno-110-12" href = "#__codelineno-110-12" > < / a > < span class = "w" > < / span > < span class = "c1" > # 迴：返回結果< / span >
< a id = "__codelineno-110-13" name = "__codelineno-110-13" href = "#__codelineno-110-13" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "o" > .< / span > < span class = "n" > empty?< / span >
< a id = "__codelineno-110-14" name = "__codelineno-110-14" href = "#__codelineno-110-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span >
< a id = "__codelineno-110-15" name = "__codelineno-110-15" href = "#__codelineno-110-15" > < / a > < span class = "w" > < / span > < span class = "k" > end< / span >
< a id = "__codelineno-110-16" name = "__codelineno-110-16" href = "#__codelineno-110-16" > < / a >
< a id = "__codelineno-110-17" name = "__codelineno-110-17" href = "#__codelineno-110-17" > < / a > < span class = "w" > < / span > < span class = "c1" > # res = 1+2+3+...+n< / span >
< a id = "__codelineno-110-18" name = "__codelineno-110-18" href = "#__codelineno-110-18" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-110-19" name = "__codelineno-110-19" href = "#__codelineno-110-19" > < / a > < span class = "k" > end< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > recursion.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-111-1" name = "__codelineno-111-1" href = "#__codelineno-111-1" > < / a > < span class = "c1" > // 使用迭代模擬遞迴< / 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" > forLoopRecur< / 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 = "c1" > // 使用一個顯式的堆疊來模擬系統呼叫堆疊< / 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" > stack< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ]< / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / 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 = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / 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-111-6" name = "__codelineno-111-6" href = "#__codelineno-111-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遞：遞迴呼叫< / span >
< a id = "__codelineno-111-7" name = "__codelineno-111-7" href = "#__codelineno-111-7" > < / 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" > usize< / 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-111-8" name = "__codelineno-111-8" href = "#__codelineno-111-8" > < / 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 = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-111-9" name = "__codelineno-111-9" href = "#__codelineno-111-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / 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 = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-111-10" name = "__codelineno-111-10" href = "#__codelineno-111-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / 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-111-11" name = "__codelineno-111-11" href = "#__codelineno-111-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-111-12" name = "__codelineno-111-12" href = "#__codelineno-111-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴：返回結果< / span >
< a id = "__codelineno-111-13" name = "__codelineno-111-13" href = "#__codelineno-111-13" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > index< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > usize< / 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-111-14" name = "__codelineno-111-14" href = "#__codelineno-111-14" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > index< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-111-15" name = "__codelineno-111-15" href = "#__codelineno-111-15" > < / a > < span class = "w" > < / span > < span class = "n" > index< / 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-111-16" name = "__codelineno-111-16" href = "#__codelineno-111-16" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "n" > index< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-111-17" name = "__codelineno-111-17" href = "#__codelineno-111-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-111-18" name = "__codelineno-111-18" href = "#__codelineno-111-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-111-19" name = "__codelineno-111-19" href = "#__codelineno-111-19" > < / 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-111-20" name = "__codelineno-111-20" href = "#__codelineno-111-20" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
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< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
2024-04-11 01:11:27 +08:00
< p > < div style = "height: 549px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=def%20for_loop_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BD%BF%E7%94%A8%E8%BF%AD%E4%BB%A3%E6%A8%A1%E6%93%AC%E9%81%9E%E8%BF%B4%22%22%22%0A%20%20%20%20%23%20%E4%BD%BF%E7%94%A8%E4%B8%80%E5%80%8B%E9%A1%AF%E5%BC%8F%E7%9A%84%E5%A0%86%E7%96%8A%E4%BE%86%E6%A8%A1%E6%93%AC%E7%B3%BB%E7%B5%B1%E5%91%BC%E5%8F%AB%E5%A0%86%E7%96%8A%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%20%E9%81%9E%EF%BC%9A%E9%81%9E%E8%BF%B4%E5%91%BC%E5%8F%AB%0A%20%20%20%20for%20i%20in%20range%28n%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%80%8F%E9%81%8E%E2%80%9C%E5%85%A5%E5%A0%86%E7%96%8A%E6%93%8D%E4%BD%9C%E2%80%9D%E6%A8%A1%E6%93%AC%E2%80%9C%E9%81%9E%E2%80%9D%0A%20%20%20%20%20%20%20%20stack.append%28i%29%0A%20%20%20%20%23%20%E8%BF%B4%EF%BC%9A%E8%BF%94%E5%9B%9E%E7%B5%90%E6%9E%9C%0A%20%20%20%20while%20stack%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%80%8F%E9%81%8E%E2%80%9C%E5%87%BA%E5%A0%86%E7%96%8A%E6%93%8D%E4%BD%9C%E2%80%9D%E6%A8%A1%E6%93%AC%E2%80%9C%E8%BF%B4%E2%80%9D%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20stack.pop%28%29%0A%20%20%20%20%23%20res%20%3D%201%2B2%2B3%2B...%2Bn%0A%20%20%20%20return%20res%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%20res%20%3D%20for_loop_recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%E4%BD%BF%E7%94%A8%E8%BF%AD%E4%BB%A3%E6%A8%A1%E6%93%AC%E9%81%9E%E8%BF%B4%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&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%20for_loop_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%BD%BF%E7%94%A8%E8%BF%AD%E4%BB%A3%E6%A8%A1%E6%93%AC%E9%81%9E%E8%BF%B4%22%22%22%0A%20%20%20%20%23%20%E4%BD%BF%E7%94%A8%E4%B8%80%E5%80%8B%E9%A1%AF%E5%BC%8F%E7%9A%84%E5%A0%86%E7%96%8A%E4%BE%86%E6%A8%A1%E6%93%AC%E7%B3%BB%E7%B5%B1%E5%91%BC%E5%8F%AB%E5%A0%86%E7%96%8A%0A%20%20%20%20stack%20%3D%20%5B%5D%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%20%E9%81%9E%EF%BC%9A%E9%81%9E%E8%BF%B4%E5%91%BC%E5%8F%AB%0A%20%20%20%20for%20i%20in%20range%28n%2C%200%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%80%8F%E9%81%8E%E2%80%9C%E5%85%A5%E5%A0%86%E7%96%8A%E6%93%8D%E4%BD%9C%E2%80%9D%E6%A8%A1%E6%93%AC%E2%80%9C%E9%81%9E%E2%80%9D%0A%20%20%20%20%20%20%20%20stack.append%28i%29%0A%20%20%20%20%23%20%E8%BF%B4%EF%BC%9A%E8%BF%94%E5%9B%9E%E7%B5%90%E6%9E%9C%0A%20%20%20%20while%20stack%3A%0A%20%20%20%20%20%20%20%20%23%20%E9%80%8F%E9%81%8E%E2%80%9C%E5%87%BA%E5%A0%86%E7%96%8A%E6%93%8D%E4%BD%9C%E2%80%9D%E6%A8%A1%E6%93%AC%E2%80%9C%E8%BF%B4%E2%80%9D%0A%20%20%20%20%20%20%20%20res%20%2B%3D%20stack.pop%28%29%0A%20%20%20%20%23%20res%20%3D%201%2B2%2B3%2B...%2Bn%0A%20%20%20%20return%20res%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%20res%20%3D%20for_loop_recur%28n%29%0A%20%20%20%20print%28f%22%5Cn%E4%BD%BF%E7%94%A8%E8%BF%AD%E4%BB%A3%E6%A8%A1%E6%93%AC%E9%81%9E%E8%BF%B4%E6%B1%82%E5%92%8C%E7%B5%90%E6%9E%9C%20res%20%3D%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&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 >
2024-04-06 03:02:26 +08:00
< / details >
< p > 觀察以上程式碼，當遞迴轉化為迭代後，程式碼變得更加複雜了。儘管迭代和遞迴在很多情況下可以互相轉化，但不一定值得這樣做，有以下兩點原因。< / p >
< ul >
< li > 轉化後的程式碼可能更加難以理解，可讀性更差。< / li >
< li > 對於某些複雜問題，模擬系統呼叫堆疊的行為可能非常困難。< / li >
< / ul >
< p > 總之，< strong > 選擇迭代還是遞迴取決於特定問題的性質< / strong > 。在程式設計實踐中，權衡兩者的優劣並根據情境選擇合適的方法至關重要。< / p >
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< script id = "__config" type = "application/json" > { "base" : "../.." , "features" : [ "announce.dismiss" , "content.action.edit" , "content.code.annotate" , "content.code.copy" , "content.tabs.link" , "content.tooltips" , "navigation.indexes" , "navigation.top" , "navigation.footer" , "navigation.tracking" , "search.highlight" , "search.share" , "search.suggest" , "toc.follow" ] , "search" : "../../assets/javascripts/workers/search.b8dbb3d2.min.js" , "translations" : { "clipboard.copied" : "\u5df2\u62f7\u8c9d" , "clipboard.copy" : "\u62f7\u8c9d" , "search.result.more.one" : "\u6b64\u9801\u5c1a\u6709 1 \u500b\u7b26\u5408\u7684\u9805\u76ee" , "search.result.more.other" : "\u6b64\u9801\u5c1a\u6709 # \u500b\u7b26\u5408\u7684\u9805\u76ee" , "search.result.none" : "\u6c92\u6709\u627e\u5230\u7b26\u5408\u689d\u4ef6\u7684\u7d50\u679c" , "search.result.one" : "\u627e\u5230 1 \u4e2a\u7b26\u5408\u689d\u4ef6\u7684\u7d50\u679c" , "search.result.other" : "\u627e\u5230 # \u500b\u7b26\u5408\u689d\u4ef6\u7684\u7d50\u679c" , "search.result.placeholder" : "\u9375\u5165\u4ee5\u958b\u59cb\u6aa2\u7d22" , "search.result.term.missing" : "\u7f3a\u5931" , "select.version" : "\u9078\u64c7\u7248\u672c" } } < / script >
< script src = "../../assets/javascripts/bundle.c18c5fb9.min.js" > < / script >
< script src = "../../javascripts/mathjax.js" > < / script >
< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
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< script src = "https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js" > < / script >
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< script > document $ . subscribe ( ( ) => { const lightbox = GLightbox ( { "touchNavigation" : true , "loop" : false , "zoomable" : true , "draggable" : false , "openEffect" : "zoom" , "closeEffect" : "zoom" , "slideEffect" : "none" } ) ; } ) < / script > < / body >
< / html >
