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第 0 章 前言
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第 0 章 前言
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0.1 关于本书
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0.2 如何使用本书
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0.3 小结
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z" / > < / svg >
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第 1 章 初识算法
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第 1 章 初识算法
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1.1 算法无处不在
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1.2 算法是什么
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1.3 小结
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第 2 章 复杂度分析
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第 2 章 复杂度分析
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2.1 算法效率评估
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2.2 迭代与递归
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2.3 时间复杂度
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2.4 空间复杂度
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2.5 小结
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第 3 章 数据结构
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第 3 章 数据结构
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3.1 数据结构分类
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3.2 基本数据类型
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3.3 数字编码 *
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3.4 字符编码 *
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3.5 小结
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第 4 章 数组与链表
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第 4 章 数组与链表
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4.1 数组
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4.2 链表
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4.3 列表
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第 5 章 栈与队列
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5.3 双向队列
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5.4 小结
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第 6 章 哈希表
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6.1 哈希表
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6.2 哈希冲突
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6.3 哈希算法
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6.4 小结
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第 7 章 树
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第 7 章 树
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7.1 二叉树
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7.2 二叉树遍历
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7.3 二叉树数组表示
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7.4 二叉搜索树
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7.5 AVL 树 *
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7.6 小结
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第 8 章 堆
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< label class = "md-nav__title" for = "__nav_9" >
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第 8 章 堆
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
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8.1 堆
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8.2 建堆操作
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< / span >
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< li class = "md-nav__item" >
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8.3 Top-K 问题
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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8.4 小结
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< / span >
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< / a >
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< div class = "md-nav__link md-nav__container" >
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
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第 9 章 图
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< / span >
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第 9 章 图
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
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9.1 图
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< / span >
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< / a >
< / li >
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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 图基础操作
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
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9.3 图的遍历
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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9.4 小结
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< / span >
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< / a >
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< / li >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_searching/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z" / > < / svg >
< span class = "md-ellipsis" >
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第 10 章 搜索
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< / span >
< / a >
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< span class = "md-nav__icon md-icon" > < / span >
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第 10 章 搜索
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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10.1 二分查找
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_insertion/" class = "md-nav__link" >
< span class = "md-ellipsis" >
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10.2 二分查找插入点
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< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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10.3 二分查找边界
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< / span >
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< span class = "md-status md-status--new" title = "最近添加" >
< / span >
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< / a >
< / li >
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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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< span class = "md-ellipsis" >
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10.4 哈希优化策略
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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10.5 重识搜索算法
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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10.6 小结
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< / span >
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< / a >
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< / ul >
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< / li >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z" / > < / svg >
< span class = "md-ellipsis" >
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第 11 章 排序
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< / 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" >
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第 11 章 排序
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
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11.1 排序算法
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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11.2 选择排序
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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11.3 冒泡排序
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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11.4 插入排序
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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11.5 快速排序
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< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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11.6 归并排序
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< / span >
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< / a >
< / li >
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11.7 堆排序
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11.8 桶排序
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11.9 计数排序
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11.10 基数排序
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11.11 小结
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第 12 章 分治
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第 12 章 分治
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12.1 分治算法
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12.4 汉诺塔问题
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12.4 汉诺塔问题
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目录
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1. 考虑基本情况
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12.5 小结
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第 13 章 回溯
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第 13 章 回溯
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13.1 回溯算法
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13.2 全排列问题
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13.4 N 皇后问题
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13.5 小结
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第 14 章 动态规划
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第 14 章 动态规划
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14.1 初探动态规划
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14.2 DP 问题特性
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14.3 DP 解题思路
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14.4 0-1 背包问题
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14.5 完全背包问题
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14.6 编辑距离问题
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14.7 小结
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第 15 章 贪心
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15.1 贪心算法
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15.2 分数背包问题
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15.3 最大容量问题
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15.4 最大切分乘积问题
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15.5 小结
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第 16 章 附录
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16.1 编程环境安装
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16.2 一起参与创作
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1. 考虑基本情况
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3. 代码实现
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< h1 id = "124" > 12.4 汉诺塔问题< a class = "headerlink" href = "#124" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > 在归并排序和构建二叉树中，我们都是将原问题分解为两个规模为原问题一半的子问题。然而对于汉诺塔问题，我们采用不同的分解策略。< / p >
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< div class = "admonition question" >
< p class = "admonition-title" > Question< / p >
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< p > 给定三根柱子，记为 < code > A< / code > 、< code > B< / code > 和 < code > C< / code > 。起始状态下，柱子 < code > A< / code > 上套着 < span class = "arithmatex" > \(n\)< / span > 个圆盘，它们从上到下按照从小到大的顺序排列。我们的任务是要把这 < span class = "arithmatex" > \(n\)< / span > 个圆盘移到柱子 < code > C< / code > 上，并保持它们的原有顺序不变。在移动圆盘的过程中，需要遵守以下规则。< / p >
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< ol >
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< li > 圆盘只能从一个柱子顶部拿出，从另一个柱子顶部放入。< / li >
< li > 每次只能移动一个圆盘。< / li >
< li > 小圆盘必须时刻位于大圆盘之上。< / li >
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< p > < img alt = "汉诺塔问题示例" src = "../hanota_problem.assets/hanota_example.png" / > < / p >
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< p align = "center" > 图 12-10 汉诺塔问题示例 < / p >
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< p > < strong > 我们将规模为 < span class = "arithmatex" > \(i\)< / span > 的汉诺塔问题记做 < span class = "arithmatex" > \(f(i)\)< / span > < / strong > 。例如 < span class = "arithmatex" > \(f(3)\)< / span > 代表将 < span class = "arithmatex" > \(3\)< / span > 个圆盘从 < code > A< / code > 移动至 < code > C< / code > 的汉诺塔问题。< / p >
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< h3 id = "1" > 1. 考虑基本情况< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 如图 12-11 所示，对于问题 < span class = "arithmatex" > \(f(1)\)< / span > ，即当只有一个圆盘时，我们将它直接从 < code > A< / code > 移动至 < code > C< / code > 即可。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "1:2" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > < 1> < / label > < label for = "__tabbed_1_2" > < 2> < / label > < / div >
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< p > < img alt = "规模为 1 问题的解" src = "../hanota_problem.assets/hanota_f1_step1.png" / > < / p >
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< p align = "center" > 图 12-11 规模为 1 问题的解 < / p >
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< p > 如图 12-12 所示，对于问题 < span class = "arithmatex" > \(f(2)\)< / span > ，即当有两个圆盘时，< strong > 由于要时刻满足小圆盘在大圆盘之上，因此需要借助 < code > B< / code > 来完成移动< / strong > 。< / p >
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< ol >
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< li > 先将上面的小圆盘从 < code > A< / code > 移至 < code > B< / code > 。< / li >
< li > 再将大圆盘从 < code > A< / code > 移至 < code > C< / code > 。< / li >
< li > 最后将小圆盘从 < code > B< / code > 移至 < code > C< / code > 。< / li >
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< p > < img alt = "规模为 2 问题的解" src = "../hanota_problem.assets/hanota_f2_step1.png" / > < / p >
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< / div >
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< / div >
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< p align = "center" > 图 12-12 规模为 2 问题的解 < / p >
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< p > 解决问题 < span class = "arithmatex" > \(f(2)\)< / span > 的过程可总结为：< strong > 将两个圆盘借助 < code > B< / code > 从 < code > A< / code > 移至 < code > C< / code > < / strong > 。其中，< code > C< / code > 称为目标柱、< code > B< / code > 称为缓冲柱。< / p >
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< h3 id = "2" > 2. 子问题分解< a class = "headerlink" href = "#2" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 对于问题 < span class = "arithmatex" > \(f(3)\)< / span > ，即当有三个圆盘时，情况变得稍微复杂了一些。< / p >
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< p > 因为已知 < span class = "arithmatex" > \(f(1)\)< / span > 和 < span class = "arithmatex" > \(f(2)\)< / span > 的解，所以我们可从分治角度思考，< strong > 将 < code > A< / code > 顶部的两个圆盘看做一个整体< / strong > ，执行图 12-13 所示的步骤。这样三个圆盘就被顺利地从 < code > A< / code > 移动至 < code > C< / code > 了。< / p >
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< ol >
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< li > 令 < code > B< / code > 为目标柱、< code > C< / code > 为缓冲柱，将两个圆盘从 < code > A< / code > 移动至 < code > B< / code > 。< / li >
< li > 将 < code > A< / code > 中剩余的一个圆盘从 < code > A< / code > 直接移动至 < code > C< / code > 。< / li >
< li > 令 < code > C< / code > 为目标柱、< code > A< / code > 为缓冲柱，将两个圆盘从 < code > B< / code > 移动至 < code > C< / code > 。< / li >
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< / ol >
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:4" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > < 1> < / label > < label for = "__tabbed_3_2" > < 2> < / label > < label for = "__tabbed_3_3" > < 3> < / label > < label for = "__tabbed_3_4" > < 4> < / label > < / div >
< div class = "tabbed-content" >
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< div class = "tabbed-block" >
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< p > < img alt = "规模为 3 问题的解" src = "../hanota_problem.assets/hanota_f3_step1.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "hanota_f3_step2" src = "../hanota_problem.assets/hanota_f3_step2.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "hanota_f3_step3" src = "../hanota_problem.assets/hanota_f3_step3.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < img alt = "hanota_f3_step4" src = "../hanota_problem.assets/hanota_f3_step4.png" / > < / p >
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< / div >
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< p align = "center" > 图 12-13 规模为 3 问题的解 < / p >
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< p > 本质上看，< strong > 我们将问题 < span class = "arithmatex" > \(f(3)\)< / span > 划分为两个子问题 < span class = "arithmatex" > \(f(2)\)< / span > 和子问题 < span class = "arithmatex" > \(f(1)\)< / span > < / strong > 。按顺序解决这三个子问题之后，原问题随之得到解决。这说明子问题是独立的，而且解是可以合并的。< / p >
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< p > 至此，我们可总结出图 12-14 所示的汉诺塔问题的分治策略：将原问题 < span class = "arithmatex" > \(f(n)\)< / span > 划分为两个子问题 < span class = "arithmatex" > \(f(n-1)\)< / span > 和一个子问题 < span class = "arithmatex" > \(f(1)\)< / span > ，并按照以下顺序解决这三个子问题。< / p >
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< ol >
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< li > 将 < span class = "arithmatex" > \(n-1\)< / span > 个圆盘借助 < code > C< / code > 从 < code > A< / code > 移至 < code > B< / code > 。< / li >
< li > 将剩余 < span class = "arithmatex" > \(1\)< / span > 个圆盘从 < code > A< / code > 直接移至 < code > C< / code > 。< / li >
< li > 将 < span class = "arithmatex" > \(n-1\)< / span > 个圆盘借助 < code > A< / code > 从 < code > B< / code > 移至 < code > C< / code > 。< / li >
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< / ol >
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< p > 对于这两个子问题 < span class = "arithmatex" > \(f(n-1)\)< / span > ， < strong > 可以通过相同的方式进行递归划分< / strong > ，直至达到最小子问题 < span class = "arithmatex" > \(f(1)\)< / span > 。而 < span class = "arithmatex" > \(f(1)\)< / span > 的解是已知的，只需一次移动操作即可。< / p >
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< p > < img alt = "汉诺塔问题的分治策略" src = "../hanota_problem.assets/hanota_divide_and_conquer.png" / > < / p >
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< p align = "center" > 图 12-14 汉诺塔问题的分治策略 < / p >
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< h3 id = "3" > 3. 代码实现< a class = "headerlink" href = "#3" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 在代码中，我们声明一个递归函数 < code > dfs(i, src, buf, tar)< / code > ，它的作用是将柱 < code > src< / code > 顶部的 < span class = "arithmatex" > \(i\)< / span > 个圆盘借助缓冲柱 < code > buf< / code > 移动至目标柱 < code > tar< / code > 。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "4:12" > < 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" / > < 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" > Zig< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > hanota.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" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / 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" > " " " 移动一个圆盘" " " < / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "c1" > # 从 src 顶部拿出一个圆盘< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "n" > pan< / span > < span class = "o" > =< / span > < span class = "n" > src< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "c1" > # 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "n" > tar< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > pan< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "k" > def< / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > buf< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]):< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 求解汉诺塔：问题 f(i)" " " < / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "c1" > # 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "k" > if< / span > < span class = "n" > i< / span > < span class = "o" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "c1" > # 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > ,< / span > < span class = "n" > buf< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "c1" > # 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "c1" > # 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > buf< / span > < span class = "p" > ,< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "k" > def< / span > < span class = "nf" > solve_hanota< / span > < span class = "p" > (< / span > < span class = "n" > A< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > B< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > C< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]):< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 求解汉诺塔" " " < / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "n" > n< / span > < span class = "o" > =< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > A< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "c1" > # 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "n" > C< / span > < span class = "p" > )< / span >
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< / code > < / pre > < / div >
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< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > hanota.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > move< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > tar< / 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 = "c1" > // 从 src 顶部拿出一个圆盘< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > pan< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "n" > back< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "n" > pop_back< / 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 = "c1" > // 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > pan< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > tar< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / 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 = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > buf< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / 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 = "n" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
2023-09-02 23:53:46 +08:00
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > solveHanota< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > C< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-07-17 04:21:02 +08:00
< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / 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" > A< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > C< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-30" name = "__codelineno-1-30" href = "#__codelineno-1-30" > < / a > < span class = "p" > }< / span >
2023-07-17 02:17:51 +08:00
< / code > < / pre > < / div >
2023-07-16 04:19:01 +08:00
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > hanota.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > move< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > tar< / 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 = "c1" > // 从 src 顶部拿出一个圆盘< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "n" > Integer< / span > < span class = "w" > < / span > < span class = "n" > pan< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "na" > remove< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "na" > size< / 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-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > pan< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / 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 = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > buf< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / 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 = "n" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > solveHanota< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > C< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / 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" > A< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > C< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / a > < span class = "p" > }< / span >
2023-07-17 02:17:51 +08:00
< / code > < / pre > < / div >
2023-07-16 04:19:01 +08:00
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > hanota.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > move< / span > < span class = "p" > (< / 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" > src< / span > < span class = "p" > ,< / span > < 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" > tar< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-07-21 22:21:21 +08:00
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从 src 顶部拿出一个圆盘< / span >
2023-09-04 03:17:06 +08:00
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > pan< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > [< / span > < span class = "o" > ^< / span > < span class = "m" > 1< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "n" > RemoveAt< / span > < span class = "p" > (< / span > < span class = "n" > src< / 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" > 1< / 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 = "c1" > // 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > pan< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < 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" > src< / span > < span class = "p" > ,< / span > < 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" > buf< / span > < span class = "p" > ,< / span > < 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" > tar< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / 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" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > buf< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / 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" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > solveHanota< / span > < span class = "p" > (< / 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" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < 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" > C< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / 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" > A< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > C< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
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< / div >
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< div class = "highlight" > < span class = "filename" > hanota.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / 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" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > list< / span > < span class = "p" > .< / span > < span class = "nx" > List< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-08-04 05:25:00 +08:00
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从 src 顶部拿出一个圆盘< / span >
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< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "nx" > pan< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > .< / span > < span class = "nx" > Back< / span > < span class = "p" > ()< / span >
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< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将圆盘放入 tar 顶部< / span >
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< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > .< / span > < span class = "nx" > PushBack< / span > < span class = "p" > (< / span > < span class = "nx" > pan< / span > < span class = "p" > .< / span > < span class = "nx" > Value< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 移除 src 顶部圆盘< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > .< / span > < span class = "nx" > Remove< / span > < span class = "p" > (< / span > < span class = "nx" > pan< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > dfsHanota< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > list< / span > < span class = "p" > .< / span > < span class = "nx" > List< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "nx" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "nx" > dfsHanota< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > buf< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "nx" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "w" > < / span > < span class = "nx" > dfsHanota< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
< a id = "__codelineno-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > solveHanota< / span > < span class = "p" > (< / span > < span class = "nx" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > C< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > list< / span > < span class = "p" > .< / span > < span class = "nx" > List< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / a > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > A< / span > < span class = "p" > .< / span > < span class = "nx" > Len< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-4-30" name = "__codelineno-4-30" href = "#__codelineno-4-30" > < / a > < span class = "w" > < / span > < span class = "nx" > dfsHanota< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > C< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-31" name = "__codelineno-4-31" href = "#__codelineno-4-31" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
2023-07-16 04:19:01 +08:00
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > hanota.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "c1" > // 从 src 顶部拿出一个圆盘< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > pan< / span > < span class = "p" > =< / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "n" > popLast< / span > < span class = "p" > ()< / span > < span class = "o" > !< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "c1" > // 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "n" > tar< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > pan< / span > < span class = "p" > )< / span >
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< 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 >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
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< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "kd" > func< / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > buf< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "k" > if< / span > < span class = "n" > i< / span > < span class = "p" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > tar< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "n" > buf< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > tar< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > buf< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > tar< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > buf< / span > < span class = "p" > ,< / span > < span class = "n" > buf< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > tar< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
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< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / a > < span class = "kd" > func< / span > < span class = "nf" > solveHanota< / span > < span class = "p" > (< / span > < span class = "n" > A< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > B< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > C< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "kd" > let< / span > < span class = "nv" > n< / span > < span class = "p" > =< / span > < span class = "n" > A< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-5-27" name = "__codelineno-5-27" href = "#__codelineno-5-27" > < / a > < span class = "c1" > // 列表尾部是柱子顶部< / span >
< a id = "__codelineno-5-28" name = "__codelineno-5-28" href = "#__codelineno-5-28" > < / a > < span class = "c1" > // 将 src 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-5-29" name = "__codelineno-5-29" href = "#__codelineno-5-29" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > src< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "n" > buf< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "n" > tar< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > C< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-30" name = "__codelineno-5-30" href = "#__codelineno-5-30" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > hanota.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / 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" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / 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 = "c1" > // 从 src 顶部拿出一个圆盘< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > pan< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > pan< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a >
< a id = "__codelineno-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
< a id = "__codelineno-6-10" name = "__codelineno-6-10" href = "#__codelineno-6-10" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-11" name = "__codelineno-6-11" href = "#__codelineno-6-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-6-12" name = "__codelineno-6-12" href = "#__codelineno-6-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "mf" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-13" name = "__codelineno-6-13" href = "#__codelineno-6-13" > < / a > < span class = "w" > < / span > < span class = "nx" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-14" name = "__codelineno-6-14" href = "#__codelineno-6-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-15" name = "__codelineno-6-15" href = "#__codelineno-6-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-16" name = "__codelineno-6-16" href = "#__codelineno-6-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-6-17" name = "__codelineno-6-17" href = "#__codelineno-6-17" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / 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" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > buf< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-18" name = "__codelineno-6-18" href = "#__codelineno-6-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-6-19" name = "__codelineno-6-19" href = "#__codelineno-6-19" > < / a > < span class = "w" > < / span > < span class = "nx" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-20" name = "__codelineno-6-20" href = "#__codelineno-6-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-6-21" name = "__codelineno-6-21" href = "#__codelineno-6-21" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / 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" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-22" name = "__codelineno-6-22" href = "#__codelineno-6-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-6-23" name = "__codelineno-6-23" href = "#__codelineno-6-23" > < / a >
< a id = "__codelineno-6-24" name = "__codelineno-6-24" href = "#__codelineno-6-24" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
< a id = "__codelineno-6-25" name = "__codelineno-6-25" href = "#__codelineno-6-25" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > solveHanota< / span > < span class = "p" > (< / span > < span class = "nx" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > C< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-26" name = "__codelineno-6-26" href = "#__codelineno-6-26" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / 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" > A< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-27" name = "__codelineno-6-27" href = "#__codelineno-6-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-6-28" name = "__codelineno-6-28" href = "#__codelineno-6-28" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > C< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-29" name = "__codelineno-6-29" href = "#__codelineno-6-29" > < / a > < span class = "p" > }< / span >
2023-07-17 02:17:51 +08:00
< / code > < / pre > < / div >
2023-07-16 04:19:01 +08:00
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > hanota.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / 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" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / 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" > tar< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-07-19 01:44:47 +08:00
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从 src 顶部拿出一个圆盘< / span >
2023-09-04 03:17:06 +08:00
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > pan< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > pan< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > i< / 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" > src< / 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" > buf< / 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" > tar< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "mf" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a > < span class = "w" > < / span > < span class = "nx" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / 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" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > buf< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "nx" > move< / span > < span class = "p" > (< / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / 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" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > solveHanota< / span > < span class = "p" > (< / span > < span class = "nx" > A< / 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" > B< / 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" > C< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / 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" > A< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-7-28" name = "__codelineno-7-28" href = "#__codelineno-7-28" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > C< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-29" name = "__codelineno-7-29" href = "#__codelineno-7-29" > < / a > < span class = "p" > }< / span >
2023-07-17 02:17:51 +08:00
< / code > < / pre > < / div >
2023-07-16 04:19:01 +08:00
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > hanota.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / 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" > src< / span > < span class = "p" > ,< / span > < 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" > tar< / 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 = "c1" > // 从 src 顶部拿出一个圆盘< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > pan< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "n" > removeLast< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > pan< / span > < span class = "p" > );< / span >
2023-09-02 23:53:46 +08:00
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
2023-09-04 03:17:06 +08:00
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < 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" > src< / span > < span class = "p" > ,< / span > < 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" > buf< / span > < span class = "p" > ,< / span > < 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" > tar< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / 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" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > buf< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "w" > < / span > < span class = "n" > move< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / 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" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
2023-09-02 23:53:46 +08:00
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
2023-09-04 03:17:06 +08:00
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > solveHanota< / span > < span class = "p" > (< / 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" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < 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" > C< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / 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" > A< / span > < span class = "p" > .< / span > < span class = "n" > length< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-8-28" name = "__codelineno-8-28" href = "#__codelineno-8-28" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > C< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-29" name = "__codelineno-8-29" href = "#__codelineno-8-29" > < / a > < span class = "p" > }< / span >
2023-07-17 02:17:51 +08:00
< / code > < / pre > < / div >
2023-07-16 04:19:01 +08:00
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > hanota.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* 移动一个圆盘 */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > move_pan< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "c1" > // 从 src 顶部拿出一个圆盘< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > pan< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "n" > remove< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > .< / span > < span class = "n" > len< / 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-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将圆盘放入 tar 顶部< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > pan< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "cm" > /* 求解汉诺塔：问题 f(i) */< / span >
< a id = "__codelineno-9-10" name = "__codelineno-9-10" href = "#__codelineno-9-10" > < / a > < span class = "k" > fn< / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > src< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > buf< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-11" name = "__codelineno-9-11" href = "#__codelineno-9-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若 src 只剩下一个圆盘，则直接将其移到 tar< / span >
< a id = "__codelineno-9-12" name = "__codelineno-9-12" href = "#__codelineno-9-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-13" name = "__codelineno-9-13" href = "#__codelineno-9-13" > < / a > < span class = "w" > < / span > < span class = "n" > move_pan< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-14" name = "__codelineno-9-14" href = "#__codelineno-9-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-15" name = "__codelineno-9-15" href = "#__codelineno-9-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-16" name = "__codelineno-9-16" href = "#__codelineno-9-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf< / span >
< a id = "__codelineno-9-17" name = "__codelineno-9-17" href = "#__codelineno-9-17" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / 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 = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > buf< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-18" name = "__codelineno-9-18" href = "#__codelineno-9-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar< / span >
< a id = "__codelineno-9-19" name = "__codelineno-9-19" href = "#__codelineno-9-19" > < / a > < span class = "w" > < / span > < span class = "n" > move_pan< / span > < span class = "p" > (< / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-20" name = "__codelineno-9-20" href = "#__codelineno-9-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar< / span >
< a id = "__codelineno-9-21" name = "__codelineno-9-21" href = "#__codelineno-9-21" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / 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 = "n" > buf< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > src< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tar< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-22" name = "__codelineno-9-22" href = "#__codelineno-9-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-9-23" name = "__codelineno-9-23" href = "#__codelineno-9-23" > < / a >
< a id = "__codelineno-9-24" name = "__codelineno-9-24" href = "#__codelineno-9-24" > < / a > < span class = "cm" > /* 求解汉诺塔 */< / span >
< a id = "__codelineno-9-25" name = "__codelineno-9-25" href = "#__codelineno-9-25" > < / a > < span class = "k" > fn< / span > < span class = "nf" > solve_hanota< / span > < span class = "p" > (< / span > < span class = "n" > A< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > B< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > C< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-26" name = "__codelineno-9-26" href = "#__codelineno-9-26" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > A< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-27" name = "__codelineno-9-27" href = "#__codelineno-9-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将 A 顶部 n 个圆盘借助 B 移到 C< / span >
< a id = "__codelineno-9-28" name = "__codelineno-9-28" href = "#__codelineno-9-28" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > A< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > B< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > C< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-29" name = "__codelineno-9-29" href = "#__codelineno-9-29" > < / a > < span class = "p" > }< / span >
2023-07-17 02:17:51 +08:00
< / code > < / pre > < / div >
2023-07-16 04:19:01 +08:00
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > hanota.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > move< / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > dfs< / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a >
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< p > 如图 12-15 所示，汉诺塔问题形成一个高度为 < span class = "arithmatex" > \(n\)< / span > 的递归树，每个节点代表一个子问题、对应一个开启的 < code > dfs()< / code > 函数，< strong > 因此时间复杂度为 < span class = "arithmatex" > \(O(2^n)\)< / span > ，空间复杂度为 < span class = "arithmatex" > \(O(n)\)< / span > < / strong > 。< / p >
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< p > < img alt = "汉诺塔问题的递归树" src = "../hanota_problem.assets/hanota_recursive_tree.png" / > < / p >
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< p align = "center" > 图 12-15 汉诺塔问题的递归树 < / p >
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< p class = "admonition-title" > Quote< / p >
< p > 汉诺塔问题源自一种古老的传说故事。在古印度的一个寺庙里，僧侣们有三根高大的钻石柱子，以及 < span class = "arithmatex" > \(64\)< / span > 个大小不一的金圆盘。僧侣们不断地移动原盘，他们相信在最后一个圆盘被正确放置的那一刻，这个世界就会结束。< / p >
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< p > 然而，即使僧侣们每秒钟移动一次，总共需要大约 < span class = "arithmatex" > \(2^{64} \approx 1.84× < / span > 秒，合约 < span class = "arithmatex" > \(5850\)< / span > 亿年，远远超过了现在对宇宙年龄的估计。所以，倘若这个传说是真的，我们应该不需要担心世界末日的到来。< / p >
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