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0. 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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1. 初识算法
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1. 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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< a href = "../../chapter_computational_complexity/" class = "md-nav__link " >
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2. 复杂度
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2. 复杂度
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2.1. 算法效率评估
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2.2. 时间复杂度
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< a href = "../../chapter_computational_complexity/space_complexity/" class = "md-nav__link" >
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2.3. 空间复杂度
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2.4. 小结
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< a href = "../../chapter_data_structure/" class = "md-nav__link " >
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z" / > < / svg >
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3. 数据结构
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3. 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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< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
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3.4. 字符编码 *
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3.5. 小结
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< a href = "../../chapter_array_and_linkedlist/" class = "md-nav__link " >
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4. 数组与链表
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4. 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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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
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4.3. 列表
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< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
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4.4. 小结
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_stack_and_queue/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z" / > < / svg >
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5. 栈与队列
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5. 栈与队列
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5.1. 栈
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< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
5.2. 队列
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
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5.3. 双向队列
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
5.4. 小结
< / span >
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< / a >
< / li >
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< / ul >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_hashing/" class = "md-nav__link " >
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< span class = "md-ellipsis" >
6. 散列表
< / span >
< / a >
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< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_7_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
6. 散列表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
6.1. 哈希表
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
6.2. 哈希冲突
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_algorithm/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
6.3. 哈希算法
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
6.4. 小结
< / span >
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< / a >
< / li >
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< / ul >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_tree/" class = "md-nav__link " >
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< span class = "md-ellipsis" >
7. 树
< / span >
< / a >
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< label class = "md-nav__link " for = "__nav_8" >
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< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
7. 树
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
7.1. 二叉树
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
7.2. 二叉树遍历
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
7.3. 二叉树数组表示
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
7.4. 二叉搜索树
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
7.5. AVL 树 *
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
7.6. 小结
< / span >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_heap/" class = "md-nav__link " >
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8. 堆
< / span >
< / a >
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< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_9_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_9" >
< span class = "md-nav__icon md-icon" > < / span >
8. 堆
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
8.1. 堆
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
8.2. 建堆操作
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/top_k/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
8.3. Top-K 问题
< / span >
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< / a >
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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" >
8.4. 小结
< / span >
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< / a >
< / li >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_graph/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
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9. 图
< / span >
< / a >
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< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
9. 图
< / 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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< span class = "md-ellipsis" >
9.1. 图
< / 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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< span class = "md-ellipsis" >
9.2. 图基础操作
< / 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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< span class = "md-ellipsis" >
9.3. 图的遍历
< / 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" >
9.4. 小结
< / span >
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< / a >
< / li >
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< / ul >
< / nav >
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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" >
10. 搜索
< / span >
< / a >
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< label class = "md-nav__link " for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
10. 搜索
< / 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" >
10.1. 二分查找
< / span >
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< / 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" >
10.2. 二分查找边界
< / 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" >
10.3. 哈希优化策略
< / 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" >
10.4. 重识搜索算法
< / 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" >
10.5. 小结
< / span >
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< / a >
< / li >
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< / ul >
< / nav >
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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" >
11. 排序
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
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< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_12_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
11. 排序
< / 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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< span class = "md-ellipsis" >
11.1. 排序算法
< / 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" >
11.2. 选择排序
< / 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" >
11.3. 冒泡排序
< / 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" >
11.4. 插入排序
< / 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" >
11.5. 快速排序
< / 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" >
11.6. 归并排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.7. 堆排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.8. 桶排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.9. 计数排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.10. 基数排序
< / span >
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
11.11. 小结
< / span >
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< / a >
< / li >
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< / ul >
< / nav >
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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_13" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
2023-07-19 16:10:17 +08:00
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< span class = "md-ellipsis" >
12. 分治
< / span >
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< span class = "md-status md-status--new" title = "最近添加" >
< / span >
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< / a >
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< label class = "md-nav__link " for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
12. 分治
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/divide_and_conquer/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
12.1. 分治算法
< / span >
< 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_divide_and_conquer/binary_search_recur/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
12.2. 分治搜索策略
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
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< / a >
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< li class = "md-nav__item" >
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< a href = "../../chapter_divide_and_conquer/build_binary_tree_problem/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
12.3. 构建树问题
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/hanota_problem/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
12.4. 汉诺塔问题
< / span >
< 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_divide_and_conquer/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
12.5. 小结
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
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< / ul >
< / nav >
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< / li >
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13.3. 子集和问题
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13.4. N 皇后问题
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13.5. 小结
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14. 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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14.5. 完全背包问题
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14.6. 编辑距离问题
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目录
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代码实现
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状态压缩
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14.7. 小结
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15. 贪心
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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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参考文献
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目录
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代码实现
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状态压缩
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< h1 id = "146" > 14.6. 编辑距离问题< a class = "headerlink" href = "#146" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > 编辑距离，也被称为 Levenshtein 距离，是两个字符串之间互相转换的最小修改次数，通常用于在信息检索和自然语言处理中度量两个序列的相似度。< / p >
< div class = "admonition question" >
< p class = "admonition-title" > Question< / p >
< p > 输入两个字符串 < span class = "arithmatex" > \(s\)< / span > 和 < span class = "arithmatex" > \(t\)< / span > ，返回将 < span class = "arithmatex" > \(s\)< / span > 转换为 < span class = "arithmatex" > \(t\)< / span > 所需的最少编辑步数。< / p >
< p > 你可以在一个字符串中进行三种编辑操作：插入一个字符、删除一个字符、替换字符为任意一个字符。< / p >
< / div >
< p > 如下图所示，将 < code > kitten< / code > 转换为 < code > sitting< / code > 需要编辑 3 步，包括 2 次替换操作与 1 次添加操作；将 < code > hello< / code > 转换为 < code > algo< / code > 需要 3 步，包括 2 次替换操作和 1 次删除操作。< / p >
< p > < img alt = "编辑距离的示例数据" src = "../edit_distance_problem.assets/edit_distance_example.png" / > < / p >
< p align = "center" > Fig. 编辑距离的示例数据 < / p >
< p > < strong > 编辑距离问题可以很自然地用决策树模型来解释< / strong > 。字符串对应树节点，一轮决策（一次编辑操作）对应树的一条边。< / p >
< p > 如下图所示，在不限制操作的情况下，每个节点都可以派生出许多条边，每条边对应一种操作。实际上，从 < code > hello< / code > 转换到 < code > algo< / code > 有许多种可能的路径，下图展示的是最短路径。从决策树的角度看，本题目标是求解节点 < code > hello< / code > 和节点 < code > algo< / code > 之间的最短路径。< / p >
< p > < img alt = "基于决策树模型表示编辑距离问题" src = "../edit_distance_problem.assets/edit_distance_decision_tree.png" / > < / p >
< p align = "center" > Fig. 基于决策树模型表示编辑距离问题 < / p >
< p > < strong > 第一步：思考每轮的决策，定义状态，从而得到 < span class = "arithmatex" > \(dp\)< / span > 表< / strong > < / p >
< p > 每一轮的决策是对字符串 < span class = "arithmatex" > \(s\)< / span > 进行一次编辑操作。< / p >
< p > 我们希望在编辑操作的过程中，问题的规模逐渐缩小，这样才能构建子问题。设字符串 < span class = "arithmatex" > \(s\)< / span > 和 < span class = "arithmatex" > \(t\)< / span > 的长度分别为 < span class = "arithmatex" > \(n\)< / span > 和 < span class = "arithmatex" > \(m\)< / span > ，我们先考虑两字符串尾部的字符 < span class = "arithmatex" > \(s[n-1]\)< / span > 和 < span class = "arithmatex" > \(t[m-1]\)< / span > ： < / p >
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< li > 若 < span class = "arithmatex" > \(s[n-1]\)< / span > 和 < span class = "arithmatex" > \(t[m-1]\)< / span > 相同，我们可以直接跳过它们，接下来考虑 < span class = "arithmatex" > \(s[n-2]\)< / span > 和 < span class = "arithmatex" > \(t[m-2]\)< / span > ;< / li >
< li > 若 < span class = "arithmatex" > \(s[n-1]\)< / span > 和 < span class = "arithmatex" > \(t[m-1]\)< / span > 不同，我们需要对 < span class = "arithmatex" > \(s\)< / span > 进行一次编辑（插入、删除、替换），使得两字符串尾部的字符相同，从而可以跳过它们，考虑规模更小的问题；< / li >
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< p > 也就是说，我们在字符串 < span class = "arithmatex" > \(s\)< / span > 中进行的每一轮决策（编辑操作），都会使得 < span class = "arithmatex" > \(s\)< / span > 和 < span class = "arithmatex" > \(t\)< / span > 中剩余的待匹配字符发生变化。因此，状态为当前在 < span class = "arithmatex" > \(s\)< / span > , < span class = "arithmatex" > \(t\)< / span > 中考虑的第 < span class = "arithmatex" > \(i\)< / span > , < span class = "arithmatex" > \(j\)< / span > 个字符，记为 < span class = "arithmatex" > \([i, j]\)< / span > 。< / p >
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< p > 状态 < span class = "arithmatex" > \([i, j]\)< / span > 对应的子问题：< strong > 将 < span class = "arithmatex" > \(s\)< / span > 的前 < span class = "arithmatex" > \(i\)< / span > 个字符更改为 < span class = "arithmatex" > \(t\)< / span > 的前 < span class = "arithmatex" > \(j\)< / span > 个字符所需的最少编辑步数< / strong > 。< / p >
< p > 至此得到一个尺寸为 < span class = "arithmatex" > \((i+1) \times (j+1)\)< / span > 的二维 < span class = "arithmatex" > \(dp\)< / span > 表。< / p >
< p > < strong > 第二步：找出最优子结构，进而推导出状态转移方程< / strong > < / p >
< p > 考虑子问题 < span class = "arithmatex" > \(dp[i, j]\)< / span > ，其对应的两个字符串的尾部字符为 < span class = "arithmatex" > \(s[i-1]\)< / span > 和 < span class = "arithmatex" > \(t[j-1]\)< / span > ，可根据不同编辑操作分为三种情况：< / p >
< ol >
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< li > 在 < span class = "arithmatex" > \(s[i-1]\)< / span > 之后添加 < span class = "arithmatex" > \(t[j-1]\)< / span > ，则剩余子问题 < span class = "arithmatex" > \(dp[i, j-1]\)< / span > ； < / li >
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< li > 删除 < span class = "arithmatex" > \(s[i-1]\)< / span > ，则剩余子问题 < span class = "arithmatex" > \(dp[i-1, j]\)< / span > ； < / li >
< li > 将 < span class = "arithmatex" > \(s[i-1]\)< / span > 替换为 < span class = "arithmatex" > \(t[j-1]\)< / span > ，则剩余子问题 < span class = "arithmatex" > \(dp[i-1, j-1]\)< / span > ； < / li >
< / ol >
< p > < img alt = "编辑距离的状态转移" src = "../edit_distance_problem.assets/edit_distance_state_transfer.png" / > < / p >
< p align = "center" > Fig. 编辑距离的状态转移 < / p >
< p > 根据以上分析，可得最优子结构：< span class = "arithmatex" > \(dp[i, j]\)< / span > 的最少编辑步数等于 < span class = "arithmatex" > \(dp[i, j-1]\)< / span > , < span class = "arithmatex" > \(dp[i-1, j]\)< / span > , < span class = "arithmatex" > \(dp[i-1, j-1]\)< / span > 三者中的最少编辑步数，再加上本次编辑的步数 < span class = "arithmatex" > \(1\)< / span > 。对应的状态转移方程为：< / p >
< div class = "arithmatex" > \[
dp[i, j] = \min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1
\]< / div >
< p > 请注意，< strong > 当 < span class = "arithmatex" > \(s[i-1]\)< / span > 和 < span class = "arithmatex" > \(t[j-1]\)< / span > 相同时，无需编辑当前字符< / strong > ，此时状态转移方程为：< / p >
< div class = "arithmatex" > \[
dp[i, j] = dp[i-1, j-1]
\]< / div >
< p > < strong > 第三步：确定边界条件和状态转移顺序< / strong > < / p >
< p > 当两字符串都为空时，编辑步数为 < span class = "arithmatex" > \(0\)< / span > ，即 < span class = "arithmatex" > \(dp[0, 0] = 0\)< / span > 。当 < span class = "arithmatex" > \(s\)< / span > 为空但 < span class = "arithmatex" > \(t\)< / span > 不为空时，最少编辑步数等于 < span class = "arithmatex" > \(t\)< / span > 的长度，即 < span class = "arithmatex" > \(dp[0, j] = j\)< / span > 。当 < span class = "arithmatex" > \(s\)< / span > 不为空但 < span class = "arithmatex" > \(t\)< / span > 为空时，等于 < span class = "arithmatex" > \(s\)< / span > 的长度，即 < span class = "arithmatex" > \(dp[i, 0] = i\)< / span > 。< / p >
< p > 观察状态转移方程，解 < span class = "arithmatex" > \(dp[i, j]\)< / span > 依赖左方、上方、左上方的解，因此通过两层循环正序遍历整个 < span class = "arithmatex" > \(dp\)< / span > 表即可。< / p >
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< h3 id = "_1" > 代码实现< a class = "headerlink" href = "#_1" title = "Permanent link" > ¶ < / a > < / h3 >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "1:11" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Java< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Python< / label > < label for = "__tabbed_1_4" > Go< / label > < label for = "__tabbed_1_5" > JavaScript< / label > < label for = "__tabbed_1_6" > TypeScript< / label > < label for = "__tabbed_1_7" > C< / label > < label for = "__tabbed_1_8" > C#< / label > < label for = "__tabbed_1_9" > Swift< / label > < label for = "__tabbed_1_10" > Zig< / label > < label for = "__tabbed_1_11" > Dart< / label > < / div >
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< div class = "highlight" > < span class = "filename" > edit_distance.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 编辑距离：动态规划 */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > editDistanceDP< / span > < span class = "p" > (< / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "w" > < / span > < span class = "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" > s< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > [][]< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > [< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ][< / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行首列< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ][< / span > < span class = "mi" > 0< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "mi" > 0< / span > < span class = "o" > ][< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余行列< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > .< / span > < span class = "na" > charAt< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "na" > charAt< / span > < span class = "p" > (< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ][< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / 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 = "o" > ][< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ][< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "na" > min< / span > < span class = "p" > (< / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "na" > min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ][< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / 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 = "o" > ][< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / 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 = "o" > ][< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / 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-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "w" > < / 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 = "p" > }< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > n< / span > < span class = "o" > ][< / span > < span class = "n" > m< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 编辑距离：动态规划 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > editDistanceDP< / span > < span class = "p" > (< / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "p" > .< / span > < span class = "n" > length< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > length< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > m< / 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 = "mi" > 0< / 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 = "c1" > // 状态转移：首行首列< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < 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" > // 状态转移：其余行列< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / 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 = "n" > j< / 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-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > min< / span > < span class = "p" > (< / span > < span class = "n" > min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > dp< / 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 = "n" > j< / span > < span class = "p" > ]),< / span > < span class = "w" > < / span > < span class = "n" > dp< / 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 = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / 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 = "p" > }< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ][< / span > < span class = "n" > m< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > edit_distance_dp< / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > ,< / span > < span class = "n" > t< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 编辑距离：动态规划" " " < / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > m< / span > < span class = "o" > =< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > ),< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > t< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "n" > dp< / span > < span class = "o" > =< / span > < span class = "p" > [[< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "n" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "k" > for< / span > < span class = "n" > _< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > +< / 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 = "c1" > # 状态转移：首行首列< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > i< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > j< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "c1" > # 状态转移：其余行列< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "k" > if< / span > < span class = "n" > s< / 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 = "o" > ==< / span > < span class = "n" > t< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "c1" > # 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > dp< / 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" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "c1" > # 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "nb" > min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "n" > dp< / 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" > j< / span > < span class = "p" > ],< / span > < span class = "n" > dp< / 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" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "k" > return< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ][< / span > < span class = "n" > m< / span > < span class = "p" > ]< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-24 13:09:54 +08:00
< div class = "highlight" > < span class = "filename" > edit_distance.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 编辑距离：动态规划 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > editDistanceDP< / span > < span class = "p" > (< / span > < span class = "nx" > s< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > s< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > t< / 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 = "nx" > dp< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([][]< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 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 = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行首列< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ][< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ][< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > j< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / 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 = "c1" > // 状态转移：其余行列< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > s< / 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 = "o" > ==< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ][< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > dp< / 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 = "nx" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ][< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > MinInt< / span > < span class = "p" > (< / span > < span class = "nx" > MinInt< / span > < span class = "p" > (< / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ][< / span > < span class = "nx" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > dp< / 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 = "nx" > j< / span > < span class = "p" > ]),< / span > < span class = "w" > < / span > < span class = "nx" > dp< / 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 = "nx" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < 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 = "p" > }< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > n< / span > < span class = "p" > ][< / span > < span class = "nx" > m< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "p" > }< / span >
2023-07-13 05:26:03 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > editDistanceDP< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > editDistanceDP< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / 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" > editDistanceDP< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-16 04:19:01 +08:00
< div class = "highlight" > < span class = "filename" > edit_distance.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 编辑距离：动态规划 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > editDistanceDP< / span > < span class = "p" > (< / span > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "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" > s< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > [,]< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "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" > m< / 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-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行首列< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "m" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > j< / 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 = "p" > }< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余行列< / span >
< a id = "__codelineno-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > s< / 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 = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / 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" > j< / 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-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "n" > Min< / span > < span class = "p" > (< / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "n" > Min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "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" > dp< / 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" > j< / span > < span class = "p" > ]),< / span > < span class = "w" > < / span > < span class = "n" > dp< / 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" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "p" > }< / span >
2023-07-13 05:26:03 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-19 01:44:47 +08:00
< div class = "highlight" > < span class = "filename" > edit_distance.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 编辑距离：动态规划 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > editDistanceDP< / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > :< / span > < span class = "nb" > String< / span > < span class = "p" > ,< / span > < span class = "n" > t< / span > < span class = "p" > :< / span > < span class = "nb" > String< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "kd" > let< / span > < span class = "nv" > n< / span > < span class = "p" > =< / span > < span class = "n" > s< / span > < span class = "p" > .< / span > < span class = "n" > utf8CString< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > m< / span > < span class = "p" > =< / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > utf8CString< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "kd" > var< / span > < span class = "nv" > dp< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "n" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ),< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "c1" > // 状态转移：首行首列< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > through< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > i< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > through< / span > < span class = "p" > :< / span > < span class = "n" > m< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > j< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "c1" > // 状态转移：其余行列< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > through< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > through< / span > < span class = "p" > :< / span > < span class = "n" > m< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "k" > if< / span > < span class = "n" > s< / span > < span class = "p" > .< / span > < span class = "n" > utf8CString< / 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 = "p" > ==< / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > utf8CString< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > dp< / 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" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "bp" > min< / span > < span class = "p" > (< / span > < span class = "bp" > min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "n" > dp< / 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" > j< / span > < span class = "p" > ]),< / span > < span class = "n" > dp< / 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" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< 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 > < span class = "p" > }< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "k" > return< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ][< / span > < span class = "n" > m< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "p" > }< / span >
2023-07-13 05:26:03 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-17 02:17:51 +08:00
< div class = "highlight" > < span class = "filename" > edit_distance.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "c1" > // 编辑距离：动态规划< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > editDistanceDP< / span > < span class = "p" > (< / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "kt" > u8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "kt" > u8< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / 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 = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "kr" > var< / 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" > s< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > len< / 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 = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "n" > _< / span > < span class = "p" > ][< / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "kt" > i32< / span > < span class = "p" > {[< / span > < span class = "n" > _< / span > < span class = "p" > ]< / span > < span class = "kt" > i32< / span > < span class = "p" > {< / span > < span class = "mi" > 0< / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )}< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行首列< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > i< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-10" name = "__codelineno-9-10" href = "#__codelineno-9-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > j< / span > < span class = "o" > |< / 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 = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > j< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-12" name = "__codelineno-9-12" href = "#__codelineno-9-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-13" name = "__codelineno-9-13" href = "#__codelineno-9-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余行列< / span >
< a id = "__codelineno-9-14" name = "__codelineno-9-14" href = "#__codelineno-9-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > i< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-15" name = "__codelineno-9-15" href = "#__codelineno-9-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > j< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-16" name = "__codelineno-9-16" href = "#__codelineno-9-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-17" name = "__codelineno-9-17" href = "#__codelineno-9-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-9-18" name = "__codelineno-9-18" href = "#__codelineno-9-18" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / 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 = "n" > j< / 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-9-19" name = "__codelineno-9-19" href = "#__codelineno-9-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-20" name = "__codelineno-9-20" href = "#__codelineno-9-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-9-21" name = "__codelineno-9-21" href = "#__codelineno-9-21" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @min< / span > < span class = "p" > (< / span > < span class = "nb" > @min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ][< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > dp< / 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 = "n" > j< / span > < span class = "p" > ]),< / span > < span class = "w" > < / span > < span class = "n" > dp< / 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 = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-22" name = "__codelineno-9-22" href = "#__codelineno-9-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-23" name = "__codelineno-9-23" href = "#__codelineno-9-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-24" name = "__codelineno-9-24" href = "#__codelineno-9-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-25" name = "__codelineno-9-25" href = "#__codelineno-9-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ][< / span > < span class = "n" > m< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-9-26" name = "__codelineno-9-26" href = "#__codelineno-9-26" > < / a > < span class = "p" > }< / span >
2023-07-13 05:26:03 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.dart< / 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" > editDistanceDP< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 如下图所示，编辑距离问题的状态转移过程与背包问题非常类似，都可以看作是填写一个二维网格的过程。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:15" > < input checked = "checked" id = "__tabbed_2_1" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_2" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_3" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_4" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_5" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_6" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_7" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_8" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_9" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_10" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_11" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_12" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_13" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_14" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_15" name = "__tabbed_2" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > < 1> < / label > < label for = "__tabbed_2_2" > < 2> < / label > < label for = "__tabbed_2_3" > < 3> < / label > < label for = "__tabbed_2_4" > < 4> < / label > < label for = "__tabbed_2_5" > < 5> < / label > < label for = "__tabbed_2_6" > < 6> < / label > < label for = "__tabbed_2_7" > < 7> < / label > < label for = "__tabbed_2_8" > < 8> < / label > < label for = "__tabbed_2_9" > < 9> < / label > < label for = "__tabbed_2_10" > < 10> < / label > < label for = "__tabbed_2_11" > < 11> < / label > < label for = "__tabbed_2_12" > < 12> < / label > < label for = "__tabbed_2_13" > < 13> < / label > < label for = "__tabbed_2_14" > < 14> < / label > < label for = "__tabbed_2_15" > < 15> < / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< p > < img alt = "编辑距离的动态规划过程" src = "../edit_distance_problem.assets/edit_distance_dp_step1.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step2" src = "../edit_distance_problem.assets/edit_distance_dp_step2.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step3" src = "../edit_distance_problem.assets/edit_distance_dp_step3.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step4" src = "../edit_distance_problem.assets/edit_distance_dp_step4.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step5" src = "../edit_distance_problem.assets/edit_distance_dp_step5.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step6" src = "../edit_distance_problem.assets/edit_distance_dp_step6.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step7" src = "../edit_distance_problem.assets/edit_distance_dp_step7.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step8" src = "../edit_distance_problem.assets/edit_distance_dp_step8.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step9" src = "../edit_distance_problem.assets/edit_distance_dp_step9.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step10" src = "../edit_distance_problem.assets/edit_distance_dp_step10.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step11" src = "../edit_distance_problem.assets/edit_distance_dp_step11.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step12" src = "../edit_distance_problem.assets/edit_distance_dp_step12.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step13" src = "../edit_distance_problem.assets/edit_distance_dp_step13.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step14" src = "../edit_distance_problem.assets/edit_distance_dp_step14.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "edit_distance_dp_step15" src = "../edit_distance_problem.assets/edit_distance_dp_step15.png" / > < / p >
< / div >
< / div >
< / div >
2023-07-21 21:53:15 +08:00
< h3 id = "_2" > 状态压缩< a class = "headerlink" href = "#_2" title = "Permanent link" > ¶ < / a > < / h3 >
2023-07-13 05:26:03 +08:00
< p > 下面考虑状态压缩，将 < span class = "arithmatex" > \(dp\)< / span > 表的第一维删除。由于 < span class = "arithmatex" > \(dp[i,j]\)< / span > 是由上方 < span class = "arithmatex" > \(dp[i-1, j]\)< / span > 、左方 < span class = "arithmatex" > \(dp[i, j-1]\)< / span > 、左上方状态 < span class = "arithmatex" > \(dp[i-1, j-1]\)< / span > 转移而来，而正序遍历会丢失左上方 < span class = "arithmatex" > \(dp[i-1, j-1]\)< / span > ，倒序遍历无法提前构建 < span class = "arithmatex" > \(dp[i, j-1]\)< / span > ，因此两种遍历顺序都不可取。< / p >
< p > 为解决此问题，我们可以使用一个变量 < code > leftup< / code > 来暂存左上方的解 < span class = "arithmatex" > \(dp[i-1, j-1]\)< / span > ，这样便只用考虑左方和上方的解，与完全背包问题的情况相同，可使用正序遍历。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:11" > < input checked = "checked" id = "__tabbed_3_1" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_2" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_3" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_4" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_5" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_6" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_7" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_8" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_9" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_10" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_11" name = "__tabbed_3" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Java< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Python< / label > < label for = "__tabbed_3_4" > Go< / label > < label for = "__tabbed_3_5" > JavaScript< / label > < label for = "__tabbed_3_6" > TypeScript< / label > < label for = "__tabbed_3_7" > C< / label > < label for = "__tabbed_3_8" > C#< / label > < label for = "__tabbed_3_9" > Swift< / label > < label for = "__tabbed_3_10" > Zig< / label > < label for = "__tabbed_3_11" > Dart< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 编辑距离：状态压缩后的动态规划 */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > editDistanceDPComp< / span > < span class = "p" > (< / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "w" > < / span > < span class = "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" > s< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > [< / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余行< / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首列< / span >
< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "mi" > 0< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存 dp[i-1, j-1]< / span >
< a id = "__codelineno-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "mi" > 0< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余列< / span >
< a id = "__codelineno-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-17" name = "__codelineno-11-17" href = "#__codelineno-11-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > .< / span > < span class = "na" > charAt< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "na" > charAt< / span > < span class = "p" > (< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-18" name = "__codelineno-11-18" href = "#__codelineno-11-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-11-19" name = "__codelineno-11-19" href = "#__codelineno-11-19" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-20" name = "__codelineno-11-20" href = "#__codelineno-11-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-21" name = "__codelineno-11-21" href = "#__codelineno-11-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-11-22" name = "__codelineno-11-22" href = "#__codelineno-11-22" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "na" > min< / span > < span class = "p" > (< / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "na" > min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-23" name = "__codelineno-11-23" href = "#__codelineno-11-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-24" name = "__codelineno-11-24" href = "#__codelineno-11-24" > < / a > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新为下一轮的 dp[i-1, j-1]< / span >
< a id = "__codelineno-11-25" name = "__codelineno-11-25" href = "#__codelineno-11-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-26" name = "__codelineno-11-26" href = "#__codelineno-11-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-27" name = "__codelineno-11-27" href = "#__codelineno-11-27" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "o" > [< / span > < span class = "n" > m< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-28" name = "__codelineno-11-28" href = "#__codelineno-11-28" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "cm" > /* 编辑距离：状态压缩后的动态规划 */< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > editDistanceDPComp< / span > < span class = "p" > (< / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "w" > < / span > < span class = "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" > s< / span > < span class = "p" > .< / span > < span class = "n" > length< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > length< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > (< / span > < span class = "n" > m< / 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 = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余行< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首列< / span >
< a id = "__codelineno-12-12" name = "__codelineno-12-12" href = "#__codelineno-12-12" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存 dp[i-1, j-1]< / span >
< a id = "__codelineno-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余列< / span >
< a id = "__codelineno-12-15" name = "__codelineno-12-15" href = "#__codelineno-12-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-16" name = "__codelineno-12-16" href = "#__codelineno-12-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-12-17" name = "__codelineno-12-17" href = "#__codelineno-12-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-18" name = "__codelineno-12-18" href = "#__codelineno-12-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-12-19" name = "__codelineno-12-19" href = "#__codelineno-12-19" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-20" name = "__codelineno-12-20" href = "#__codelineno-12-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-21" name = "__codelineno-12-21" href = "#__codelineno-12-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-12-22" name = "__codelineno-12-22" href = "#__codelineno-12-22" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > min< / span > < span class = "p" > (< / span > < span class = "n" > min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]),< / span > < span class = "w" > < / span > < span class = "n" > leftup< / 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-12-23" name = "__codelineno-12-23" href = "#__codelineno-12-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-24" name = "__codelineno-12-24" href = "#__codelineno-12-24" > < / a > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新为下一轮的 dp[i-1, j-1]< / span >
< a id = "__codelineno-12-25" name = "__codelineno-12-25" href = "#__codelineno-12-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-26" name = "__codelineno-12-26" href = "#__codelineno-12-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-27" name = "__codelineno-12-27" href = "#__codelineno-12-27" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > m< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-12-28" name = "__codelineno-12-28" href = "#__codelineno-12-28" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > edit_distance_dp_comp< / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > ,< / span > < span class = "n" > t< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 编辑距离：状态压缩后的动态规划" " " < / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > m< / span > < span class = "o" > =< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > ),< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > t< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "n" > dp< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "n" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "c1" > # 状态转移：首行< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > j< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "c1" > # 状态转移：其余行< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "c1" > # 状态转移：首列< / span >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "n" > leftup< / span > < span class = "o" > =< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "c1" > # 暂存 dp[i-1, j-1]< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a > < span class = "c1" > # 状态转移：其余列< / span >
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / a > < span class = "n" > temp< / span > < span class = "o" > =< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-13-16" name = "__codelineno-13-16" href = "#__codelineno-13-16" > < / a > < span class = "k" > if< / span > < span class = "n" > s< / 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 = "o" > ==< / span > < span class = "n" > t< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-13-17" name = "__codelineno-13-17" href = "#__codelineno-13-17" > < / a > < span class = "c1" > # 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-13-18" name = "__codelineno-13-18" href = "#__codelineno-13-18" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > leftup< / span >
< a id = "__codelineno-13-19" name = "__codelineno-13-19" href = "#__codelineno-13-19" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-20" name = "__codelineno-13-20" href = "#__codelineno-13-20" > < / a > < span class = "c1" > # 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-13-21" name = "__codelineno-13-21" href = "#__codelineno-13-21" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "nb" > min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ],< / span > < span class = "n" > leftup< / span > < span class = "p" > )< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-13-22" name = "__codelineno-13-22" href = "#__codelineno-13-22" > < / a > < span class = "n" > leftup< / span > < span class = "o" > =< / span > < span class = "n" > temp< / span > < span class = "c1" > # 更新为下一轮的 dp[i-1, j-1]< / span >
< a id = "__codelineno-13-23" name = "__codelineno-13-23" href = "#__codelineno-13-23" > < / a > < span class = "k" > return< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > m< / span > < span class = "p" > ]< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-24 13:09:54 +08:00
< div class = "highlight" > < span class = "filename" > edit_distance.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "cm" > /* 编辑距离：状态压缩后的动态规划 */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > editDistanceDPComp< / span > < span class = "p" > (< / span > < span class = "nx" > s< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > s< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > t< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行< / span >
< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > j< / span >
< a id = "__codelineno-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-10" name = "__codelineno-14-10" href = "#__codelineno-14-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余行< / span >
< a id = "__codelineno-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首列< / span >
< a id = "__codelineno-14-13" name = "__codelineno-14-13" href = "#__codelineno-14-13" > < / a > < span class = "w" > < / span > < span class = "nx" > leftUp< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存 dp[i-1, j-1]< / span >
< a id = "__codelineno-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-14-15" name = "__codelineno-14-15" href = "#__codelineno-14-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余列< / span >
< a id = "__codelineno-14-16" name = "__codelineno-14-16" href = "#__codelineno-14-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-17" name = "__codelineno-14-17" href = "#__codelineno-14-17" > < / a > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-14-18" name = "__codelineno-14-18" href = "#__codelineno-14-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > s< / 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 = "o" > ==< / span > < span class = "w" > < / span > < span class = "nx" > t< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-19" name = "__codelineno-14-19" href = "#__codelineno-14-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-14-20" name = "__codelineno-14-20" href = "#__codelineno-14-20" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > leftUp< / span >
< a id = "__codelineno-14-21" name = "__codelineno-14-21" href = "#__codelineno-14-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-22" name = "__codelineno-14-22" href = "#__codelineno-14-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-14-23" name = "__codelineno-14-23" href = "#__codelineno-14-23" > < / a > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > MinInt< / span > < span class = "p" > (< / span > < span class = "nx" > MinInt< / span > < span class = "p" > (< / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]),< / span > < span class = "w" > < / span > < span class = "nx" > leftUp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-14-24" name = "__codelineno-14-24" href = "#__codelineno-14-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-25" name = "__codelineno-14-25" href = "#__codelineno-14-25" > < / a > < span class = "w" > < / span > < span class = "nx" > leftUp< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "w" > < / span > < span class = "c1" > // 更新为下一轮的 dp[i-1, j-1]< / span >
< a id = "__codelineno-14-26" name = "__codelineno-14-26" href = "#__codelineno-14-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-27" name = "__codelineno-14-27" href = "#__codelineno-14-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-28" name = "__codelineno-14-28" href = "#__codelineno-14-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > dp< / span > < span class = "p" > [< / span > < span class = "nx" > m< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-14-29" name = "__codelineno-14-29" href = "#__codelineno-14-29" > < / a > < span class = "p" > }< / span >
2023-07-13 05:26:03 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > editDistanceDPComp< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > editDistanceDPComp< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > edit_distance.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / 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" > editDistanceDPComp< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-16 04:19:01 +08:00
< div class = "highlight" > < span class = "filename" > edit_distance.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 编辑距离：状态压缩后的动态规划 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > editDistanceDPComp< / span > < span class = "p" > (< / span > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "w" > < / span > < span class = "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" > s< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > [< / span > < span class = "n" > m< / 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-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余行< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首列< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "m" > 0< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存 dp[i-1, j-1]< / span >
< a id = "__codelineno-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "m" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余列< / span >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > s< / 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 = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-18" name = "__codelineno-18-18" href = "#__codelineno-18-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-18-19" name = "__codelineno-18-19" href = "#__codelineno-18-19" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-20" name = "__codelineno-18-20" href = "#__codelineno-18-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-21" name = "__codelineno-18-21" href = "#__codelineno-18-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-18-22" name = "__codelineno-18-22" href = "#__codelineno-18-22" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "n" > Min< / span > < span class = "p" > (< / span > < span class = "n" > Math< / span > < span class = "p" > .< / span > < span class = "n" > Min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]),< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-23" name = "__codelineno-18-23" href = "#__codelineno-18-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-24" name = "__codelineno-18-24" href = "#__codelineno-18-24" > < / a > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新为下一轮的 dp[i-1, j-1]< / span >
< a id = "__codelineno-18-25" name = "__codelineno-18-25" href = "#__codelineno-18-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-26" name = "__codelineno-18-26" href = "#__codelineno-18-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-27" name = "__codelineno-18-27" href = "#__codelineno-18-27" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > m< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-18-28" name = "__codelineno-18-28" href = "#__codelineno-18-28" > < / a > < span class = "p" > }< / span >
2023-07-13 05:26:03 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-19 01:44:47 +08:00
< div class = "highlight" > < span class = "filename" > edit_distance.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "cm" > /* 编辑距离：状态压缩后的动态规划 */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > editDistanceDPComp< / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > :< / span > < span class = "nb" > String< / span > < span class = "p" > ,< / span > < span class = "n" > t< / span > < span class = "p" > :< / span > < span class = "nb" > String< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "kd" > let< / span > < span class = "nv" > n< / span > < span class = "p" > =< / span > < span class = "n" > s< / span > < span class = "p" > .< / span > < span class = "n" > utf8CString< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > m< / span > < span class = "p" > =< / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > utf8CString< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a > < span class = "kd" > var< / span > < span class = "nv" > dp< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "n" > m< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "c1" > // 状态转移：首行< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > through< / span > < span class = "p" > :< / span > < span class = "n" > m< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > j< / span >
< a id = "__codelineno-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "c1" > // 状态转移：其余行< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > through< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / a > < span class = "c1" > // 状态转移：首列< / span >
< a id = "__codelineno-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / a > < span class = "kd" > var< / span > < span class = "nv" > leftup< / span > < span class = "p" > =< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "c1" > // 暂存 dp[i-1, j-1]< / span >
< a id = "__codelineno-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > i< / span >
< a id = "__codelineno-19-15" name = "__codelineno-19-15" href = "#__codelineno-19-15" > < / a > < span class = "c1" > // 状态转移：其余列< / span >
< a id = "__codelineno-19-16" name = "__codelineno-19-16" href = "#__codelineno-19-16" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > through< / span > < span class = "p" > :< / span > < span class = "n" > m< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-17" name = "__codelineno-19-17" href = "#__codelineno-19-17" > < / a > < span class = "kd" > let< / span > < span class = "nv" > temp< / span > < span class = "p" > =< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-19-18" name = "__codelineno-19-18" href = "#__codelineno-19-18" > < / a > < span class = "k" > if< / span > < span class = "n" > s< / span > < span class = "p" > .< / span > < span class = "n" > utf8CString< / 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 = "p" > ==< / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > utf8CString< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-19" name = "__codelineno-19-19" href = "#__codelineno-19-19" > < / a > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-19-20" name = "__codelineno-19-20" href = "#__codelineno-19-20" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > leftup< / span >
< a id = "__codelineno-19-21" name = "__codelineno-19-21" href = "#__codelineno-19-21" > < / a > < span class = "p" > }< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-22" name = "__codelineno-19-22" href = "#__codelineno-19-22" > < / a > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-19-23" name = "__codelineno-19-23" href = "#__codelineno-19-23" > < / a > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "bp" > min< / span > < span class = "p" > (< / span > < span class = "bp" > min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]),< / span > < span class = "n" > leftup< / span > < span class = "p" > )< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-19-24" name = "__codelineno-19-24" href = "#__codelineno-19-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-25" name = "__codelineno-19-25" href = "#__codelineno-19-25" > < / a > < span class = "n" > leftup< / span > < span class = "p" > =< / span > < span class = "n" > temp< / span > < span class = "c1" > // 更新为下一轮的 dp[i-1, j-1]< / span >
< a id = "__codelineno-19-26" name = "__codelineno-19-26" href = "#__codelineno-19-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-27" name = "__codelineno-19-27" href = "#__codelineno-19-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-28" name = "__codelineno-19-28" href = "#__codelineno-19-28" > < / a > < span class = "k" > return< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > m< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-19-29" name = "__codelineno-19-29" href = "#__codelineno-19-29" > < / a > < span class = "p" > }< / span >
2023-07-13 05:26:03 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-17 02:17:51 +08:00
< div class = "highlight" > < span class = "filename" > edit_distance.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "c1" > // 编辑距离：状态压缩后的动态规划< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > editDistanceDPComp< / span > < span class = "p" > (< / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "n" > s< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "kt" > u8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "kt" > u8< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / a > < span class = "w" > < / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "kr" > var< / 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" > s< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "w" > < / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "n" > _< / span > < span class = "p" > ]< / span > < span class = "kt" > i32< / span > < span class = "p" > {< / span > < span class = "mi" > 0< / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > m< / 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-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首行< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > j< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-8" name = "__codelineno-20-8" href = "#__codelineno-20-8" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > j< / span > < span class = "p" > );< / span >
< a id = "__codelineno-20-9" name = "__codelineno-20-9" href = "#__codelineno-20-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-10" name = "__codelineno-20-10" href = "#__codelineno-20-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余行< / span >
< a id = "__codelineno-20-11" name = "__codelineno-20-11" href = "#__codelineno-20-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > i< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-12" name = "__codelineno-20-12" href = "#__codelineno-20-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：首列< / span >
< a id = "__codelineno-20-13" name = "__codelineno-20-13" href = "#__codelineno-20-13" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存 dp[i-1, j-1]< / span >
< a id = "__codelineno-20-14" name = "__codelineno-20-14" href = "#__codelineno-20-14" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-20-15" name = "__codelineno-20-15" href = "#__codelineno-20-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 状态转移：其余列< / span >
< a id = "__codelineno-20-16" name = "__codelineno-20-16" href = "#__codelineno-20-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > j< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-17" name = "__codelineno-20-17" href = "#__codelineno-20-17" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-20-18" name = "__codelineno-20-18" href = "#__codelineno-20-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > s< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > t< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-19" name = "__codelineno-20-19" href = "#__codelineno-20-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若两字符相等，则直接跳过此两字符< / span >
< a id = "__codelineno-20-20" name = "__codelineno-20-20" href = "#__codelineno-20-20" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-21" name = "__codelineno-20-21" href = "#__codelineno-20-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-22" name = "__codelineno-20-22" href = "#__codelineno-20-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1< / span >
< a id = "__codelineno-20-23" name = "__codelineno-20-23" href = "#__codelineno-20-23" > < / a > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @min< / span > < span class = "p" > (< / span > < span class = "nb" > @min< / span > < span class = "p" > (< / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]),< / span > < span class = "w" > < / span > < span class = "n" > leftup< / 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-20-24" name = "__codelineno-20-24" href = "#__codelineno-20-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-25" name = "__codelineno-20-25" href = "#__codelineno-20-25" > < / a > < span class = "w" > < / span > < span class = "n" > leftup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新为下一轮的 dp[i-1, j-1]< / span >
< a id = "__codelineno-20-26" name = "__codelineno-20-26" href = "#__codelineno-20-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-27" name = "__codelineno-20-27" href = "#__codelineno-20-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-28" name = "__codelineno-20-28" href = "#__codelineno-20-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > dp< / span > < span class = "p" > [< / span > < span class = "n" > m< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-20-29" name = "__codelineno-20-29" href = "#__codelineno-20-29" > < / a > < span class = "p" > }< / span >
2023-07-13 05:26:03 +08:00
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< div class = "highlight" > < span class = "filename" > edit_distance.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / 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" > editDistanceDPComp< / span > < span class = "p" > }< / span >
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< script src = "../../assets/javascripts/bundle.f11ae8b1.min.js" > < / script >
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< script src = "../../javascripts/mathjax.js" > < / script >
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< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
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< script src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
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< / body >
< / html >
