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Hello 算法
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9.3. 图的遍历
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0. 写在前面
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0. 写在前面
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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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1. 引言
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1. 引言
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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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2. 复杂度分析
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2. 复杂度分析
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< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/performance_evaluation/" class = "md-nav__link" >
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2.1. 算法效率评估
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/time_complexity/" class = "md-nav__link" >
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2.2. 时间复杂度
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< / a >
< / li >
< li class = "md-nav__item" >
< 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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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/space_time_tradeoff/" class = "md-nav__link" >
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2.4. 权衡时间与空间
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
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2.5. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
< label class = "md-nav__link" for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
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3. 数据结构简介
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_4_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
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3. 数据结构简介
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/data_and_memory/" class = "md-nav__link" >
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3.1. 数据与内存
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
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3.2. 数据结构分类
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
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3.3. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
< label class = "md-nav__link" for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
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4. 数组与链表
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_5_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
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4. 数组与链表
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
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4.1. 数组（ ）
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
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4.2. 链表（ ）
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< / a >
< / li >
< 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 >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
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4.4. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
< label class = "md-nav__link" for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
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5. 栈与队列
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_6_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
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5. 栈与队列
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
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5.1. 栈（ ）
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
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5.2. 队列（ ）
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< / a >
< / li >
< 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（ ）
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
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5.4. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
< label class = "md-nav__link" for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
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6. 散列表
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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6. 散列表
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
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6.1. 哈希表（ ）
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
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6.2. 哈希冲突处理
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
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6.3. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
< label class = "md-nav__link" for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
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7. 二叉树
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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7. 二叉树
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
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7.1. 二叉树（ ）
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
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7.2. 二叉树遍历
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
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7.3. 二叉搜索树
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
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7.4. AVL 树 *
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
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7.5. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
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< label class = "md-nav__link" for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
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8. 堆
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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8. 堆
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
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8.1. 堆（ ）
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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" >
8.2. 建堆操作 *
< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
8.3. 小结
< / a >
< / li >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" checked >
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< label class = "md-nav__link" for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
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9. 图
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
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9. 图
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../graph/" class = "md-nav__link" >
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9.1. 图（ ）
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../graph_operations/" class = "md-nav__link" >
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9.2. 图基础操作
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< / a >
< / li >
< li class = "md-nav__item md-nav__item--active" >
< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
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9.3. 图的遍历
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
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9.3. 图的遍历
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< / a >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#931" class = "md-nav__link" >
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9.3.1. 广度优先遍历
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< / a >
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< nav class = "md-nav" aria-label = "9.3.1. 广度优先遍历" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#_1" class = "md-nav__link" >
算法实现
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_2" class = "md-nav__link" >
复杂度分析
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#932" class = "md-nav__link" >
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9.3.2. 深度优先遍历
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< / a >
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< nav class = "md-nav" aria-label = "9.3.2. 深度优先遍历" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#_3" class = "md-nav__link" >
算法实现
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#_4" class = "md-nav__link" >
复杂度分析
< / a >
< / li >
< / ul >
< / nav >
< / li >
< / ul >
< / nav >
< / li >
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< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
9.4. 小结
< / a >
< / li >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
< label class = "md-nav__link" for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
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10. 查找算法
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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10. 查找算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/linear_search/" class = "md-nav__link" >
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10.1. 线性查找
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.2. 二分查找
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/hashing_search/" class = "md-nav__link" >
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10.3. 哈希查找
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.4. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
< label class = "md-nav__link" for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
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11. 排序算法
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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11. 排序算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/intro_to_sort/" class = "md-nav__link" >
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11.1. 排序简介
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.2. 冒泡排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.3. 插入排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.4. 快速排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.5. 归并排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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11.6. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
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12. 附录
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12. 附录
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12.2. 一起参与创作
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9.3.1. 广度优先遍历
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算法实现
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复杂度分析
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9.3.2. 深度优先遍历
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复杂度分析
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< h1 id = "93" > 9.3. 图的遍历< a class = "headerlink" href = "#93" title = "Permanent link" > ¶ < / a > < / h1 >
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< div class = "admonition note" >
< p class = "admonition-title" > 图与树的关系< / p >
< p > 树代表的是“一对多”的关系，而图则自由度更高，可以代表任意“多对多”关系。本质上，< strong > 可以把树看作是图的一类特例< / strong > 。那么显然，树遍历操作也是图遍历操作的一个特例，两者的方法是非常类似的，建议你在学习本章节的过程中将两者融会贯通。< / p >
< / div >
< p > 「图」与「树」都是非线性数据结构，都需要使用「搜索算法」来实现遍历操作。< / p >
< p > 类似地，图的遍历方式也分为两种，即「广度优先遍历 Breadth-First Traversal」和「深度优先遍历 Depth-First Travsersal」， ， < / p >
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< h2 id = "931" > 9.3.1. 广度优先遍历< a class = "headerlink" href = "#931" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > < strong > 广度优先遍历优是一种由近及远的遍历方式，从距离最近的顶点开始访问，并一层层向外扩张< / strong > 。具体地，从某个顶点出发，先遍历该顶点的所有邻接顶点，随后遍历下个顶点的所有邻接顶点，以此类推……< / p >
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< p > < img alt = "图的广度优先遍历" src = "../graph_traversal.assets/graph_bfs.png" / > < / p >
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< p align = "center" > Fig. 图的广度优先遍历 < / p >
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< h3 id = "_1" > 算法实现< a class = "headerlink" href = "#_1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > BFS 常借助「队列」来实现。队列具有“先入先出”的性质，这与 BFS “由近及远”的思想是异曲同工的。< / p >
< ol >
< li > 将遍历起始顶点 < code > startVet< / code > 加入队列，并开启循环；< / li >
< li > 在循环的每轮迭代中，弹出队首顶点弹出并记录访问，并将该顶点的所有邻接顶点加入到队列尾部；< / li >
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< li > 循环 < code > 2.< / code > ，直到所有顶点访问完成后结束；< / li >
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< / ol >
< p > 为了防止重复遍历顶点，我们需要借助一个哈希表 < code > visited< / code > 来记录哪些结点已被访问。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:10" > < 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" / > < 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 > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > graph_bfs.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nf" > graphBFS< / span > < span class = "p" > (< / span > < span class = "n" > GraphAdjList< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "n" > Set< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > HashSet< / span > < span class = "o" > < > < / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {{< / span > < span class = "w" > < / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span > < span class = "w" > < / 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 = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "n" > Queue< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > LinkedList< / span > < span class = "o" > < > < / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {{< / span > < span class = "w" > < / span > < span class = "n" > offer< / span > < span class = "p" > (< / span > < span class = "n" > startVet< / 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 = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "na" > isEmpty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "na" > poll< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > adjVet< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > .< / span > < span class = "na" > adjList< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > vet< / 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 = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "na" > contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "na" > offer< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "w" > < / 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 = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
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< div class = "highlight" > < span class = "filename" > graph_bfs.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "p" > [< / span > < span class = "k" > 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" > graphBFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
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< div class = "highlight" > < span class = "filename" > graph_bfs.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "sd" > " " " 广度优先遍历 BFS " " " < / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "c1" > # 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "k" > def< / span > < span class = "nf" > graph_bfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "n" > start_vet< / span > < span class = "p" > :< / span > < span class = "n" > Vertex< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "n" > List< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "c1" > # 顶点遍历序列< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "c1" > # 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "n" > visited< / span > < span class = "o" > =< / span > < span class = "nb" > set< / span > < span class = "p" > ([< / span > < span class = "n" > start_vet< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "c1" > # 队列用于实现 BFS< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "n" > que< / span > < span class = "o" > =< / span > < span class = "n" > collections< / span > < span class = "o" > .< / span > < span class = "n" > deque< / span > < span class = "p" > ([< / span > < span class = "n" > start_vet< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "c1" > # 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "k" > while< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > que< / span > < span class = "p" > )< / span > < span class = "o" > > < / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "n" > vet< / span > < span class = "o" > =< / span > < span class = "n" > que< / span > < span class = "o" > .< / span > < span class = "n" > popleft< / span > < span class = "p" > ()< / span > < span class = "c1" > # 队首顶点出队< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "c1" > # 记录访问顶点< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "c1" > # 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "k" > for< / span > < span class = "n" > adj_vet< / span > < span class = "ow" > in< / span > < span class = "n" > graph< / span > < span class = "o" > .< / span > < span class = "n" > adj_list< / span > < span class = "p" > [< / span > < span class = "n" > vet< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "k" > if< / span > < span class = "n" > adj_vet< / span > < span class = "ow" > in< / span > < span class = "n" > visited< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "k" > continue< / span > < span class = "c1" > # 跳过已被访问过的顶点< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "n" > que< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > adj_vet< / span > < span class = "p" > )< / span > < span class = "c1" > # 只入队未访问的顶点< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "n" > visited< / span > < span class = "o" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > adj_vet< / span > < span class = "p" > )< / span > < span class = "c1" > # 标记该顶点已被访问< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "c1" > # 返回顶点遍历序列< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-28 00:16:29 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > graphBFS< / span > < span class = "p" > (< / span > < span class = "nx" > g< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > graphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "w" > < / span > < span class = "nx" > Vertex< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "nx" > Vertex< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > (< / span > < span class = "kd" > map< / span > < span class = "p" > [< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ]< / span > < span class = "kd" > struct< / 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 = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > startVet< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kd" > struct< / 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" > // 队列用于实现 BFS, 使用切片模拟队列< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / 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" > queue< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "nx" > queue< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / 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 = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > queue< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / 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 = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / 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 = "nx" > queue< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > :]< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > g< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > [< / span > < span class = "nx" > vet< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > isExist< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > adjVet< / 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 = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > !< / span > < span class = "nx" > isExist< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "nx" > queue< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kd" > struct< / 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 = "p" > }< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-25 02:19:21 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > graphBFS< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Set< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "nx" > startVet< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > shift< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > graph< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > .< / span > < span class = "nx" > get< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ??< / span > < span class = "w" > < / span > < span class = "p" > [])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > has< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_bfs.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > graphBFS< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > Vertex< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Set< / span > < span class = "o" > < < / span > < span class = "nx" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Set< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "nx" > startVet< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > shift< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > graph< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > .< / span > < span class = "nx" > get< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ??< / span > < span class = "w" > < / span > < span class = "p" > [])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > has< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 只入队未访问< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_bfs.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" > graphBFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_bfs.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > graph_bfs< / 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" > graphBFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_bfs.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "kd" > func< / span > < span class = "nf" > graphBFS< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "n" > startVet< / span > < span class = "p" > :< / span > < span class = "n" > Vertex< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "kd" > var< / span > < span class = "nv" > visited< / span > < span class = "p" > :< / span > < span class = "n" > Set< / span > < span class = "p" > < < / span > < span class = "n" > Vertex< / span > < span class = "p" > > < / span > < span class = "p" > =< / span > < span class = "p" > [< / span > < span class = "n" > startVet< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "kd" > var< / span > < span class = "nv" > que< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > [< / span > < span class = "n" > startVet< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "k" > while< / span > < span class = "o" > !< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "bp" > isEmpty< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "kd" > let< / span > < span class = "nv" > vet< / span > < span class = "p" > =< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > removeFirst< / span > < span class = "p" > ()< / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "k" > for< / span > < span class = "n" > adjVet< / span > < span class = "k" > in< / span > < span class = "n" > graph< / span > < span class = "p" > .< / span > < span class = "n" > adjList< / span > < span class = "p" > [< / span > < span class = "n" > vet< / span > < span class = "p" > ]< / span > < span class = "p" > ??< / 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" > visited< / span > < span class = "p" > .< / span > < span class = "bp" > contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / 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 = "k" > continue< / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > )< / span > < span class = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "bp" > insert< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > )< / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "p" > }< / 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 = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_bfs.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / 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" > graphBFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
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< p > 代码相对抽象，建议对照以下动画图示来加深理解。< / p >
2023-02-22 00:57:11 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:11" > < 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" / > < 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 > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< p > < img alt = "图的广度优先遍历步骤" src = "../graph_traversal.assets/graph_bfs_step1.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step2" src = "../graph_traversal.assets/graph_bfs_step2.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step3" src = "../graph_traversal.assets/graph_bfs_step3.png" / > < / p >
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< p > < img alt = "graph_bfs_step4" src = "../graph_traversal.assets/graph_bfs_step4.png" / > < / p >
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< p > < img alt = "graph_bfs_step5" src = "../graph_traversal.assets/graph_bfs_step5.png" / > < / p >
< / div >
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< p > < img alt = "graph_bfs_step6" src = "../graph_traversal.assets/graph_bfs_step6.png" / > < / p >
< / div >
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< p > < img alt = "graph_bfs_step7" src = "../graph_traversal.assets/graph_bfs_step7.png" / > < / p >
< / div >
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< p > < img alt = "graph_bfs_step8" src = "../graph_traversal.assets/graph_bfs_step8.png" / > < / p >
< / div >
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< p > < img alt = "graph_bfs_step9" src = "../graph_traversal.assets/graph_bfs_step9.png" / > < / p >
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< p > < img alt = "graph_bfs_step10" src = "../graph_traversal.assets/graph_bfs_step10.png" / > < / p >
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< p > < img alt = "graph_bfs_step11" src = "../graph_traversal.assets/graph_bfs_step11.png" / > < / p >
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< div class = "admonition question" >
< p class = "admonition-title" > 广度优先遍历的序列是否唯一？< / p >
2023-02-24 11:43:41 +08:00
< p > 不唯一。广度优先遍历只要求“由近及远”，< strong > 而多个相同距离的顶点的遍历顺序允许被任意打乱< / strong > 。以上图为例，顶点 < span class = "arithmatex" > \(1\)< / span > , < span class = "arithmatex" > \(3\)< / span > 的访问顺序可以交换、顶点 < span class = "arithmatex" > \(2\)< / span > , < span class = "arithmatex" > \(4\)< / span > , < span class = "arithmatex" > \(6\)< / span > 的访问顺序也可以任意交换、以此类推……< / p >
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< / div >
< h3 id = "_2" > 复杂度分析< a class = "headerlink" href = "#_2" title = "Permanent link" > ¶ < / a > < / h3 >
< p > < strong > 时间复杂度：< / strong > 所有顶点都会入队、出队一次，使用 < span class = "arithmatex" > \(O(|V|)\)< / span > 时间；在遍历邻接顶点的过程中，由于是无向图，因此所有边都会被访问 < span class = "arithmatex" > \(2\)< / span > 次，使用 < span class = "arithmatex" > \(O(2|E|)\)< / span > 时间；总体使用 < span class = "arithmatex" > \(O(|V| + |E|)\)< / span > 时间。< / p >
< p > < strong > 空间复杂度：< / strong > 列表 < code > res< / code > ，哈希表 < code > visited< / code > ，队列 < code > que< / code > 中的顶点数量最多为 < span class = "arithmatex" > \(|V|\)< / span > ，使用 < span class = "arithmatex" > \(O(|V|)\)< / span > 空间。< / p >
2023-02-24 18:46:22 +08:00
< h2 id = "932" > 9.3.2. 深度优先遍历< a class = "headerlink" href = "#932" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > < strong > 深度优先遍历是一种优先走到底、无路可走再回头的遍历方式< / strong > 。具体地，从某个顶点出发，不断地访问当前结点的某个邻接顶点，直到走到尽头时回溯，再继续走到底 + 回溯，以此类推……直至所有顶点遍历完成时结束。< / p >
2023-02-26 18:18:03 +08:00
< p > < img alt = "图的深度优先遍历" src = "../graph_traversal.assets/graph_dfs.png" / > < / p >
2023-02-26 19:53:32 +08:00
< p align = "center" > Fig. 图的深度优先遍历 < / p >
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< h3 id = "_3" > 算法实现< a class = "headerlink" href = "#_3" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 这种“走到头 + 回溯”的算法形式一般基于递归来实现。与 BFS 类似，在 DFS 中我们也需要借助一个哈希表 < code > visited< / code > 来记录已被访问的顶点，以避免重复访问顶点。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:10" > < 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" / > < 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 > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > graph_dfs.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > GraphAdjList< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Set< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > adjVet< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > .< / span > < span class = "na" > adjList< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "na" > contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > adjVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-13" name = "__codelineno-10-13" href = "#__codelineno-10-13" > < / a >
< a id = "__codelineno-10-14" name = "__codelineno-10-14" href = "#__codelineno-10-14" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-10-15" name = "__codelineno-10-15" href = "#__codelineno-10-15" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-10-16" name = "__codelineno-10-16" href = "#__codelineno-10-16" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nf" > graphDFS< / span > < span class = "p" > (< / span > < span class = "n" > GraphAdjList< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-17" name = "__codelineno-10-17" href = "#__codelineno-10-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-10-18" name = "__codelineno-10-18" href = "#__codelineno-10-18" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-10-19" name = "__codelineno-10-19" href = "#__codelineno-10-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-10-20" name = "__codelineno-10-20" href = "#__codelineno-10-20" > < / a > < span class = "w" > < / span > < span class = "n" > Set< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > HashSet< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-10-21" name = "__codelineno-10-21" href = "#__codelineno-10-21" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-22" name = "__codelineno-10-22" href = "#__codelineno-10-22" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-23" name = "__codelineno-10-23" href = "#__codelineno-10-23" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-25 02:19:21 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "p" > [< / span > < span class = "k" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > dfs< / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "p" > [< / span > < span class = "k" > 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" > graphDFS< / span > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-23 20:23:42 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "sd" > " " " 深度优先遍历 DFS 辅助函数 " " " < / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "k" > def< / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "n" > visited< / span > < span class = "p" > :< / span > < span class = "n" > Set< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ],< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "n" > List< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ],< / span > < span class = "n" > vet< / span > < span class = "p" > :< / span > < span class = "n" > Vertex< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "c1" > # 记录访问顶点< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "n" > visited< / span > < span class = "o" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "c1" > # 标记该顶点已被访问< / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "c1" > # 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "k" > for< / span > < span class = "n" > adjVet< / span > < span class = "ow" > in< / span > < span class = "n" > graph< / span > < span class = "o" > .< / span > < span class = "n" > adj_list< / span > < span class = "p" > [< / span > < span class = "n" > vet< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a > < span class = "k" > if< / span > < span class = "n" > adjVet< / span > < span class = "ow" > in< / span > < span class = "n" > visited< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a > < span class = "k" > continue< / span > < span class = "c1" > # 跳过已被访问过的顶点< / span >
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "c1" > # 递归访问邻接顶点< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > adjVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a >
< a id = "__codelineno-12-12" name = "__codelineno-12-12" href = "#__codelineno-12-12" > < / a > < span class = "sd" > " " " 深度优先遍历 DFS " " " < / span >
< a id = "__codelineno-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / a > < span class = "c1" > # 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / a > < span class = "k" > def< / span > < span class = "nf" > graph_dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "n" > start_vet< / span > < span class = "p" > :< / span > < span class = "n" > Vertex< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "n" > List< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-12-15" name = "__codelineno-12-15" href = "#__codelineno-12-15" > < / a > < span class = "c1" > # 顶点遍历序列< / span >
< a id = "__codelineno-12-16" name = "__codelineno-12-16" href = "#__codelineno-12-16" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-12-17" name = "__codelineno-12-17" href = "#__codelineno-12-17" > < / a > < span class = "c1" > # 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-12-18" name = "__codelineno-12-18" href = "#__codelineno-12-18" > < / a > < span class = "n" > visited< / span > < span class = "o" > =< / span > < span class = "nb" > set< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-12-19" name = "__codelineno-12-19" href = "#__codelineno-12-19" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > start_vet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-20" name = "__codelineno-12-20" href = "#__codelineno-12-20" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-28 00:16:29 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > g< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > graphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "w" > < / span > < span class = "kd" > map< / span > < span class = "p" > [< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ]< / span > < span class = "kd" > struct< / span > < span class = "p" > {},< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "w" > < / span > < span class = "nx" > Vertex< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // append 操作会返回新的的引用， < / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > vet< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kd" > struct< / span > < span class = "p" > {}{}< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > g< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > [< / span > < span class = "nx" > vet< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > isExist< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > !< / span > < span class = "nx" > isExist< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > g< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / a >
< a id = "__codelineno-13-16" name = "__codelineno-13-16" href = "#__codelineno-13-16" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-13-17" name = "__codelineno-13-17" href = "#__codelineno-13-17" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-13-18" name = "__codelineno-13-18" href = "#__codelineno-13-18" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > graphDFS< / span > < span class = "p" > (< / span > < span class = "nx" > g< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > graphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "w" > < / span > < span class = "nx" > Vertex< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "nx" > Vertex< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-19" name = "__codelineno-13-19" href = "#__codelineno-13-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-13-20" name = "__codelineno-13-20" href = "#__codelineno-13-20" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-21" name = "__codelineno-13-21" href = "#__codelineno-13-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-13-22" name = "__codelineno-13-22" href = "#__codelineno-13-22" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > (< / span > < span class = "kd" > map< / span > < span class = "p" > [< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ]< / span > < span class = "kd" > struct< / span > < span class = "p" > {})< / span >
< a id = "__codelineno-13-23" name = "__codelineno-13-23" href = "#__codelineno-13-23" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > g< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-24" name = "__codelineno-13-24" href = "#__codelineno-13-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-13-25" name = "__codelineno-13-25" href = "#__codelineno-13-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-13-26" name = "__codelineno-13-26" href = "#__codelineno-13-26" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_dfs.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / 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" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / 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 = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > graph< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > .< / span > < span class = "nx" > get< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > ))< / 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 = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > has< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-14-10" name = "__codelineno-14-10" href = "#__codelineno-14-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-14-13" name = "__codelineno-14-13" href = "#__codelineno-14-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-14-15" name = "__codelineno-14-15" href = "#__codelineno-14-15" > < / a >
< a id = "__codelineno-14-16" name = "__codelineno-14-16" href = "#__codelineno-14-16" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-14-17" name = "__codelineno-14-17" href = "#__codelineno-14-17" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-14-18" name = "__codelineno-14-18" href = "#__codelineno-14-18" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > graphDFS< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / 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" > // 顶点遍历序列< / span >
< a id = "__codelineno-14-20" name = "__codelineno-14-20" href = "#__codelineno-14-20" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-14-21" name = "__codelineno-14-21" href = "#__codelineno-14-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-14-22" name = "__codelineno-14-22" href = "#__codelineno-14-22" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Set< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-14-23" name = "__codelineno-14-23" href = "#__codelineno-14-23" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-14-24" name = "__codelineno-14-24" href = "#__codelineno-14-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-14-25" name = "__codelineno-14-25" href = "#__codelineno-14-25" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-25 02:19:21 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Set< / span > < span class = "o" > < < / span > < span class = "nx" > Vertex< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > graph< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > .< / span > < span class = "nx" > get< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > has< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-15-9" name = "__codelineno-15-9" href = "#__codelineno-15-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-12" name = "__codelineno-15-12" href = "#__codelineno-15-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-13" name = "__codelineno-15-13" href = "#__codelineno-15-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-15-14" name = "__codelineno-15-14" href = "#__codelineno-15-14" > < / a >
< a id = "__codelineno-15-15" name = "__codelineno-15-15" href = "#__codelineno-15-15" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-15-16" name = "__codelineno-15-16" href = "#__codelineno-15-16" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-15-17" name = "__codelineno-15-17" href = "#__codelineno-15-17" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > graphDFS< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > Vertex< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-18" name = "__codelineno-15-18" href = "#__codelineno-15-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-15-19" name = "__codelineno-15-19" href = "#__codelineno-15-19" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-15-20" name = "__codelineno-15-20" href = "#__codelineno-15-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-15-21" name = "__codelineno-15-21" href = "#__codelineno-15-21" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Set< / span > < span class = "o" > < < / span > < span class = "nx" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Set< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-15-22" name = "__codelineno-15-22" href = "#__codelineno-15-22" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-23" name = "__codelineno-15-23" href = "#__codelineno-15-23" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-24" name = "__codelineno-15-24" href = "#__codelineno-15-24" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
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< div class = "highlight" > < span class = "filename" > graph_dfs.c< / 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 = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > dfs< / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a >
< a id = "__codelineno-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > graphDFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_dfs.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > graph_dfs< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > dfs< / span > < span class = "p" > }< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / a >
< a id = "__codelineno-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > graph_dfs< / 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" > graphDFS< / span > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > graph_dfs.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "n" > visited< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "n" > Set< / span > < span class = "p" > < < / span > < span class = "n" > Vertex< / span > < span class = "p" > > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ],< / span > < span class = "n" > vet< / span > < span class = "p" > :< / span > < span class = "n" > Vertex< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "bp" > insert< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "k" > for< / span > < span class = "n" > adjVet< / span > < span class = "k" > in< / span > < span class = "n" > graph< / span > < span class = "p" > .< / span > < span class = "n" > adjList< / span > < span class = "p" > [< / span > < span class = "n" > vet< / span > < span class = "p" > ]< / span > < span class = "p" > ??< / span > < span class = "p" > []< / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "k" > if< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "bp" > contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / a > < span class = "k" > continue< / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "n" > visited< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > vet< / span > < span class = "p" > :< / span > < span class = "n" > adjVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / a > < span class = "kd" > func< / span > < span class = "nf" > graphDFS< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "n" > startVet< / span > < span class = "p" > :< / span > < span class = "n" > Vertex< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-18" name = "__codelineno-18-18" href = "#__codelineno-18-18" > < / a > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-18-19" name = "__codelineno-18-19" href = "#__codelineno-18-19" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-18-20" name = "__codelineno-18-20" href = "#__codelineno-18-20" > < / a > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-18-21" name = "__codelineno-18-21" href = "#__codelineno-18-21" > < / a > < span class = "kd" > var< / span > < span class = "nv" > visited< / span > < span class = "p" > :< / span > < span class = "n" > Set< / span > < span class = "p" > < < / span > < span class = "n" > Vertex< / span > < span class = "p" > > < / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-18-22" name = "__codelineno-18-22" href = "#__codelineno-18-22" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "n" > visited< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > vet< / span > < span class = "p" > :< / span > < span class = "n" > startVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-18-23" name = "__codelineno-18-23" href = "#__codelineno-18-23" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-18-24" name = "__codelineno-18-24" href = "#__codelineno-18-24" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_dfs.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / 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" > dfs< / span > < span class = "p" > }< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > graphDFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 深度优先遍历的算法流程如下图所示，其中< / p >
< ul >
< li > < strong > 直虚线代表向下递推< / strong > ，代表开启了一个新的递归方法来访问新顶点；< / li >
< li > < strong > 曲虚线代表向上回溯< / strong > ，代表此递归方法已经返回，回溯到了开启此递归方法的位置；< / li >
< / ul >
< p > 为了加深理解，请你将图示与代码结合起来，在脑中（或者用笔画下来）模拟整个 DFS 过程，包括每个递归方法何时开启、何时返回。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "4:11" > < input checked = "checked" id = "__tabbed_4_1" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_2" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_3" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_4" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_5" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_6" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_7" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_8" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_9" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_10" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_11" name = "__tabbed_4" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_4_1" > < 1> < / label > < label for = "__tabbed_4_2" > < 2> < / label > < label for = "__tabbed_4_3" > < 3> < / label > < label for = "__tabbed_4_4" > < 4> < / label > < label for = "__tabbed_4_5" > < 5> < / label > < label for = "__tabbed_4_6" > < 6> < / label > < label for = "__tabbed_4_7" > < 7> < / label > < label for = "__tabbed_4_8" > < 8> < / label > < label for = "__tabbed_4_9" > < 9> < / label > < label for = "__tabbed_4_10" > < 10> < / label > < label for = "__tabbed_4_11" > < 11> < / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< p > < img alt = "图的深度优先遍历步骤" src = "../graph_traversal.assets/graph_dfs_step1.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step2" src = "../graph_traversal.assets/graph_dfs_step2.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step3" src = "../graph_traversal.assets/graph_dfs_step3.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step4" src = "../graph_traversal.assets/graph_dfs_step4.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step5" src = "../graph_traversal.assets/graph_dfs_step5.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step6" src = "../graph_traversal.assets/graph_dfs_step6.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step7" src = "../graph_traversal.assets/graph_dfs_step7.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step8" src = "../graph_traversal.assets/graph_dfs_step8.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step9" src = "../graph_traversal.assets/graph_dfs_step9.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step10" src = "../graph_traversal.assets/graph_dfs_step10.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step11" src = "../graph_traversal.assets/graph_dfs_step11.png" / > < / p >
< / div >
< / div >
< / div >
< div class = "admonition question" >
< p class = "admonition-title" > 深度优先遍历的序列是否唯一？< / p >
< p > 与广度优先遍历类似，深度优先遍历序列的顺序也不是唯一的。给定某顶点，先往哪个方向探索都行，都是深度优先遍历。< / p >
< p > 以树的遍历为例，“根 < span class = "arithmatex" > \(\rightarrow\)< / span > 左 < span class = "arithmatex" > \(\rightarrow\)< / span > 右”、“左 < span class = "arithmatex" > \(\rightarrow\)< / span > 根 < span class = "arithmatex" > \(\rightarrow\)< / span > 右”、“左 < span class = "arithmatex" > \(\rightarrow\)< / span > 右 < span class = "arithmatex" > \(\rightarrow\)< / span > 根”分别对应前序、中序、后序遍历，体现三种不同的遍历优先级，而三者都属于深度优先遍历。< / p >
< / div >
< h3 id = "_4" > 复杂度分析< a class = "headerlink" href = "#_4" title = "Permanent link" > ¶ < / a > < / h3 >
< p > < strong > 时间复杂度：< / strong > 所有顶点都被访问一次；所有边都被访问了 < span class = "arithmatex" > \(2\)< / span > 次，使用 < span class = "arithmatex" > \(O(2|E|)\)< / span > 时间；总体使用 < span class = "arithmatex" > \(O(|V| + |E|)\)< / span > 时间。< / p >
< p > < strong > 空间复杂度：< / strong > 列表 < code > res< / code > ，哈希表 < code > visited< / code > 顶点数量最多为 < span class = "arithmatex" > \(|V|\)< / span > ，递归深度最大为 < span class = "arithmatex" > \(|V|\)< / span > ，因此使用 < span class = "arithmatex" > \(O(|V|)\)< / span > 空间。< / p >
< h2 id = "__comments" > 评论< / h2 >
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