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< title > 9.3 < / title >
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跳转至
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Hello 算法
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9.3 图的遍历
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正在初始化搜索引擎
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第 0 章 前言
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第 0 章 前言
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0.1 关于本书
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0.2 如何使用本书
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0.3 小结
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第 1 章 初识算法
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第 1 章 初识算法
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1.1 算法无处不在
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1.2 算法是什么
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1.3 小结
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第 2 章 复杂度分析
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第 2 章 复杂度分析
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2.1 算法效率评估
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2.2 迭代与递归
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2.3 时间复杂度
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2.4 空间复杂度
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2.5 小结
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第 3 章 数据结构
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第 3 章 数据结构
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3.1 数据结构分类
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第 5 章 栈与队列
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第 6 章 哈希表
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第 7 章 树
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第 7 章 树
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7.2 二叉树遍历
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7.3 二叉树数组表示
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7.4 二叉搜索树
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7.5 AVL 树 *
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7.6 小结
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第 8 章 堆
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第 8 章 堆
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8.1 堆
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8.2 建堆操作
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8.3 Top-K 问题
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8.4 小结
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第 9 章 图
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第 9 章 图
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9.1 图
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9.2 图基础操作
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9.3 图的遍历
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9.3 图的遍历
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9.3.1 广度优先遍历
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9.4 小结
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< div class = "md-nav__link md-nav__container" >
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第 10 章 搜索
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第 10 章 搜索
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.1 二分查找
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_insertion/" class = "md-nav__link" >
< span class = "md-ellipsis" >
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10.2 二分查找插入点
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
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10.3 二分查找边界
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< / span >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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10.4 哈希优化策略
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< / span >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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10.5 重识搜索算法
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< / span >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.6 小结
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< / span >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z" / > < / svg >
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第 11 章 排序
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< / span >
< / a >
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第 11 章 排序
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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11.1 排序算法
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
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11.2 选择排序
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.3 冒泡排序
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< li class = "md-nav__item" >
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11.4 插入排序
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.5 快速排序
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.6 归并排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
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11.7 堆排序
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< / span >
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
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11.8 桶排序
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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11.9 计数排序
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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11.10 基数排序
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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11.11 小结
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z" / > < / svg >
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第 12 章 分治
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第 12 章 分治
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< / label >
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12.1 分治算法
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< li class = "md-nav__item" >
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< span class = "md-ellipsis" >
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12.2 分治搜索策略
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12.3 构建树问题
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< li class = "md-nav__item" >
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12.4 汉诺塔问题
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< a href = "../../chapter_divide_and_conquer/summary/" class = "md-nav__link" >
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12.5 小结
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第 13 章 回溯
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13.1 回溯算法
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13.3 子集和问题
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13.4 N 皇后问题
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13.5 小结
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14.2 DP 问题特性
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14.4 0-1 背包问题
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14.7 小结
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第 16 章 附录
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16.2 一起参与创作
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9.3.1 广度优先遍历
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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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< p > 树代表的是“一对多”的关系，而图则具有更高的自由度，可以表示任意的“多对多”关系。因此，我们可以把树看作是图的一种特例。显然，< strong > 树的遍历操作也是图的遍历操作的一种特例< / strong > 。< / p >
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< p > 图和树都需要应用搜索算法来实现遍历操作。图的遍历方式可分为两种：「广度优先遍历 breadth-first traversal」和「深度优先遍历 depth-first traversal」。它们也常被称为「广度优先搜索 breadth-first search」和「深度优先搜索 depth-first search」， < / 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 > 广度优先遍历是一种由近及远的遍历方式，从某个节点出发，始终优先访问距离最近的顶点，并一层层向外扩张< / strong > 。如图 9-9 所示，从左上角顶点出发，先遍历该顶点的所有邻接顶点，然后遍历下一个顶点的所有邻接顶点，以此类推，直至所有顶点访问完毕。< / p >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "图的广度优先遍历" src = "../graph_traversal.assets/graph_bfs.png" / > < / a > < / p >
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< p align = "center" > 图 9-9 图的广度优先遍历 < / p >
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< h3 id = "1" > 1. 算法实现< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > BFS 通常借助队列来实现。队列具有“先入先出”的性质，这与 BFS 的“由近及远”的思想异曲同工。< / p >
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< ol >
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< 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，弹出队首顶点并记录访问，然后将该顶点的所有邻接顶点加入到队列尾部。< / li >
< li > 循环步骤 < code > 2.< / code > ，直到所有顶点被访问完成后结束。< / li >
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< / ol >
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< 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 > 来记录哪些节点已被访问。< / p >
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< div class = "highlight" > < span class = "filename" > graph_bfs.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > 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 = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 广度优先遍历 BFS" " " < / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / 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-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < 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 = "n" > res< / 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 = "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 = "n" > visited< / span > < span class = "o" > =< / span > < span class = "nb" > set< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]([< / span > < span class = "n" > start_vet< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < 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 = "n" > que< / span > < span class = "o" > =< / span > < span class = "n" > deque< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]([< / span > < span class = "n" > start_vet< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / 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-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / 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-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / 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-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / 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-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < 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 = "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-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / 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-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "k" > continue< / 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 = "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-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / 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-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "c1" > # 返回顶点遍历序列< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / 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.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / 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-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "n" > graphBFS< / span > < span class = "p" > (< / span > < span class = "n" > GraphAdjList< / span > < span class = "w" > < / span > < span class = "o" > & < / 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 = "o" > *< / span > < span class = "n" > startVet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / 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-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "n" > unordered_set< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / 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 = "p" > {< / span > < span class = "n" > startVet< / span > < span class = "p" > };< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "w" > < / span > < span class = "n" > queue< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > empty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / 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 = "n" > front< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / 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-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "k" > auto< / span > < span class = "w" > < / span > < span class = "n" > adjVet< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > count< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "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-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > push< / 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-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > emplace< / 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-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / 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.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* 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 = "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-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < 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 = "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-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / 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-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / 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 >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / 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" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / 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 >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / 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" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / 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-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / 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-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / 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-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / 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-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / 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-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / 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-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / 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-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / 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-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / 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-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / 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.cs< / 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 >
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< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / 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 = "n" > 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 >
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< 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 >
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< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / 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 = "p" > ();< / span >
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< 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 >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "n" > HashSet< / 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 = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "w" > < / span > < span class = "p" > };< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / 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 = "p" > ();< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > Enqueue< / span > < span class = "p" > (< / span > < span class = "n" > startVet< / 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 = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / 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 = "n" > Dequeue< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > 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-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "k" > foreach< / 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 = "k" > in< / span > < span class = "w" > < / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > Contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "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-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > Enqueue< / 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-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > 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-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.go< / 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" > 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-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 = "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-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 = "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-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" > 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-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, 使用切片模拟队列< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / 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-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / 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-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / 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-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / 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-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / 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-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / 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-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / 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-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / 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-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / 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-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / 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-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / 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-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / 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-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-4-30" name = "__codelineno-4-30" href = "#__codelineno-4-30" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-4-31" name = "__codelineno-4-31" href = "#__codelineno-4-31" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.swift< / 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" > 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-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < 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 = "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-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < 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 = "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-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / 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-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / 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-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / 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-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / 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-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / 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-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / 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-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / 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-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "k" > continue< / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / 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-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / 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-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / 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.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / 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-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / 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-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / 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-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / 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-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / 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-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / 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-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-6-10" name = "__codelineno-6-10" href = "#__codelineno-6-10" > < / 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-6-11" name = "__codelineno-6-11" href = "#__codelineno-6-11" > < / 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-6-12" name = "__codelineno-6-12" href = "#__codelineno-6-12" > < / 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-6-13" name = "__codelineno-6-13" href = "#__codelineno-6-13" > < / 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-6-14" name = "__codelineno-6-14" href = "#__codelineno-6-14" > < / 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-6-15" name = "__codelineno-6-15" href = "#__codelineno-6-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-6-16" name = "__codelineno-6-16" href = "#__codelineno-6-16" > < / 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-6-17" name = "__codelineno-6-17" href = "#__codelineno-6-17" > < / 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-6-18" name = "__codelineno-6-18" href = "#__codelineno-6-18" > < / 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-6-19" name = "__codelineno-6-19" href = "#__codelineno-6-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-20" name = "__codelineno-6-20" href = "#__codelineno-6-20" > < / a > < span class = "w" > < / span > < span class = "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-6-21" name = "__codelineno-6-21" href = "#__codelineno-6-21" > < / 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-6-22" name = "__codelineno-6-22" href = "#__codelineno-6-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-23" name = "__codelineno-6-23" href = "#__codelineno-6-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-24" name = "__codelineno-6-24" href = "#__codelineno-6-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-6-25" name = "__codelineno-6-25" href = "#__codelineno-6-25" > < / 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-6-26" name = "__codelineno-6-26" href = "#__codelineno-6-26" > < / 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-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / 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-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / 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-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / 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-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / 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-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / 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-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / 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-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / 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-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / 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-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / 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-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / 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-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / 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-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / 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-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / 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-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / 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-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "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-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / 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-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / 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-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.dart< / 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 = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > 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-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "w" > < / span > < 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-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "w" > < / span > < 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 = "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 = "p" > [];< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / 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-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / 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 = "p" > {};< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / 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 = "n" > Queue< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / 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-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > isNotEmpty< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "w" > < / span > < span class = "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 = "n" > removeFirst< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > 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-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / 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 = "k" > in< / span > < span class = "w" > < / 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 = "o" > !< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / 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-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > add< / 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-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > 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-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / 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-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "k" > fn< / span > < span class = "nf" > graph_bfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > : < span class = "nc" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > start_vet< / span > : < span class = "nc" > Vertex< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "fm" > vec!< / span > < span class = "p" > [];< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > HashSet< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > insert< / span > < span class = "p" > (< / span > < span class = "n" > start_vet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-9-10" name = "__codelineno-9-10" href = "#__codelineno-9-10" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > VecDeque< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-11" name = "__codelineno-9-11" href = "#__codelineno-9-11" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > start_vet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-12" name = "__codelineno-9-12" href = "#__codelineno-9-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-9-13" name = "__codelineno-9-13" href = "#__codelineno-9-13" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > is_empty< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-14" name = "__codelineno-9-14" href = "#__codelineno-9-14" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / 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 = "n" > pop_front< / span > < span class = "p" > ().< / span > < span class = "n" > unwrap< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-9-15" name = "__codelineno-9-15" href = "#__codelineno-9-15" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-9-16" name = "__codelineno-9-16" href = "#__codelineno-9-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-9-17" name = "__codelineno-9-17" href = "#__codelineno-9-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nb" > Some< / span > < span class = "p" > (< / span > < span class = "n" > adj_vets< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > .< / span > < span class = "n" > adj_list< / span > < span class = "p" > .< / span > < span class = "n" > get< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-18" name = "__codelineno-9-18" href = "#__codelineno-9-18" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > adj_vet< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > adj_vets< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-19" name = "__codelineno-9-19" href = "#__codelineno-9-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > contains< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > adj_vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-20" name = "__codelineno-9-20" href = "#__codelineno-9-20" > < / a > < span class = "w" > < / span > < span class = "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-9-21" name = "__codelineno-9-21" href = "#__codelineno-9-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-22" name = "__codelineno-9-22" href = "#__codelineno-9-22" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > adj_vet< / 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-9-23" name = "__codelineno-9-23" href = "#__codelineno-9-23" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > insert< / span > < span class = "p" > (< / span > < span class = "n" > adj_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-9-24" name = "__codelineno-9-24" href = "#__codelineno-9-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-25" name = "__codelineno-9-25" href = "#__codelineno-9-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-26" name = "__codelineno-9-26" href = "#__codelineno-9-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-27" name = "__codelineno-9-27" href = "#__codelineno-9-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-9-28" name = "__codelineno-9-28" href = "#__codelineno-9-28" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-9-29" name = "__codelineno-9-29" href = "#__codelineno-9-29" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
2023-06-02 02:38:32 +08:00
< div class = "tabbed-block" >
2023-10-29 20:01:38 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 节点队列结构体 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "k" > typedef< / span > < span class = "w" > < / span > < span class = "k" > struct< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > vertices< / span > < span class = "p" > [< / span > < span class = "n" > MAX_SIZE< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > front< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > rear< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "n" > Queue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "cm" > /* 构造函数 */< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "n" > Queue< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > newQueue< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "w" > < / span > < span class = "n" > Queue< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > q< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Queue< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )< / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > Queue< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a > < span class = "w" > < / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > front< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > rear< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > q< / 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" > /* 判断队列是否为空 */< / span >
< a id = "__codelineno-10-15" name = "__codelineno-10-15" href = "#__codelineno-10-15" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > isEmpty< / span > < span class = "p" > (< / span > < span class = "n" > Queue< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > q< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-16" name = "__codelineno-10-16" href = "#__codelineno-10-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-17" name = "__codelineno-10-17" href = "#__codelineno-10-17" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-18" name = "__codelineno-10-18" href = "#__codelineno-10-18" > < / a >
< a id = "__codelineno-10-19" name = "__codelineno-10-19" href = "#__codelineno-10-19" > < / a > < span class = "cm" > /* 入队操作 */< / span >
< a id = "__codelineno-10-20" name = "__codelineno-10-20" href = "#__codelineno-10-20" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > enqueue< / span > < span class = "p" > (< / span > < span class = "n" > Queue< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > q< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / 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" > q< / span > < span class = "o" > -> < / span > < span class = "n" > vertices< / span > < span class = "p" > [< / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > rear< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > vet< / 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 = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > rear< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > rear< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "n" > MAX_SIZE< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-23" name = "__codelineno-10-23" href = "#__codelineno-10-23" > < / a > < span class = "w" > < / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-24" name = "__codelineno-10-24" href = "#__codelineno-10-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-25" name = "__codelineno-10-25" href = "#__codelineno-10-25" > < / a >
< a id = "__codelineno-10-26" name = "__codelineno-10-26" href = "#__codelineno-10-26" > < / a > < span class = "cm" > /* 出队操作 */< / span >
< a id = "__codelineno-10-27" name = "__codelineno-10-27" href = "#__codelineno-10-27" > < / a > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > dequeue< / span > < span class = "p" > (< / span > < span class = "n" > Queue< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > q< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-28" name = "__codelineno-10-28" href = "#__codelineno-10-28" > < / a > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > vet< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > vertices< / span > < span class = "p" > [< / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > front< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-10-29" name = "__codelineno-10-29" href = "#__codelineno-10-29" > < / a > < span class = "w" > < / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > front< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > front< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "n" > MAX_SIZE< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-30" name = "__codelineno-10-30" href = "#__codelineno-10-30" > < / a > < span class = "w" > < / span > < span class = "n" > q< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "o" > --< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-31" name = "__codelineno-10-31" href = "#__codelineno-10-31" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-32" name = "__codelineno-10-32" href = "#__codelineno-10-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-33" name = "__codelineno-10-33" href = "#__codelineno-10-33" > < / a >
< a id = "__codelineno-10-34" name = "__codelineno-10-34" href = "#__codelineno-10-34" > < / a > < span class = "cm" > /* 检查顶点是否已被访问 */< / span >
< a id = "__codelineno-10-35" name = "__codelineno-10-35" href = "#__codelineno-10-35" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > isVisited< / span > < span class = "p" > (< / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-36" name = "__codelineno-10-36" href = "#__codelineno-10-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历查找节点，使用 O(n) 时间< / span >
< a id = "__codelineno-10-37" name = "__codelineno-10-37" href = "#__codelineno-10-37" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-38" name = "__codelineno-10-38" href = "#__codelineno-10-38" > < / 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 = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-10-39" name = "__codelineno-10-39" href = "#__codelineno-10-39" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-40" name = "__codelineno-10-40" href = "#__codelineno-10-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-41" name = "__codelineno-10-41" href = "#__codelineno-10-41" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-42" name = "__codelineno-10-42" href = "#__codelineno-10-42" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-43" name = "__codelineno-10-43" href = "#__codelineno-10-43" > < / a >
< a id = "__codelineno-10-44" name = "__codelineno-10-44" href = "#__codelineno-10-44" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-10-45" name = "__codelineno-10-45" href = "#__codelineno-10-45" > < / 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-10-46" name = "__codelineno-10-46" href = "#__codelineno-10-46" > < / a > < span class = "kt" > void< / 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 = "o" > *< / 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 = "o" > *< / span > < span class = "n" > startVet< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > visitedSize< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-47" name = "__codelineno-10-47" href = "#__codelineno-10-47" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-10-48" name = "__codelineno-10-48" href = "#__codelineno-10-48" > < / a > < span class = "w" > < / span > < span class = "n" > Queue< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > queue< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newQueue< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-10-49" name = "__codelineno-10-49" href = "#__codelineno-10-49" > < / a > < span class = "w" > < / span > < span class = "n" > enqueue< / span > < span class = "p" > (< / span > < span class = "n" > queue< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-50" name = "__codelineno-10-50" href = "#__codelineno-10-50" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > [(< / span > < span class = "o" > *< / span > < span class = "n" > visitedSize< / span > < span class = "p" > )< / span > < span class = "o" > ++< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-51" name = "__codelineno-10-51" href = "#__codelineno-10-51" > < / 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-10-52" name = "__codelineno-10-52" href = "#__codelineno-10-52" > < / 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" > isEmpty< / span > < span class = "p" > (< / span > < span class = "n" > queue< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-53" name = "__codelineno-10-53" href = "#__codelineno-10-53" > < / a > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > vet< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dequeue< / span > < span class = "p" > (< / span > < span class = "n" > queue< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-10-54" name = "__codelineno-10-54" href = "#__codelineno-10-54" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > [(< / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > )< / span > < span class = "o" > ++< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / 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-10-55" name = "__codelineno-10-55" href = "#__codelineno-10-55" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-10-56" name = "__codelineno-10-56" href = "#__codelineno-10-56" > < / a > < span class = "w" > < / span > < span class = "n" > AdjListNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > findNode< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-57" name = "__codelineno-10-57" href = "#__codelineno-10-57" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "nb" > NULL< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-58" name = "__codelineno-10-58" href = "#__codelineno-10-58" > < / a > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-10-59" name = "__codelineno-10-59" href = "#__codelineno-10-59" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > isVisited< / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > visitedSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > vertex< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-60" name = "__codelineno-10-60" href = "#__codelineno-10-60" > < / a > < span class = "w" > < / span > < span class = "n" > enqueue< / span > < span class = "p" > (< / span > < span class = "n" > queue< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > vertex< / 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-10-61" name = "__codelineno-10-61" href = "#__codelineno-10-61" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > [(< / span > < span class = "o" > *< / span > < span class = "n" > visitedSize< / span > < span class = "p" > )< / span > < span class = "o" > ++< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > vertex< / 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-10-62" name = "__codelineno-10-62" href = "#__codelineno-10-62" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-63" name = "__codelineno-10-63" href = "#__codelineno-10-63" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > next< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-64" name = "__codelineno-10-64" href = "#__codelineno-10-64" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-65" name = "__codelineno-10-65" href = "#__codelineno-10-65" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-66" name = "__codelineno-10-66" href = "#__codelineno-10-66" > < / a > < span class = "w" > < / span > < span class = "c1" > // 释放内存< / span >
< a id = "__codelineno-10-67" name = "__codelineno-10-67" href = "#__codelineno-10-67" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > queue< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-68" name = "__codelineno-10-68" href = "#__codelineno-10-68" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
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< 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-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / 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 >
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< / div >
< / div >
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< p > 代码相对抽象，建议对照图 9-10 来加深理解。< / p >
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< 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 > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step1.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "图的广度优先遍历步骤" src = "../graph_traversal.assets/graph_bfs_step1.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step2.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step2" src = "../graph_traversal.assets/graph_bfs_step2.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step3.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step3" src = "../graph_traversal.assets/graph_bfs_step3.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step4.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step4" src = "../graph_traversal.assets/graph_bfs_step4.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step5.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step5" src = "../graph_traversal.assets/graph_bfs_step5.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step6.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step6" src = "../graph_traversal.assets/graph_bfs_step6.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step7.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step7" src = "../graph_traversal.assets/graph_bfs_step7.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step8.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step8" src = "../graph_traversal.assets/graph_bfs_step8.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step9.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step9" src = "../graph_traversal.assets/graph_bfs_step9.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step10.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step10" src = "../graph_traversal.assets/graph_bfs_step10.png" / > < / a > < / p >
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< / div >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_bfs_step11.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_bfs_step11" src = "../graph_traversal.assets/graph_bfs_step11.png" / > < / a > < / p >
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< p align = "center" > 图 9-10 图的广度优先遍历步骤 < / 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 >
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< p > 不唯一。广度优先遍历只要求按“由近及远”的顺序遍历，< strong > 而多个相同距离的顶点的遍历顺序是允许被任意打乱的< / strong > 。以图 9-10 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。< / p >
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< h3 id = "2" > 2. 复杂度分析< a class = "headerlink" href = "#2" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > < strong > 时间复杂度：< / strong > 所有顶点都会入队并出队一次，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 >
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< 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 >
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< 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 > 。如图 9-11 所示，从左上角顶点出发，访问当前顶点的某个邻接顶点，直到走到尽头时返回，再继续走到尽头并返回，以此类推，直至所有顶点遍历完成。< / p >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "图的深度优先遍历" src = "../graph_traversal.assets/graph_dfs.png" / > < / a > < / p >
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< p align = "center" > 图 9-11 图的深度优先遍历 < / p >
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< h3 id = "1_1" > 1. 算法实现< a class = "headerlink" href = "#1_1" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 这种“走到尽头再返回”的算法范式通常基于递归来实现。与广度优先遍历类似，在深度优先遍历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 >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "3:12" > < input checked = "checked" id = "__tabbed_3_1" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_2" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_3" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_4" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_5" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_6" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_7" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_8" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_9" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_10" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_11" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_12" name = "__tabbed_3" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Python< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Java< / label > < label for = "__tabbed_3_4" > C#< / label > < label for = "__tabbed_3_5" > Go< / label > < label for = "__tabbed_3_6" > Swift< / label > < label for = "__tabbed_3_7" > JS< / label > < label for = "__tabbed_3_8" > TS< / label > < label for = "__tabbed_3_9" > Dart< / label > < label for = "__tabbed_3_10" > Rust< / label > < label for = "__tabbed_3_11" > C< / label > < label for = "__tabbed_3_12" > Zig< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_dfs.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / 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 = "nb" > 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 = "nb" > 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-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 深度优先遍历 DFS 辅助函数" " " < / 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 = "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 = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 深度优先遍历 DFS" " " < / span >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / 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-12-15" 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 > < span class = "n" > Vertex< / 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 >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_dfs.cpp< / 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 = "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 = "o" > & < / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > unordered_set< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / 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 = "o" > *< / span > < span class = "n" > vet< / 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 = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / 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-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > emplace< / 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-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / 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 = "o" > *< / span > < span class = "n" > adjVet< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > count< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "w" > < / span > < span class = "k" > 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-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 = "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-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a >
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / 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-13-16" name = "__codelineno-13-16" href = "#__codelineno-13-16" > < / a > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "n" > graphDFS< / span > < span class = "p" > (< / span > < span class = "n" > GraphAdjList< / span > < span class = "w" > < / span > < span class = "o" > & < / 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 = "o" > *< / span > < span class = "n" > startVet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-17" name = "__codelineno-13-17" href = "#__codelineno-13-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-13-18" name = "__codelineno-13-18" href = "#__codelineno-13-18" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-13-19" name = "__codelineno-13-19" href = "#__codelineno-13-19" > < / 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-13-20" name = "__codelineno-13-20" href = "#__codelineno-13-20" > < / a > < span class = "w" > < / span > < span class = "n" > unordered_set< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "n" > visited< / 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 = "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-13-22" name = "__codelineno-13-22" href = "#__codelineno-13-22" > < / 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-13-23" name = "__codelineno-13-23" href = "#__codelineno-13-23" > < / 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.java< / 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 辅助函数 */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / 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-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / 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-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / 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-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / 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-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / 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-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / 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-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-14-10" name = "__codelineno-14-10" href = "#__codelineno-14-10" > < / 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-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-14-13" name = "__codelineno-14-13" href = "#__codelineno-14-13" > < / a >
< a id = "__codelineno-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-14-15" name = "__codelineno-14-15" href = "#__codelineno-14-15" > < / 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-14-16" name = "__codelineno-14-16" href = "#__codelineno-14-16" > < / 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-14-17" name = "__codelineno-14-17" href = "#__codelineno-14-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-14-18" name = "__codelineno-14-18" href = "#__codelineno-14-18" > < / 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-14-19" name = "__codelineno-14-19" href = "#__codelineno-14-19" > < / 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-14-20" name = "__codelineno-14-20" href = "#__codelineno-14-20" > < / 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-14-21" name = "__codelineno-14-21" href = "#__codelineno-14-21" > < / 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-14-22" name = "__codelineno-14-22" href = "#__codelineno-14-22" > < / 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-14-23" name = "__codelineno-14-23" href = "#__codelineno-14-23" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.cs< / 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 >
2023-10-15 21:18:34 +08:00
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "k" > 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" > HashSet< / 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 >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > 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-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > 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-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" > foreach< / 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 = "k" > in< / span > < span class = "w" > < / 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 = "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 = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > Contains< / span > < span class = "p" > (< / span > < span class = "n" > 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 >
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< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / 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 >
2023-10-06 14:10:31 +08:00
< 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 >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-15-17" name = "__codelineno-15-17" href = "#__codelineno-15-17" > < / 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 = "n" > 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 >
2023-10-06 14:10:31 +08:00
< 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 >
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< a id = "__codelineno-15-19" name = "__codelineno-15-19" href = "#__codelineno-15-19" > < / 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 = "p" > ();< / span >
2023-10-06 14:10:31 +08:00
< 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 >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-15-21" name = "__codelineno-15-21" href = "#__codelineno-15-21" > < / a > < span class = "w" > < / span > < span class = "n" > HashSet< / 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 = "p" > ();< / span >
2023-10-15 21:18:34 +08:00
< a id = "__codelineno-15-22" name = "__codelineno-15-22" href = "#__codelineno-15-22" > < / 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 >
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< 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 = "n" > 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 >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_dfs.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / 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-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // append 操作会返回新的的引用， < / span >
< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / 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-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / 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-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / 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-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / 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-16-9" name = "__codelineno-16-9" href = "#__codelineno-16-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-16-10" name = "__codelineno-16-10" href = "#__codelineno-16-10" > < / 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-16-11" name = "__codelineno-16-11" href = "#__codelineno-16-11" > < / 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-16-12" name = "__codelineno-16-12" href = "#__codelineno-16-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-13" name = "__codelineno-16-13" href = "#__codelineno-16-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-14" name = "__codelineno-16-14" href = "#__codelineno-16-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-16-15" name = "__codelineno-16-15" href = "#__codelineno-16-15" > < / a >
< a id = "__codelineno-16-16" name = "__codelineno-16-16" href = "#__codelineno-16-16" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-16-17" name = "__codelineno-16-17" href = "#__codelineno-16-17" > < / 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-16-18" name = "__codelineno-16-18" href = "#__codelineno-16-18" > < / 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-16-19" name = "__codelineno-16-19" href = "#__codelineno-16-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-16-20" name = "__codelineno-16-20" href = "#__codelineno-16-20" > < / 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-16-21" name = "__codelineno-16-21" href = "#__codelineno-16-21" > < / 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-16-22" name = "__codelineno-16-22" href = "#__codelineno-16-22" > < / 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-16-23" name = "__codelineno-16-23" href = "#__codelineno-16-23" > < / 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-16-24" name = "__codelineno-16-24" href = "#__codelineno-16-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-16-25" name = "__codelineno-16-25" href = "#__codelineno-16-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-16-26" name = "__codelineno-16-26" href = "#__codelineno-16-26" > < / 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.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / 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-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / 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-17-4" name = "__codelineno-17-4" href = "#__codelineno-17-4" > < / 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-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / a > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / 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-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / 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-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / a > < span class = "k" > continue< / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-17-9" name = "__codelineno-17-9" href = "#__codelineno-17-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-10" name = "__codelineno-17-10" href = "#__codelineno-17-10" > < / a > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-17-11" name = "__codelineno-17-11" href = "#__codelineno-17-11" > < / 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-17-12" name = "__codelineno-17-12" href = "#__codelineno-17-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-13" name = "__codelineno-17-13" href = "#__codelineno-17-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-14" name = "__codelineno-17-14" href = "#__codelineno-17-14" > < / a >
< a id = "__codelineno-17-15" name = "__codelineno-17-15" href = "#__codelineno-17-15" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-17-16" name = "__codelineno-17-16" href = "#__codelineno-17-16" > < / 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-17-17" name = "__codelineno-17-17" href = "#__codelineno-17-17" > < / 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-17-18" name = "__codelineno-17-18" href = "#__codelineno-17-18" > < / a > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-17-19" name = "__codelineno-17-19" href = "#__codelineno-17-19" > < / 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-17-20" name = "__codelineno-17-20" href = "#__codelineno-17-20" > < / a > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-17-21" name = "__codelineno-17-21" href = "#__codelineno-17-21" > < / 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-17-22" name = "__codelineno-17-22" href = "#__codelineno-17-22" > < / 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-17-23" name = "__codelineno-17-23" href = "#__codelineno-17-23" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-17-24" name = "__codelineno-17-24" href = "#__codelineno-17-24" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.js< / 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 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / 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-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / 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-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / 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-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / 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-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "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-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / 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-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / 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-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / 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-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a >
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / 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-18-18" name = "__codelineno-18-18" href = "#__codelineno-18-18" > < / 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-18-19" name = "__codelineno-18-19" href = "#__codelineno-18-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-18-20" name = "__codelineno-18-20" href = "#__codelineno-18-20" > < / 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-18-21" name = "__codelineno-18-21" href = "#__codelineno-18-21" > < / 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-18-22" name = "__codelineno-18-22" href = "#__codelineno-18-22" > < / 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-18-23" name = "__codelineno-18-23" href = "#__codelineno-18-23" > < / 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-18-24" name = "__codelineno-18-24" href = "#__codelineno-18-24" > < / 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-18-25" name = "__codelineno-18-25" href = "#__codelineno-18-25" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "w" > < / span > < span class = "nx" > graph< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > GraphAdjList< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < 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 >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a > < 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 >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / a > < 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-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / 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-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / 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-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / 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-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / 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-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / 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-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-19-15" name = "__codelineno-19-15" href = "#__codelineno-19-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-19-16" name = "__codelineno-19-16" href = "#__codelineno-19-16" > < / 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-19-17" name = "__codelineno-19-17" href = "#__codelineno-19-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-19-18" name = "__codelineno-19-18" href = "#__codelineno-19-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-19" name = "__codelineno-19-19" href = "#__codelineno-19-19" > < / a >
< a id = "__codelineno-19-20" name = "__codelineno-19-20" href = "#__codelineno-19-20" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-19-21" name = "__codelineno-19-21" href = "#__codelineno-19-21" > < / 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-19-22" name = "__codelineno-19-22" href = "#__codelineno-19-22" > < / 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-19-23" name = "__codelineno-19-23" href = "#__codelineno-19-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-19-24" name = "__codelineno-19-24" href = "#__codelineno-19-24" > < / 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-19-25" name = "__codelineno-19-25" href = "#__codelineno-19-25" > < / 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-19-26" name = "__codelineno-19-26" href = "#__codelineno-19-26" > < / 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-19-27" name = "__codelineno-19-27" href = "#__codelineno-19-27" > < / 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-19-28" name = "__codelineno-19-28" href = "#__codelineno-19-28" > < / 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-19-29" name = "__codelineno-19-29" href = "#__codelineno-19-29" > < / a > < span class = "p" > }< / span >
2023-06-02 02:38:32 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / a > < span class = "w" > < / span > < span class = "n" > GraphAdjList< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "w" > < / span > < span class = "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 >
< a id = "__codelineno-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / 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 = "p" > ,< / span >
< a id = "__codelineno-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / a > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / a > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-8" name = "__codelineno-20-8" href = "#__codelineno-20-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > 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-20-9" name = "__codelineno-20-9" href = "#__codelineno-20-9" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > 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-20-10" name = "__codelineno-20-10" href = "#__codelineno-20-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-20-11" name = "__codelineno-20-11" href = "#__codelineno-20-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > adjVet< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / 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 = "o" > !< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-12" name = "__codelineno-20-12" href = "#__codelineno-20-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-13" name = "__codelineno-20-13" href = "#__codelineno-20-13" > < / 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-20-14" name = "__codelineno-20-14" href = "#__codelineno-20-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-15" name = "__codelineno-20-15" href = "#__codelineno-20-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-20-16" name = "__codelineno-20-16" href = "#__codelineno-20-16" > < / 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-20-17" name = "__codelineno-20-17" href = "#__codelineno-20-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-18" name = "__codelineno-20-18" href = "#__codelineno-20-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-20-19" name = "__codelineno-20-19" href = "#__codelineno-20-19" > < / a >
< a id = "__codelineno-20-20" name = "__codelineno-20-20" href = "#__codelineno-20-20" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-20-21" name = "__codelineno-20-21" href = "#__codelineno-20-21" > < / 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 = "n" > 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-20-22" name = "__codelineno-20-22" href = "#__codelineno-20-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-20-23" name = "__codelineno-20-23" href = "#__codelineno-20-23" > < / 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 = "p" > [];< / span >
< a id = "__codelineno-20-24" name = "__codelineno-20-24" href = "#__codelineno-20-24" > < / 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-20-25" name = "__codelineno-20-25" href = "#__codelineno-20-25" > < / 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 = "p" > {};< / span >
< a id = "__codelineno-20-26" name = "__codelineno-20-26" href = "#__codelineno-20-26" > < / 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-20-27" name = "__codelineno-20-27" href = "#__codelineno-20-27" > < / 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-20-28" name = "__codelineno-20-28" href = "#__codelineno-20-28" > < / a > < span class = "p" > }< / span >
2023-07-26 10:57:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-21-2" name = "__codelineno-21-2" href = "#__codelineno-21-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > : < span class = "kp" > & < / span > < span class = "nc" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > visited< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "n" > HashSet< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > : < span class = "nc" > Vertex< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-3" name = "__codelineno-21-3" href = "#__codelineno-21-3" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push< / 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-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > insert< / 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-21-5" name = "__codelineno-21-5" href = "#__codelineno-21-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-21-6" name = "__codelineno-21-6" href = "#__codelineno-21-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nb" > Some< / span > < span class = "p" > (< / span > < span class = "n" > adj_vets< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > .< / span > < span class = "n" > adj_list< / span > < span class = "p" > .< / span > < span class = "n" > get< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > adj_vet< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > adj_vets< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-8" name = "__codelineno-21-8" href = "#__codelineno-21-8" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "n" > contains< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > adj_vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-9" name = "__codelineno-21-9" href = "#__codelineno-21-9" > < / 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-21-10" name = "__codelineno-21-10" href = "#__codelineno-21-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-11" name = "__codelineno-21-11" href = "#__codelineno-21-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-21-12" name = "__codelineno-21-12" href = "#__codelineno-21-12" > < / 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" > adj_vet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-21-13" name = "__codelineno-21-13" href = "#__codelineno-21-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-14" name = "__codelineno-21-14" href = "#__codelineno-21-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-15" name = "__codelineno-21-15" href = "#__codelineno-21-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-21-16" name = "__codelineno-21-16" href = "#__codelineno-21-16" > < / a >
< a id = "__codelineno-21-17" name = "__codelineno-21-17" href = "#__codelineno-21-17" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-21-18" name = "__codelineno-21-18" href = "#__codelineno-21-18" > < / 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-21-19" name = "__codelineno-21-19" href = "#__codelineno-21-19" > < / a > < span class = "k" > fn< / span > < span class = "nf" > graph_dfs< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > : < span class = "nc" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > start_vet< / span > : < span class = "nc" > Vertex< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-20" name = "__codelineno-21-20" href = "#__codelineno-21-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-21-21" name = "__codelineno-21-21" href = "#__codelineno-21-21" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "fm" > vec!< / span > < span class = "p" > [];< / span >
< a id = "__codelineno-21-22" name = "__codelineno-21-22" href = "#__codelineno-21-22" > < / 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-21-23" name = "__codelineno-21-23" href = "#__codelineno-21-23" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > HashSet< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-21-24" name = "__codelineno-21-24" href = "#__codelineno-21-24" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > start_vet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-21-25" name = "__codelineno-21-25" href = "#__codelineno-21-25" > < / a >
< a id = "__codelineno-21-26" name = "__codelineno-21-26" href = "#__codelineno-21-26" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-21-27" name = "__codelineno-21-27" href = "#__codelineno-21-27" > < / a > < span class = "p" > }< / span >
2023-07-26 10:57:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-29 20:01:38 +08:00
< div class = "highlight" > < span class = "filename" > graph_dfs.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "cm" > /* 检查顶点是否已被访问 */< / span >
< a id = "__codelineno-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > isVisited< / span > < span class = "p" > (< / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历查找节点，使用 O(n) 时间< / span >
< a id = "__codelineno-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-5" name = "__codelineno-22-5" href = "#__codelineno-22-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-6" name = "__codelineno-22-6" href = "#__codelineno-22-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-7" name = "__codelineno-22-7" href = "#__codelineno-22-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-8" name = "__codelineno-22-8" href = "#__codelineno-22-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-9" name = "__codelineno-22-9" href = "#__codelineno-22-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-10" name = "__codelineno-22-10" href = "#__codelineno-22-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-22-11" name = "__codelineno-22-11" href = "#__codelineno-22-11" > < / a >
< a id = "__codelineno-22-12" name = "__codelineno-22-12" href = "#__codelineno-22-12" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-22-13" name = "__codelineno-22-13" href = "#__codelineno-22-13" > < / 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 = "o" > *< / 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 = "o" > **< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-14" name = "__codelineno-22-14" href = "#__codelineno-22-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-22-15" name = "__codelineno-22-15" href = "#__codelineno-22-15" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > [(< / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > )< / span > < span class = "o" > ++< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-16" name = "__codelineno-22-16" href = "#__codelineno-22-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-22-17" name = "__codelineno-22-17" href = "#__codelineno-22-17" > < / a > < span class = "w" > < / span > < span class = "n" > AdjListNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > findNode< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-18" name = "__codelineno-22-18" href = "#__codelineno-22-18" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "nb" > NULL< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-19" name = "__codelineno-22-19" href = "#__codelineno-22-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-22-20" name = "__codelineno-22-20" href = "#__codelineno-22-20" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > isVisited< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > vertex< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-21" name = "__codelineno-22-21" href = "#__codelineno-22-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-22-22" name = "__codelineno-22-22" href = "#__codelineno-22-22" > < / 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" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > resSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > vertex< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-23" name = "__codelineno-22-23" href = "#__codelineno-22-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-24" name = "__codelineno-22-24" href = "#__codelineno-22-24" > < / a > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "o" > -> < / span > < span class = "n" > next< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-25" name = "__codelineno-22-25" href = "#__codelineno-22-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-26" name = "__codelineno-22-26" href = "#__codelineno-22-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-22-27" name = "__codelineno-22-27" href = "#__codelineno-22-27" > < / a >
< a id = "__codelineno-22-28" name = "__codelineno-22-28" href = "#__codelineno-22-28" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-22-29" name = "__codelineno-22-29" href = "#__codelineno-22-29" > < / 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-22-30" name = "__codelineno-22-30" href = "#__codelineno-22-30" > < / a > < span class = "kt" > void< / 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 = "o" > *< / 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 = "o" > *< / span > < span class = "n" > startVet< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > resSize< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-31" name = "__codelineno-22-31" href = "#__codelineno-22-31" > < / 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" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > resSize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-32" name = "__codelineno-22-32" href = "#__codelineno-22-32" > < / 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-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / 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-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / a >
< a id = "__codelineno-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / 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 >
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< p > 深度优先遍历的算法流程如图 9-12 所示。< / p >
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< ul >
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< li > < strong > 直虚线代表向下递推< / strong > ，表示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 > ，表示此递归方法已经返回，回溯到了开启此递归方法的位置。< / li >
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< / ul >
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< p > 为了加深理解，建议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 > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step1.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "图的深度优先遍历步骤" src = "../graph_traversal.assets/graph_dfs_step1.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step2.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step2" src = "../graph_traversal.assets/graph_dfs_step2.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step3.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step3" src = "../graph_traversal.assets/graph_dfs_step3.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step4.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step4" src = "../graph_traversal.assets/graph_dfs_step4.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step5.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step5" src = "../graph_traversal.assets/graph_dfs_step5.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step6.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step6" src = "../graph_traversal.assets/graph_dfs_step6.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step7.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step7" src = "../graph_traversal.assets/graph_dfs_step7.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step8.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step8" src = "../graph_traversal.assets/graph_dfs_step8.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step9.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step9" src = "../graph_traversal.assets/graph_dfs_step9.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p > < a class = "glightbox" href = "../graph_traversal.assets/graph_dfs_step10.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "graph_dfs_step10" src = "../graph_traversal.assets/graph_dfs_step10.png" / > < / a > < / p >
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< / div >
< div class = "tabbed-block" >
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< p align = "center" > 图 9-12 图的深度优先遍历步骤 < / p >
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< div class = "admonition question" >
< p class = "admonition-title" > 深度优先遍历的序列是否唯一？< / p >
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< 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可以，即邻接顶点的顺序可以任意打乱，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，它们展示了三种不同的遍历优先级，然而这三者都属于深度优先遍历。< / p >
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< h3 id = "2_1" > 2. 复杂度分析< a class = "headerlink" href = "#2_1" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > < strong > 时间复杂度：< / strong > 所有顶点都会被访问 < span class = "arithmatex" > \(1\)< / span > 次，使用 < span class = "arithmatex" > \(O(|V|)\)< / span > 时间；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 >
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< 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 >
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