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Hello 算法
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9.3. 图的遍历
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0. 写在前面
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0.1. 关于本书
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0.2. 如何使用本书
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1. 引言
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1.1. 算法无处不在
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1.2. 算法是什么
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1.3. 小结
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2. 复杂度分析
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2.1. 算法效率评估
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2.2. 时间复杂度
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2.3. 空间复杂度
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2.4. 小结
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3. 数据结构简介
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3.1. 数据结构分类
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3.2. 基本数据类型
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3.3. 数字编码 *
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3.4. 字符编码 *
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3.5. 小结
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4. 数组与链表
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4.1. 数组
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4.2. 链表
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4.3. 列表
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4.4. 小结
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5. 栈与队列
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5.1. 栈
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5.2. 队列
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5.3. 双向队列
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5.4. 小结
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6. 散列表
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6.1. 哈希表（ ）
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6.2. 哈希冲突（ ）
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6.4. 小结
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7. 树
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7.1. 二叉树
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7.2. 二叉树遍历
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7.3. 二叉树数组表示
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7.4. 二叉搜索树
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7.5. AVL 树 *
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7.6. 小结
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8. 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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9. 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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目录
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9.3.1. 广度优先遍历
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11.10. 基数排序
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
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< h1 id = "93" > 9.3. 图的遍历< a class = "headerlink" href = "#93" title = "Permanent link" > ¶ < / a > < / h1 >
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< div class = "admonition note" >
< p class = "admonition-title" > 图与树的关系< / p >
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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 > ，建议你在学习本章节时融会贯通两者的概念与实现方法。< / p >
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< / div >
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< p > 「图」和「树」都是非线性数据结构，都需要使用「搜索算法」来实现遍历操作。< / p >
< p > 与树类似，图的遍历方式也可分为两种，即「广度优先遍历 Breadth-First Traversal」和「深度优先遍历 Depth-First Traversal」， ， < / 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，从距离最近的顶点开始访问，并一层层向外扩张< / strong > 。具体来说，从某个顶点出发，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 > < img alt = "图的广度优先遍历" src = "../graph_traversal.assets/graph_bfs.png" / > < / p >
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< p align = "center" > Fig. 图的广度优先遍历 < / p >
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< h3 id = "_1" > 算法实现< a class = "headerlink" href = "#_1" title = "Permanent link" > ¶ < / a > < / h3 >
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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 >
< li > 将遍历起始顶点 < code > startVet< / code > 加入队列，并开启循环；< / li >
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< 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 = "tabbed-set tabbed-alternate" data-tabs = "1:11" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Java< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Python< / label > < label for = "__tabbed_1_4" > Go< / label > < label for = "__tabbed_1_5" > JavaScript< / label > < label for = "__tabbed_1_6" > TypeScript< / label > < label for = "__tabbed_1_7" > C< / label > < label for = "__tabbed_1_8" > C#< / label > < label for = "__tabbed_1_9" > Swift< / label > < label for = "__tabbed_1_10" > Zig< / label > < label for = "__tabbed_1_11" > Dart< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > graph_bfs.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nf" > graphBFS< / span > < span class = "p" > (< / span > < span class = "n" > GraphAdjList< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "n" > Set< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > HashSet< / span > < span class = "o" > < > < / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {{< / span > < span class = "w" > < / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "p" > }};< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "n" > Queue< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > LinkedList< / span > < span class = "o" > < > < / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {{< / span > < span class = "w" > < / span > < span class = "n" > offer< / span > < span class = "p" > (< / span > < span class = "n" > startVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "p" > }};< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "na" > isEmpty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "w" > < / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > vet< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "na" > poll< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Vertex< / span > < span class = "w" > < / span > < span class = "n" > adjVet< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > .< / span > < span class = "na" > adjList< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "na" > contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "na" > offer< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / 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 >
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< 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 >
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< 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 >
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< 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 >
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< 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 >
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< 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 >
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< 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 >
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< 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 >
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< 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 >
2023-04-14 04:01:48 +08:00
< 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 >
2023-03-02 18:49:24 +08:00
< 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 >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-23 18:57:04 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "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 >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 广度优先遍历 BFS" " " < / span >
2023-03-03 02:46:43 +08:00
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / 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 >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "c1" > # 顶点遍历序列< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "c1" > # 哈希表，用于记录已被访问过的顶点< / span >
2023-03-23 18:57:04 +08:00
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "n" > visited< / span > < span class = "o" > =< / span > < span class = "nb" > set< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]([< / span > < span class = "n" > start_vet< / span > < span class = "p" > ])< / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "c1" > # 队列用于实现 BFS< / span >
2023-03-23 18:57:04 +08:00
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "n" > que< / span > < span class = "o" > =< / span > < span class = "n" > 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 >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "c1" > # 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "k" > while< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > que< / span > < span class = "p" > )< / span > < span class = "o" > > < / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "n" > vet< / span > < span class = "o" > =< / span > < span class = "n" > que< / span > < span class = "o" > .< / span > < span class = "n" > popleft< / span > < span class = "p" > ()< / span > < span class = "c1" > # 队首顶点出队< / span >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "c1" > # 记录访问顶点< / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "c1" > # 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "k" > for< / span > < span class = "n" > adj_vet< / span > < span class = "ow" > in< / span > < span class = "n" > graph< / span > < span class = "o" > .< / span > < span class = "n" > adj_list< / span > < span class = "p" > [< / span > < span class = "n" > vet< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "k" > if< / span > < span class = "n" > adj_vet< / span > < span class = "ow" > in< / span > < span class = "n" > visited< / span > < span class = "p" > :< / span >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "k" > continue< / span > < span class = "c1" > # 跳过已被访问过的顶点< / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "n" > que< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > adj_vet< / span > < span class = "p" > )< / span > < span class = "c1" > # 只入队未访问的顶点< / span >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "n" > visited< / span > < span class = "o" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > adj_vet< / span > < span class = "p" > )< / span > < span class = "c1" > # 标记该顶点已被访问< / span >
2023-02-23 20:23:42 +08:00
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "c1" > # 返回顶点遍历序列< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-28 00:16:29 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > graphBFS< / span > < span class = "p" > (< / span > < span class = "nx" > g< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > graphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "w" > < / span > < span class = "nx" > Vertex< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "nx" > Vertex< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > (< / span > < span class = "kd" > map< / span > < span class = "p" > [< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ]< / span > < span class = "kd" > struct< / span > < span class = "p" > {})< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > startVet< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kd" > struct< / span > < span class = "p" > {}{}< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS, 使用切片模拟队列< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "nx" > Vertex< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "nx" > queue< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > queue< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > :]< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > g< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > [< / span > < span class = "nx" > vet< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > isExist< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > !< / span > < span class = "nx" > isExist< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "nx" > queue< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "nx" > queue< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kd" > struct< / span > < span class = "p" > {}{}< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-25 02:19:21 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > graphBFS< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Set< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "nx" > startVet< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-04-17 21:57:50 +08:00
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > shift< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
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< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > graph< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > .< / span > < span class = "nx" > get< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ??< / span > < span class = "w" > < / span > < span class = "p" > [])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > has< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-04-17 21:57:50 +08:00
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
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< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-04-17 21:57:50 +08:00
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
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< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-25 02:19:21 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > graphBFS< / span > < span class = "p" > (< / span > < span class = "nx" > graph< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > startVet< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > Vertex< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Vertex< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Set< / span > < span class = "o" > < < / span > < span class = "nx" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Set< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > startVet< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "nx" > startVet< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-03-03 02:46:43 +08:00
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > vet< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > shift< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录访问顶点< / span >
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< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > adjVet< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > graph< / span > < span class = "p" > .< / span > < span class = "nx" > adjList< / span > < span class = "p" > .< / span > < span class = "nx" > get< / span > < span class = "p" > (< / span > < span class = "nx" > vet< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ??< / span > < span class = "w" > < / span > < span class = "p" > [])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > has< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-03-03 02:46:43 +08:00
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
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< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-03-03 02:46:43 +08:00
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "w" > < / span > < span class = "nx" > que< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 只入队未访问< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > adjVet< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 标记该顶点已被访问< / span >
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< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_bfs.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > graphBFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_bfs.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "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 >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / 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 >
< 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 = "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" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / 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 = "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 = "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 = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > startVet< / span > < span class = "w" > < / span > < span class = "p" > };< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "n" > Queue< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > que< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Queue< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "w" > < / span > < span class = "n" > 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-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 = "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-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / 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-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / 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-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / 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-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / 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-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / 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-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "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-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / 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-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a >
< 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 = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-23 20:23:42 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "kd" > func< / span > < span class = "nf" > graphBFS< / span > < span class = "p" > (< / span > < span class = "n" > graph< / span > < span class = "p" > :< / span > < span class = "n" > GraphAdjList< / span > < span class = "p" > ,< / span > < span class = "n" > startVet< / span > < span class = "p" > :< / span > < span class = "n" > Vertex< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "kd" > var< / span > < span class = "nv" > visited< / span > < span class = "p" > :< / span > < span class = "n" > Set< / span > < span class = "p" > < < / span > < span class = "n" > Vertex< / span > < span class = "p" > > < / span > < span class = "p" > =< / span > < span class = "p" > [< / span > < span class = "n" > startVet< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "kd" > var< / span > < span class = "nv" > que< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > Vertex< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > [< / span > < span class = "n" > startVet< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "c1" > // 以顶点 vet 为起点，循环直至访问完所有顶点< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "k" > while< / span > < span class = "o" > !< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "bp" > isEmpty< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "kd" > let< / span > < span class = "nv" > vet< / span > < span class = "p" > =< / span > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > removeFirst< / span > < span class = "p" > ()< / span > < span class = "c1" > // 队首顶点出队< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > vet< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录访问顶点< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "k" > for< / span > < span class = "n" > adjVet< / span > < span class = "k" > in< / span > < span class = "n" > graph< / span > < span class = "p" > .< / span > < span class = "n" > adjList< / span > < span class = "p" > [< / span > < span class = "n" > vet< / span > < span class = "p" > ]< / span > < span class = "p" > ??< / span > < span class = "p" > []< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "k" > if< / span > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "bp" > contains< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "k" > continue< / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "n" > que< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > )< / span > < span class = "c1" > // 只入队未访问的顶点< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "n" > visited< / span > < span class = "p" > .< / span > < span class = "bp" > insert< / span > < span class = "p" > (< / span > < span class = "n" > adjVet< / span > < span class = "p" > )< / span > < span class = "c1" > // 标记该顶点已被访问< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
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2023-02-25 02:19:21 +08:00
< div class = "highlight" > < span class = "filename" > graph_bfs.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > graphBFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
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2023-06-02 02:38:32 +08:00
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > graph_bfs.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 广度优先遍历 BFS */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / 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-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / 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-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / 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-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / 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-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / 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-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / 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-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 队列用于实现 BFS< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / 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-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / 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-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / 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-10-13" name = "__codelineno-10-13" href = "#__codelineno-10-13" > < / 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-10-14" name = "__codelineno-10-14" href = "#__codelineno-10-14" > < / 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-10-15" name = "__codelineno-10-15" href = "#__codelineno-10-15" > < / 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-10-16" name = "__codelineno-10-16" href = "#__codelineno-10-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-10-17" name = "__codelineno-10-17" href = "#__codelineno-10-17" > < / 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-10-18" name = "__codelineno-10-18" href = "#__codelineno-10-18" > < / 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-10-19" name = "__codelineno-10-19" href = "#__codelineno-10-19" > < / 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-10-20" name = "__codelineno-10-20" href = "#__codelineno-10-20" > < / a > < 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" > 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-10-22" name = "__codelineno-10-22" href = "#__codelineno-10-22" > < / 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-10-23" name = "__codelineno-10-23" href = "#__codelineno-10-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-24" name = "__codelineno-10-24" href = "#__codelineno-10-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-25" name = "__codelineno-10-25" href = "#__codelineno-10-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-10-26" name = "__codelineno-10-26" href = "#__codelineno-10-26" > < / 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-10-27" name = "__codelineno-10-27" href = "#__codelineno-10-27" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
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< / div >
< / div >
< p > 代码相对抽象，建议对照以下动画图示来加深理解。< / 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 > < img alt = "图的广度优先遍历步骤" src = "../graph_traversal.assets/graph_bfs_step1.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step2" src = "../graph_traversal.assets/graph_bfs_step2.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step3" src = "../graph_traversal.assets/graph_bfs_step3.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step4" src = "../graph_traversal.assets/graph_bfs_step4.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step5" src = "../graph_traversal.assets/graph_bfs_step5.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step6" src = "../graph_traversal.assets/graph_bfs_step6.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step7" src = "../graph_traversal.assets/graph_bfs_step7.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step8" src = "../graph_traversal.assets/graph_bfs_step8.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step9" src = "../graph_traversal.assets/graph_bfs_step9.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step10" src = "../graph_traversal.assets/graph_bfs_step10.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_bfs_step11" src = "../graph_traversal.assets/graph_bfs_step11.png" / > < / p >
< / div >
< / div >
< / div >
< 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 > 。以上图为例，顶点 < span class = "arithmatex" > \(1\)< / span > , < span class = "arithmatex" > \(3\)< / span > 的访问顺序可以交换、顶点 < span class = "arithmatex" > \(2\)< / span > , < span class = "arithmatex" > \(4\)< / span > , < span class = "arithmatex" > \(6\)< / span > 的访问顺序也可以任意交换。< / p >
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< / div >
< h3 id = "_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 >
2023-05-21 19:29:51 +08:00
< h2 id = "932" > 9.3.2. 深度优先遍历< a class = "headerlink" href = "#932" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > < strong > 深度优先遍历是一种优先走到底、无路可走再回头的遍历方式< / strong > 。具体地，从某个顶点出发，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 > < img alt = "图的深度优先遍历" src = "../graph_traversal.assets/graph_dfs.png" / > < / p >
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< p align = "center" > Fig. 图的深度优先遍历 < / p >
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< h3 id = "_3" > 算法实现< a class = "headerlink" href = "#_3" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 这种“走到尽头 + 回溯”的算法形式通常基于递归来实现。与 BFS 类似，在 DFS 中我们也需要借助一个哈希表 < code > visited< / code > 来记录已被访问的顶点，以避免重复访问顶点。< / p >
2023-06-02 02:38:32 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:11" > < input checked = "checked" id = "__tabbed_3_1" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_2" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_3" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_4" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_5" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_6" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_7" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_8" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_9" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_10" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_11" name = "__tabbed_3" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Java< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Python< / label > < label for = "__tabbed_3_4" > Go< / label > < label for = "__tabbed_3_5" > JavaScript< / label > < label for = "__tabbed_3_6" > TypeScript< / label > < label for = "__tabbed_3_7" > C< / label > < label for = "__tabbed_3_8" > C#< / label > < label for = "__tabbed_3_9" > Swift< / label > < label for = "__tabbed_3_10" > Zig< / label > < label for = "__tabbed_3_11" > Dart< / label > < / div >
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< div class = "tabbed-content" >
< 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-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / 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-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / 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-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / 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 >
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< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
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< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "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-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / 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 >
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< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / 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 >
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< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / 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-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / a >
< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / 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 >
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< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / 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 >
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< a id = "__codelineno-11-17" name = "__codelineno-11-17" href = "#__codelineno-11-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
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< a id = "__codelineno-11-18" name = "__codelineno-11-18" href = "#__codelineno-11-18" > < / 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 >
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< a id = "__codelineno-11-19" name = "__codelineno-11-19" href = "#__codelineno-11-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
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< a id = "__codelineno-11-20" name = "__codelineno-11-20" href = "#__codelineno-11-20" > < / 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 >
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< a id = "__codelineno-11-21" name = "__codelineno-11-21" href = "#__codelineno-11-21" > < / 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-11-22" name = "__codelineno-11-22" href = "#__codelineno-11-22" > < / 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-11-23" name = "__codelineno-11-23" href = "#__codelineno-11-23" > < / 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.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "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-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / 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-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / 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-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "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-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / 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-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / 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-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "w" > < / span > < 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 = "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-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-12" name = "__codelineno-12-12" href = "#__codelineno-12-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / a >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-12-15" name = "__codelineno-12-15" href = "#__codelineno-12-15" > < / 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-12-16" name = "__codelineno-12-16" href = "#__codelineno-12-16" > < / 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-12-17" name = "__codelineno-12-17" href = "#__codelineno-12-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-12-18" name = "__codelineno-12-18" href = "#__codelineno-12-18" > < / 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-12-19" name = "__codelineno-12-19" href = "#__codelineno-12-19" > < / 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-12-20" name = "__codelineno-12-20" href = "#__codelineno-12-20" > < / 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-12-21" name = "__codelineno-12-21" href = "#__codelineno-12-21" > < / 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-12-22" name = "__codelineno-12-22" href = "#__codelineno-12-22" > < / 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-12-23" name = "__codelineno-12-23" href = "#__codelineno-12-23" > < / 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.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > 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-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 深度优先遍历 DFS 辅助函数" " " < / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / 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-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / 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-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < 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 = "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-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / 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-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "k" > continue< / 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 = "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 = "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-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / 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-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 深度优先遍历 DFS" " " < / span >
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "c1" > # 顶点遍历序列< / span >
< a id = "__codelineno-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-13-16" name = "__codelineno-13-16" href = "#__codelineno-13-16" > < / a > < span class = "c1" > # 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-13-17" name = "__codelineno-13-17" href = "#__codelineno-13-17" > < / 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-13-18" name = "__codelineno-13-18" href = "#__codelineno-13-18" > < / 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-13-19" name = "__codelineno-13-19" href = "#__codelineno-13-19" > < / 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.go< / 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 = "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-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // append 操作会返回新的的引用， < / span >
< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / 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-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "w" > < / span > < span class = "nx" > visited< / span > < span class = "p" > [< / span > < span class = "nx" > 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 >
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< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
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< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / 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-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / 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-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 = "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-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / 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-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
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< a id = "__codelineno-14-13" name = "__codelineno-14-13" href = "#__codelineno-14-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-14-15" name = "__codelineno-14-15" href = "#__codelineno-14-15" > < / a >
< a id = "__codelineno-14-16" name = "__codelineno-14-16" href = "#__codelineno-14-16" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-14-17" name = "__codelineno-14-17" href = "#__codelineno-14-17" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
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< a id = "__codelineno-14-18" name = "__codelineno-14-18" href = "#__codelineno-14-18" > < / 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 >
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< a id = "__codelineno-14-19" name = "__codelineno-14-19" href = "#__codelineno-14-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
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< a id = "__codelineno-14-20" name = "__codelineno-14-20" href = "#__codelineno-14-20" > < / 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 >
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< a id = "__codelineno-14-21" name = "__codelineno-14-21" href = "#__codelineno-14-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
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< a id = "__codelineno-14-22" name = "__codelineno-14-22" href = "#__codelineno-14-22" > < / 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-14-23" name = "__codelineno-14-23" href = "#__codelineno-14-23" > < / a > < span class = "w" > < / span > < span class = "nx" > dfs< / span > < span class = "p" > (< / span > < span class = "nx" > 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-14-24" name = "__codelineno-14-24" href = "#__codelineno-14-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回顶点遍历序列< / span >
< a id = "__codelineno-14-25" name = "__codelineno-14-25" href = "#__codelineno-14-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-14-26" name = "__codelineno-14-26" href = "#__codelineno-14-26" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_dfs.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / 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-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / 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-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / 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-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / 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-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / 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-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / 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-15-9" name = "__codelineno-15-9" href = "#__codelineno-15-9" > < / 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-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-15-12" name = "__codelineno-15-12" href = "#__codelineno-15-12" > < / 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-15-13" name = "__codelineno-15-13" href = "#__codelineno-15-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-14" name = "__codelineno-15-14" href = "#__codelineno-15-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-15-15" name = "__codelineno-15-15" href = "#__codelineno-15-15" > < / a >
< a id = "__codelineno-15-16" name = "__codelineno-15-16" href = "#__codelineno-15-16" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-15-17" name = "__codelineno-15-17" href = "#__codelineno-15-17" > < / 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-15-18" name = "__codelineno-15-18" href = "#__codelineno-15-18" > < / 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-15-19" name = "__codelineno-15-19" href = "#__codelineno-15-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-15-20" name = "__codelineno-15-20" href = "#__codelineno-15-20" > < / 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-15-21" name = "__codelineno-15-21" href = "#__codelineno-15-21" > < / 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-15-22" name = "__codelineno-15-22" href = "#__codelineno-15-22" > < / 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-15-23" name = "__codelineno-15-23" href = "#__codelineno-15-23" > < / 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-15-24" name = "__codelineno-15-24" href = "#__codelineno-15-24" > < / 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-15-25" name = "__codelineno-15-25" href = "#__codelineno-15-25" > < / 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_dfs.ts< / 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" > function< / span > < span class = "w" > < / span > < span class = "nx" > dfs< / 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 = "nx" > graph< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > GraphAdjList< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a > < span class = "w" > < / span > < span class = "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-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / 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-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / 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-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / 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-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / 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-16-9" name = "__codelineno-16-9" href = "#__codelineno-16-9" > < / 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-16-10" name = "__codelineno-16-10" href = "#__codelineno-16-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-16-11" name = "__codelineno-16-11" href = "#__codelineno-16-11" > < / 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-16-12" name = "__codelineno-16-12" href = "#__codelineno-16-12" > < / 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-16-13" name = "__codelineno-16-13" href = "#__codelineno-16-13" > < / 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-16-14" name = "__codelineno-16-14" href = "#__codelineno-16-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-15" name = "__codelineno-16-15" href = "#__codelineno-16-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-16-16" name = "__codelineno-16-16" href = "#__codelineno-16-16" > < / 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-16-17" name = "__codelineno-16-17" href = "#__codelineno-16-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-18" name = "__codelineno-16-18" href = "#__codelineno-16-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-16-19" name = "__codelineno-16-19" href = "#__codelineno-16-19" > < / a >
< a id = "__codelineno-16-20" name = "__codelineno-16-20" href = "#__codelineno-16-20" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-16-21" name = "__codelineno-16-21" href = "#__codelineno-16-21" > < / 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-16-22" name = "__codelineno-16-22" href = "#__codelineno-16-22" > < / 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-16-23" name = "__codelineno-16-23" href = "#__codelineno-16-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-16-24" name = "__codelineno-16-24" href = "#__codelineno-16-24" > < / 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-16-25" name = "__codelineno-16-25" href = "#__codelineno-16-25" > < / 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-16-26" name = "__codelineno-16-26" href = "#__codelineno-16-26" > < / 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-16-27" name = "__codelineno-16-27" href = "#__codelineno-16-27" > < / 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-16-28" name = "__codelineno-16-28" href = "#__codelineno-16-28" > < / 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-16-29" name = "__codelineno-16-29" href = "#__codelineno-16-29" > < / 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.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > dfs< / span > < span class = "p" > }< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / a >
< a id = "__codelineno-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > graphDFS< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > graph_dfs.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 深度优先遍历 DFS 辅助函数 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "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 >
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / 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-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / 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-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / 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-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / 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-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / 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-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "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-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
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< a id = "__codelineno-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "c1" > // 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点< / span >
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< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / 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 >
< a id = "__codelineno-18-18" name = "__codelineno-18-18" href = "#__codelineno-18-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-18-19" name = "__codelineno-18-19" href = "#__codelineno-18-19" > < / a > < span class = "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" > List< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-20" name = "__codelineno-18-20" href = "#__codelineno-18-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-18-21" name = "__codelineno-18-21" href = "#__codelineno-18-21" > < / a > < span class = "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 = "w" > < / span > < span class = "n" > HashSet< / span > < span class = "o" > < < / span > < span class = "n" > Vertex< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-22" name = "__codelineno-18-22" href = "#__codelineno-18-22" > < / 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 >
< a id = "__codelineno-18-23" name = "__codelineno-18-23" href = "#__codelineno-18-23" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
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< a id = "__codelineno-18-24" name = "__codelineno-18-24" href = "#__codelineno-18-24" > < / a > < span class = "p" > }< / span >
2023-02-15 03:42:47 +08:00
< / 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-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" > 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-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / 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-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / 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-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / 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-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / 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-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "k" > continue< / span > < span class = "c1" > // 跳过已被访问过的顶点< / span >
< a id = "__codelineno-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / 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-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / a >
< a id = "__codelineno-19-15" name = "__codelineno-19-15" href = "#__codelineno-19-15" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-19-16" name = "__codelineno-19-16" href = "#__codelineno-19-16" > < / 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-19-17" name = "__codelineno-19-17" href = "#__codelineno-19-17" > < / 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-19-18" name = "__codelineno-19-18" href = "#__codelineno-19-18" > < / a > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-19-19" name = "__codelineno-19-19" href = "#__codelineno-19-19" > < / 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-19-20" name = "__codelineno-19-20" href = "#__codelineno-19-20" > < / a > < span class = "c1" > // 哈希表，用于记录已被访问过的顶点< / span >
< a id = "__codelineno-19-21" name = "__codelineno-19-21" href = "#__codelineno-19-21" > < / 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-19-22" name = "__codelineno-19-22" href = "#__codelineno-19-22" > < / 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-19-23" name = "__codelineno-19-23" href = "#__codelineno-19-23" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-19-24" name = "__codelineno-19-24" href = "#__codelineno-19-24" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > graph_dfs.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / 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-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / 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 >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > graph_dfs.dart< / 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 = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > dfs< / 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" > GraphAdjList< / span > < span class = "w" > < / span > < span class = "n" > graph< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "w" > < / span > < span class = "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-21-5" name = "__codelineno-21-5" href = "#__codelineno-21-5" > < / 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-21-6" name = "__codelineno-21-6" href = "#__codelineno-21-6" > < / 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-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / a > < span class = "p" > )< / 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 = "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-21-9" name = "__codelineno-21-9" href = "#__codelineno-21-9" > < / 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-21-10" name = "__codelineno-21-10" href = "#__codelineno-21-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历该顶点的所有邻接顶点< / span >
< a id = "__codelineno-21-11" name = "__codelineno-21-11" href = "#__codelineno-21-11" > < / 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-21-12" name = "__codelineno-21-12" href = "#__codelineno-21-12" > < / 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-21-13" name = "__codelineno-21-13" href = "#__codelineno-21-13" > < / 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-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 = "w" > < / span > < span class = "c1" > // 递归访问邻接顶点< / span >
< a id = "__codelineno-21-16" name = "__codelineno-21-16" href = "#__codelineno-21-16" > < / 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-21-17" name = "__codelineno-21-17" href = "#__codelineno-21-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-18" name = "__codelineno-21-18" href = "#__codelineno-21-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-21-19" name = "__codelineno-21-19" href = "#__codelineno-21-19" > < / a >
< a id = "__codelineno-21-20" name = "__codelineno-21-20" href = "#__codelineno-21-20" > < / a > < span class = "cm" > /* 深度优先遍历 DFS */< / span >
< a id = "__codelineno-21-21" name = "__codelineno-21-21" href = "#__codelineno-21-21" > < / 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-21-22" name = "__codelineno-21-22" href = "#__codelineno-21-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 顶点遍历序列< / span >
< a id = "__codelineno-21-23" name = "__codelineno-21-23" href = "#__codelineno-21-23" > < / 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-21-24" name = "__codelineno-21-24" href = "#__codelineno-21-24" > < / 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-21-25" name = "__codelineno-21-25" href = "#__codelineno-21-25" > < / 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-21-26" name = "__codelineno-21-26" href = "#__codelineno-21-26" > < / 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-21-27" name = "__codelineno-21-27" href = "#__codelineno-21-27" > < / 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-21-28" name = "__codelineno-21-28" href = "#__codelineno-21-28" > < / a > < 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下图所示，其中：< / 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 > < img alt = "图的深度优先遍历步骤" src = "../graph_traversal.assets/graph_dfs_step1.png" / > < / p >
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< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step2" src = "../graph_traversal.assets/graph_dfs_step2.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step3" src = "../graph_traversal.assets/graph_dfs_step3.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step4" src = "../graph_traversal.assets/graph_dfs_step4.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step5" src = "../graph_traversal.assets/graph_dfs_step5.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step6" src = "../graph_traversal.assets/graph_dfs_step6.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step7" src = "../graph_traversal.assets/graph_dfs_step7.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step8" src = "../graph_traversal.assets/graph_dfs_step8.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step9" src = "../graph_traversal.assets/graph_dfs_step9.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step10" src = "../graph_traversal.assets/graph_dfs_step10.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "graph_dfs_step11" src = "../graph_traversal.assets/graph_dfs_step11.png" / > < / p >
< / div >
< / div >
< / div >
< div class = "admonition question" >
< p class = "admonition-title" > 深度优先遍历的序列是否唯一？< / p >
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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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< / div >
< h3 id = "_4" > 复杂度分析< a class = "headerlink" href = "#_4" 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 >
< h2 id = "__comments" > 评论< / h2 >
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< script id = "__config" type = "application/json" > { "base" : "../.." , "features" : [ "content.action.edit" , "content.code.annotate" , "content.code.copy" , "content.tabs.link" , "content.tooltips" , "navigation.indexes" , "navigation.sections" , "navigation.top" , "navigation.footer" , "navigation.tracking" , "search.highlight" , "search.share" , "search.suggest" , "toc.follow" ] , "search" : "../../assets/javascripts/workers/search.208ed371.min.js" , "translations" : { "clipboard.copied" : "\u5df2\u590d\u5236" , "clipboard.copy" : "\u590d\u5236" , "search.result.more.one" : "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.more.other" : "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.none" : "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.one" : "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.other" : "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.placeholder" : "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22" , "search.result.term.missing" : "\u7f3a\u5c11" , "select.version" : "\u9009\u62e9\u5f53\u524d\u7248\u672c" } } < / script >
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< script src = "../../assets/javascripts/bundle.fac441b0.min.js" > < / script >
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< script src = "../../javascripts/mathjax.js" > < / script >
< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
< script src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
< / body >
< / html >
