深度优先搜索检测有向图有无环路算法

给定有向图 G = (V, E)，需要判断该图中是否存在环路（Cycle）。例如，下面的图 G 中包含 4 个顶点和 6 条边。

实际上，上图中存在 3 个环路：0->2->0, 0->1->2->0, 3->3。

深度优先搜索（DFS：Depth-First Search）可以用于检测图中是否存在环。DFS 会对一个连通的图构造一颗树，如果在构造树的过程中出现反向边（Back Edge），则认为图中存在环路。

对于非连通图，可以对图中的不同部分分别进行 DFS 构造树结构，对于每棵树分别检测反向边的存在。

在 DFS 对图进行遍历时，将遍历过的顶点放入递归栈中，如果新遍历的顶点已经存在于递归栈中，则说明存在一个反向边，即存在一个环。

  1 using System;
  2 using System.Collections.Generic;
  3 using System.Linq;
  4 
  5 namespace GraphAlgorithmTesting
  6 {
  7   class Program
  8   {
  9     static void Main(string[] args)
 10     {
 11       Graph g = new Graph(6);
 12       g.AddEdge(0, 1, 16);
 13       g.AddEdge(0, 2, 13);
 14       g.AddEdge(1, 2, 10);
 15       g.AddEdge(1, 3, 12);
 16       g.AddEdge(2, 1, 4);
 17       g.AddEdge(2, 4, 14);
 18       //g.AddEdge(3, 2, 9);
 19       g.AddEdge(3, 5, 20);
 20       //g.AddEdge(4, 3, 7);
 21       //g.AddEdge(4, 5, 4);
 22 
 23       Console.WriteLine();
 24       Console.WriteLine("Graph Vertex Count : {0}", g.VertexCount);
 25       Console.WriteLine("Graph Edge Count : {0}", g.EdgeCount);
 26       Console.WriteLine();
 27 
 28       Console.WriteLine("Is there cycle in graph: {0}", g.HasCycle());
 29 
 30       Console.ReadKey();
 31     }
 32 
 33     class Edge
 34     {
 35       public Edge(int begin, int end, int weight)
 36       {
 37         this.Begin = begin;
 38         this.End = end;
 39         this.Weight = weight;
 40       }
 41 
 42       public int Begin { get; private set; }
 43       public int End { get; private set; }
 44       public int Weight { get; private set; }
 45 
 46       public override string ToString()
 47       {
 48         return string.Format(
 49           "Begin[{0}], End[{1}], Weight[{2}]",
 50           Begin, End, Weight);
 51       }
 52     }
 53 
 54     class Graph
 55     {
 56       private Dictionary<int, List> _adjacentEdges
 57         = new Dictionary<int, List>();
 58 
 59       public Graph(int vertexCount)
 60       {
 61         this.VertexCount = vertexCount;
 62       }
 63 
 64       public int VertexCount { get; private set; }
 65 
 66       public IEnumerable<int> Vertices { get { return _adjacentEdges.Keys; } }
 67 
 68       public IEnumerable Edges
 69       {
 70         get { return _adjacentEdges.Values.SelectMany(e => e); }
 71       }
 72 
 73       public int EdgeCount { get { return this.Edges.Count(); } }
 74 
 75       public void AddEdge(int begin, int end, int weight)
 76       {
 77         if (!_adjacentEdges.ContainsKey(begin))
 78         {
 79           var edges = new List();
 80           _adjacentEdges.Add(begin, edges);
 81         }
 82 
 83         _adjacentEdges[begin].Add(new Edge(begin, end, weight));
 84       }
 85 
 86       public bool HasCycle()
 87       {
 88         // mark all the vertices as not visited 
 89         // and not part of recursion stack
 90         bool[] visited = new bool[VertexCount];
 91         bool[] recursionStack = new bool[VertexCount];
 92         for (int i = 0; i < VertexCount; i++)
 93         {
 94           visited[i] = false;
 95           recursionStack[i] = false;
 96         }
 97 
 98         // call the recursive helper function to 
 99         // detect cycle in different DFS trees
100         for (int i = 0; i < VertexCount; i++)
101           if (CheckCyclic(i, visited, recursionStack))
102             return true;
103 
104         return false;
105       }
106 
107       private bool CheckCyclic(int v, bool[] visited, bool[] recursionStack)
108       {
109         if (!visited[v])
110         {
111           // mark the current node as visited 
112           // and part of recursion stack
113           visited[v] = true;
114           recursionStack[v] = true;
115 
116           // recur for all the vertices adjacent to this vertex
117           if (_adjacentEdges.ContainsKey(v))
118           {
119             foreach (var edge in _adjacentEdges[v])
120             {
121               if (!visited[edge.End]
122                 && CheckCyclic(edge.End, visited, recursionStack))
123                 return true;
124               else if (recursionStack[edge.End])
125                 return true;
126             }
127           }
128         }
129 
130         // remove the vertex from recursion stack
131         recursionStack[v] = false;
132 
133         return false;
134       }
135     }
136   }
137 }

本篇文章《DFS 检测有向图有无环算法》由 Dennis Gao 发表自博客园，未经作者本人同意禁止任何形式的转载，任何自动或人为的爬虫转载行为均为耍流氓。

转载于:https://www.cnblogs.com/gaochundong/p/dfs_detect_cycle_in_a_directed_graph.html