Geeks - Detect Cycle in a Directed Graph 推断图是否有环

Detect Cycle in a Directed Graph

推断一个图是否有环，有环图例如以下：

这里唯一注意的就是，这是个有向图， 边组成一个环，不一定成环，由于方向能够不一致。

这里就是添加一个数组保存当前已经訪问过的路径信息 recStack[]；

而visited[]数组是訪问过的点的信息，两者作用是不一样的。

知道这个知识点，这道题就非常easy了。

原文：

http://www.geeksforgeeks.org/detect-cycle-in-a-graph/

#include <stdio.h>
#include <list>
#include <limits.h>
#include <iostream>
using namespace std;

class DetectCycleinaDirectedGraph
{
	int size;
	list<int> *adj;

	bool isCycleUtil(int v, bool visited[], bool *recStack)
	{
		if (!visited[v])
		{
			//本题巧妙之处：额外添加recStack,because it is directed, if it is undirected, then we don't really need recStack.
			visited[v] = recStack[v] = true;
			list<int>::iterator it = adj[v].begin();
			for ( ; it != adj[v].end(); it++)
			{
				if (!visited[*it] && isCycleUtil(*it, visited, recStack))
					return true;
				else if (recStack[*it]) return true;
			}
			recStack[v] = false;
		}
		return false;
	}
public:
	DetectCycleinaDirectedGraph(int v) : size(v)
	{
		adj = new list<int>[size];
	}

	void addEdge(int v, int w)
	{
		adj[v].push_back(w);
	}

	bool isCyclic()
	{
		bool *visited = new bool[size];
		bool *recStack = new bool[size];
		fill(visited, visited+size, false);
		fill(recStack, recStack+size, false);

		for (int i = 0; i < size; i++)
		{
			if (isCycleUtil(i, visited, recStack)) return true;
		}
		return false;
	}	
};

void DetectCycleinaDirectedGraph_RUN()
{
	DetectCycleinaDirectedGraph g(4);
	g.addEdge(0, 1);
	g.addEdge(0, 2);
	g.addEdge(1, 2);
	g.addEdge(2, 0);
	g.addEdge(2, 3);
	g.addEdge(3, 3);

	if(g.isCyclic())
		cout << "Graph contains cycle\n";
	else
		cout << "Graph doesn't contain cycle\n";
}