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C Program to Detect Cycle in a Directed Graph

  • Last Updated : 02 Jan, 2019

Given a directed graph, check whether the graph contains a cycle or not. Your function should return true if the given graph contains at least one cycle, else return false. For example, the following graph contains three cycles 0->2->0, 0->1->2->0 and 3->3, so your function must return true.

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.


// A C++ Program to detect cycle in a graph
#include <iostream>
#include <limits.h>
#include <list>
using namespace std;
class Graph {
    int V; // No. of vertices
    list<int>* adj; // Pointer to an array containing adjacency lists
    bool isCyclicUtil(int v, bool visited[], bool* rs); // used by isCyclic()
    Graph(int V); // Constructor
    void addEdge(int v, int w); // to add an edge to graph
    bool isCyclic(); // returns true if there is a cycle in this graph
Graph::Graph(int V)
    this->V = V;
    adj = new list<int>[V];
void Graph::addEdge(int v, int w)
    adj[v].push_back(w); // Add w to v’s list.
// This function is a variation of DFSUytil()
// in https://
bool Graph::isCyclicUtil(int v, bool visited[], bool* recStack)
    if (visited[v] == false) {
        // Mark the current node as visited and part of recursion stack
        visited[v] = true;
        recStack[v] = true;
        // Recur for all the vertices adjacent to this vertex
        list<int>::iterator i;
        for (i = adj[v].begin(); i != adj[v].end(); ++i) {
            if (!visited[*i] && isCyclicUtil(*i, visited, recStack))
                return true;
            else if (recStack[*i])
                return true;
    recStack[v] = false; // remove the vertex from recursion stack
    return false;
// Returns true if the graph contains a cycle, else false.
// This function is a variation of DFS()
// in https://
bool Graph::isCyclic()
    // Mark all the vertices as not visited and not part of recursion
    // stack
    bool* visited = new bool[V];
    bool* recStack = new bool[V];
    for (int i = 0; i < V; i++) {
        visited[i] = false;
        recStack[i] = false;
    // Call the recursive helper function to detect cycle in different
    // DFS trees
    for (int i = 0; i < V; i++)
        if (isCyclicUtil(i, visited, recStack))
            return true;
    return false;
int main()
    // Create a graph given in the above diagram
    Graph 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";
        cout << "Graph doesn't contain cycle";
    return 0;
Graph contains cycle

Please refer complete article on Detect Cycle in a Directed Graph for more details!

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