Detect cycle in an undirected graph

// A C++ Program to detect cycle in an undirected graph
#include<iostream>
#include <list>
#include <limits.h>
using namespace std;

// Class for an undirected graph
class Graph
{
    int V;    // No. of vertices
    list<int> *adj;    // Pointer to an array containing adjacency lists
    bool isCyclicUtil(int v, bool visited[], int parent);
public:
    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
};

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.
    adj[w].push_back(v); // Add v to w’s list.
}

// A recursive function that uses visited[] and parent to detect
// cycle in subgraph reachable from vertex v.
bool Graph::isCyclicUtil(int v, bool visited[], int parent)
{
    // Mark the current node as visited
    visited[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 an adjacent is not visited, then recur for that adjacent
        if (!visited[*i])
        {
           if (isCyclicUtil(*i, visited, v))
              return true;
        }

        // If an adjacent is visited and not parent of current vertex,
        // then there is a cycle.
        else if (*i != parent)
           return true;
    }
    return false;
}

// Returns true if the graph contains a cycle, else false.
bool Graph::isCyclic()
{
    // Mark all the vertices as not visited and not part of recursion
    // stack
    bool *visited = new bool[V];
    for (int i = 0; i < V; i++)
        visited[i] = false;

    // Call the recursive helper function to detect cycle in different
    // DFS trees
    for (int u = 0; u < V; u++)
        if (!visited[u]) // Don't recur for u if it is already visited
          if (isCyclicUtil(u, visited, -1))
             return true;

    return false;
}

// Driver program to test above functions
int main()
{
    Graph g1(5);
    g1.addEdge(1, 0);
    g1.addEdge(0, 2);
    g1.addEdge(2, 0);
    g1.addEdge(0, 3);
    g1.addEdge(3, 4);
    g1.isCyclic()? cout << "Graph contains cycle\n":
                   cout << "Graph doesn't contain cycle\n";

    Graph g2(3);
    g2.addEdge(0, 1);
    g2.addEdge(1, 2);
    g2.isCyclic()? cout << "Graph contains cycle\n":
                   cout << "Graph doesn't contain cycle\n";

    return 0;
}

// A Java Program to detect cycle in an undirected graph
import java.io.*;
import java.util.*;

// This class represents a directed graph using adjacency list
// representation
class Graph
{
    private int V;   // No. of vertices
    private LinkedList<Integer> adj[]; // Adjacency List Represntation

    // Constructor
    Graph(int v) {
        V = v;
        adj = new LinkedList[v];
        for(int i=0; i<v; ++i)
            adj[i] = new LinkedList();
    }

    // Function to add an edge into the graph
    void addEdge(int v,int w) {
        adj[v].add(w);
        adj[w].add(v);
    }

    // A recursive function that uses visited[] and parent to detect
    // cycle in subgraph reachable from vertex v.
    Boolean isCyclicUtil(int v, Boolean visited[], int parent)
    {
        // Mark the current node as visited
        visited[v] = true;
        Integer i;

        // Recur for all the vertices adjacent to this vertex
        Iterator<Integer> it = adj[v].iterator();
        while (it.hasNext())
        {
            i = it.next();

            // If an adjacent is not visited, then recur for that
            // adjacent
            if (!visited[i])
            {
                if (isCyclicUtil(i, visited, v))
                    return true;
            }

            // If an adjacent is visited and not parent of current
            // vertex, then there is a cycle.
            else if (i != parent)
                return true;
        }
        return false;
    }

    // Returns true if the graph contains a cycle, else false.
    Boolean isCyclic()
    {
        // Mark all the vertices as not visited and not part of
        // recursion stack
        Boolean visited[] = new Boolean[V];
        for (int i = 0; i < V; i++)
            visited[i] = false;

        // Call the recursive helper function to detect cycle in
        // different DFS trees
        for (int u = 0; u < V; u++)
            if (!visited[u]) // Don't recur for u if already visited
                if (isCyclicUtil(u, visited, -1))
                    return true;

        return false;
    }


    // Driver method to test above methods
    public static void main(String args[])
    {
        // Create a graph given in the above diagram
        Graph g1 = new Graph(5);
        g1.addEdge(1, 0);
        g1.addEdge(0, 2);
        g1.addEdge(2, 0);
        g1.addEdge(0, 3);
        g1.addEdge(3, 4);
        if (g1.isCyclic())
            System.out.println("Graph contains cycle");
        else
            System.out.println("Graph doesn't contains cycle");

        Graph g2 = new Graph(3);
        g2.addEdge(0, 1);
        g2.addEdge(1, 2);
        if (g2.isCyclic())
            System.out.println("Graph contains cycle");
        else
            System.out.println("Graph doesn't contains cycle");
    }
}
// This code is contributed by Aakash Hasija

# Python Program to detect cycle in an undirected graph

from collections import defaultdict
 
#This class represents a undirected graph using adjacency list representation
class Graph:
 
    def __init__(self,vertices):
        self.V= vertices #No. of vertices
        self.graph = defaultdict(list) # default dictionary to store graph

 
    # function to add an edge to graph
    def addEdge(self,v,w):
        self.graph[v].append(w) #Add w to v_s list
        self.graph[w].append(v) #Add v to w_s list
 
    # A recursive function that uses visited[] and parent to detect
    # cycle in subgraph reachable from vertex v.
    def isCyclicUtil(self,v,visited,parent):

        #Mark the current node as visited 
        visited[v]= True

        #Recur for all the vertices adjacent to this vertex
        for i in self.graph[v]:
            # If the node is not visited then recurse on it
            if  visited[i]==False : 
                if(self.isCyclicUtil(i,visited,v)):
                    return True
            # If an adjacent vertex is visited and not parent of current vertex,
            # then there is a cycle
            elif  parent!=i:
                return True
        
        return False
         
 
    #Returns true if the graph contains a cycle, else false.
    def isCyclic(self):
        # Mark all the vertices as not visited
        visited =[False]*(self.V)
        # Call the recursive helper function to detect cycle in different
        #DFS trees
        for i in range(self.V):
            if visited[i] ==False: #Don't recur for u if it is already visited
                if(self.isCyclicUtil(i,visited,-1))== True:
                    return True
        
        return False

# Create a graph given in the above diagram
g = Graph(5)
g.addEdge(1, 0)
g.addEdge(0, 2)
g.addEdge(2, 0)
g.addEdge(0, 3)
g.addEdge(3, 4)

if g.isCyclic():
    print "Graph contains cycle"
else :
    print "Graph does not contain cycle "
g1 = Graph(3)
g1.addEdge(0,1)
g1.addEdge(1,2)


if g1.isCyclic():
    print "Graph contains cycle"
else :
    print "Graph does not contain cycle "
 
#This code is contributed by Neelam Yadav