Graph: How to detect cycles in a undirectd graph using DFS

Question

Following is my DFS implementation, now I want to implement it such that I can detect if there are any cycles present in a graph or not.(The below code is basically used to find the number of connected elements)

#include <iostream>
#include <vector>
using namespace std;

vector <int> adj[10];
int visited[10];
bool flag=false;

void dfs(int s) {
    visited[s] = 0;
    for(int i = 0;i < adj[s].size();++i)    {
     if(visited[adj[s][i]] == -1)
         dfs(adj[s][i]);
     else if (visited[adj[s][i]] ==1){
        flag=true;
        // cout<<"g";  
        return;
     }
    }
    visited[s]=1;
}

void initialize() {
    for(int i = 0;i < 10;++i)
     visited[i] = -1;
}

int main() {
    int nodes, edges, x, y ;
    cin >> nodes;                       //Number of nodes
    cin >> edges;                       //Number of edges
    for(int i = 0;i < edges;++i) {
     cin >> x >> y;     
     adj[x].push_back(y);                   //Edge from vertex x to vertex y
     adj[y].push_back(x);                   //Edge from vertex y to vertex x
    }

    initialize();                           //Initialize all nodes as not visited

    for(int i = 1;i <= nodes;++i) {
     if(visited[i] == false)     {
         dfs(i);
     }

    }
    if (flag)
        cout<<"Graph contains cycles"<<endl;
    else
        cout<<"No cycles"<<endl;
    return 0;
}

I am not sure how to implement it, could anyone help me with it.

Edit : I have tried to implement it. Don't know where I am going wrong

Answer 1

I've changed the loop after the initialization call to:

for(int i = 0;i < nodes;++i) {
  if(visited[i] == -1)     {
    dfs(i);
  }
}

Your code did not start checking because each element in the visited was set to -1 and therefore skipped. So with this change it does work.

I suggest to look at size of your global variables adj and visted , make them local if possible. When 11 or more nodes are entered this code will stop working.

Edit for question “Can you tell me how do I check for disconnected graph?”

Change the same loop to this:

int nr_of_graphs = 0;
for(int i = 0;i < nodes;++i) {
  if(visited[i] == -1)     {
    ++nr_of_graphs;
    dfs(i);
  }
}
cout << "Nr of disconnected subgraphs " << nr_of_graphs << endl; 

dfs(i) is called for each not yet visited node. So count the amount of times this function is called from main, gives the number of disconnected subgraphs.