cycle detection(dfs)

class Solution {
public:
    bool detect(int node, int parent, vector<int>& vis, vector<vector<int>>& adj) {
        vis[node] = 1;  // Mark the current node as visited
        for (auto adjacentNode : adj[node]) {
            if (!vis[adjacentNode]) {  // If the adjacent node is not visited
                if (detect(adjacentNode, node, vis, adj)) 
                    return true;
            } 
            else if (adjacentNode != parent) {  // If the adjacent node is visited and not the parent, a cycle is found
                return true;
            }
        }
        return false;
    }

    bool isCycle(vector<vector<int>>& adj) {
        int v = adj.size();  // Number of vertices
        vector<int> vis(v, 0);  // Initialize the visited vector with 0s

        for (int i = 0; i < v; i++) {
            if (!vis[i]) {  // If the node is not visited
                if (detect(i, -1, vis, adj)) 
                    return true;
            }
        }
        return false;  // No cycle found
    }
};