Added Detect Cycle in Directed Graph using DFS with clear comments

[Mayank29903]

#include <bits/stdc++.h>
using namespace std;

// Function to check if a cycle exists using DFS
bool dfs(int node, vector adj[], vector &visited, vector &recStack) {
visited[node] = 1; // Mark the current node as visited
recStack[node] = 1; // Add this node to the recursion stack

// Visit all adjacent vertices
for (auto neighbor : adj[node]) {
    // If the neighbor is not visited, do a DFS on it
    if (!visited[neighbor]) {
        if (dfs(neighbor, adj, visited, recStack)) {
            return true; // Found a cycle
        }
    }
    // If the neighbor is already in recursion stack → cycle found
    else if (recStack[neighbor]) {
        return true;
    }
}

// Remove the node from recursion stack before returning
recStack[node] = 0;
return false;

}

// Function to check if the directed graph has a cycle
bool isCyclic(int V, vector adj[]) {
vector visited(V, 0);
vector recStack(V, 0);

// Check each node (for disconnected graphs)
for (int i = 0; i < V; i++) {
    if (!visited[i]) {
        if (dfs(i, adj, visited, recStack)) {
            return true; // If cycle found
        }
    }
}
return false; // No cycle

}

int main() {
int V, E;
cout << "Enter number of vertices and edges: ";
cin >> V >> E;

vector<int> adj[V];
cout << "Enter edges (u -> v):\n";
for (int i = 0; i < E; i++) {
    int u, v;
    cin >> u >> v;
    adj[u].push_back(v); // Directed edge
}

if (isCyclic(V, adj))
    cout << "Cycle detected in the graph.\n";
else
    cout << "No cycle found in the graph.\n";

return 0;

}

[Mayank29903]

Please review and merge.