import java.util.*;
import java.io.*;

class CycleDetectionDirectedGraphDFS {

    // DFS
    public static boolean dfsCheck(int node, boolean visited[],
                              boolean pathVis[],
                              ArrayList<ArrayList<Integer>> adj){

        visited[node] = true;
        pathVis[node] = true;

        for(int next : adj.get(node)){

            if(!visited[next]){
                if(dfsCheck(next, visited, pathVis, adj)) return true;
            }
            else if(pathVis[next]){
                return true;
            }
        }

        pathVis[node] = false;
        return false;
    }


    public static boolean isCyclic(int V, ArrayList<ArrayList<Integer>> adj){

        boolean visited[] = new boolean[V];
        boolean pathVis[] = new boolean[V];

        for(int i=0;i<V;i++){
            if(!visited[i]){
                if(dfsCheck(i, visited, pathVis, adj)) return true;
            }
        }

        return false;
    }


    // helper to create adjacency list
    public static ArrayList<ArrayList<Integer>> makeGraph(int V){
        ArrayList<ArrayList<Integer>> adj = new ArrayList<>();
        for(int i=0;i<V;i++) adj.add(new ArrayList<>());
        return adj;
    }


    // DRIVER
    public static void main(String args[]){

        // ================= CASE 1 =================
        {
            int V = 6;
            ArrayList<ArrayList<Integer>> adj = makeGraph(V);

            /*
                0 → 1 → 2 → 3
                    ↑     ↓
                    └─────┘
                4 → 5
            */

            adj.get(0).add(1);
            adj.get(1).add(2);
            adj.get(2).add(3);
            adj.get(3).add(1);
            adj.get(4).add(5);

            System.out.printf("Case 1: %s\n",
                isCyclic(V, adj) ? "Cycle detected" : "No cycle");
        }


        // ================= CASE 2 =================
        {
            int V = 4;
            ArrayList<ArrayList<Integer>> adj = makeGraph(V);

            /*
                0 → 1 → 2 → 3
                No cycle
            */

            adj.get(0).add(1);
            adj.get(1).add(2);
            adj.get(2).add(3);

            System.out.printf("Case 2: %s\n",
                isCyclic(V, adj) ? "Cycle detected" : "No cycle");
        }


        // ================= CASE 3 =================
        {
            int V = 3;
            ArrayList<ArrayList<Integer>> adj = makeGraph(V);

            /*
                0 → 1
                1 → 2
                2 → 0
            */

            adj.get(0).add(1);
            adj.get(1).add(2);
            adj.get(2).add(0);

            System.out.printf("Case 3: %s\n",
                isCyclic(V, adj) ? "Cycle detected" : "No cycle");
        }


        // ================= CASE 4 =================
        {
            int V = 5;
            ArrayList<ArrayList<Integer>> adj = makeGraph(V);

            /*
                disconnected, no cycle
                0 → 1
                2 → 3
                4 alone
            */

            adj.get(0).add(1);
            adj.get(2).add(3);

            System.out.printf("Case 4: %s\n",
                isCyclic(V, adj) ? "Cycle detected" : "No cycle");
        }
    }
}