Added detect cycle in directed graph

Author: pavan-patel-93

Graphs/14_detectCycleInDirectedGraph.cpp

@@ -0,0 +1,79 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+class Solution{
+    private:
+        /**
+         * Detecting of cycle using DFS
+         */
+        bool detectCycleUsingDFS(int node, vector<vector<int>>& adj, vector<int>& visited, vector<int>& pathVisited){
+            visited[node] = 1;
+            pathVisited[node] = 1;
+
+            for(auto it: adj[node]){
+                if(!visited[it]){
+                    if(detectCycleUsingDFS(it, adj, visited, pathVisited)) return true;
+                }else{
+                    // If the node has been previously visited but it has to be be visited on the same path
+                    if(pathVisited[it]){
+                        return true;
+                    }
+                }
+            }
+
+            pathVisited[node] = 0; // while moving backwards, making nodes as not path visited
+            return false;
+        }
+    public:
+        bool hasCycle(vector<vector<int>>& adj){
+            int n = adj.size();
+            vector<int> visited(n, 0);
+            vector<int> pathVisited(n, 0);
+
+            for(int i=0 ; i<n ; i++){
+                if(!visited[i]){
+                    if(detectCycleUsingDFS(i, adj, visited, pathVisited)) return true;
+                }
+            }
+            return false;
+        }
+};
+
+int main() {
+    int n = 10;
+    vector<vector<int>> adj(n+1);
+    /**
+     *      1--> 2 -------> 3 --> 4
+     *           ^          |     |
+     *           |          v     v
+     *           8 <--10    7 --> 5 --> 6
+     *           \>   />
+     *              9
+     */
+
+    adj[1].push_back(2);  // 1 -> 2
+
+    adj[2].push_back(3);  // 2 -> 3
+
+    adj[3].push_back(4);  // 3 -> 4
+    adj[3].push_back(7);  // 3 -> 7
+
+    adj[4].push_back(5);  // 4 -> 5
+
+    adj[5].push_back(6);  // 5 -> 6
+
+    adj[7].push_back(5);  // 7 -> 5
+
+    adj[8].push_back(2);  // 8 -> 2 (cycle)
+    adj[8].push_back(9);  // 8 -> 9
+
+    adj[9].push_back(10); // 9 -> 10
+
+    adj[10].push_back(8); // 10 -> 8 (cycle)
+
+    Solution sol;
+    bool isCycle = sol.hasCycle(adj);
+    cout << ( isCycle ? "The graph has cycle" : "The graph does not have a cycle" ) << endl;
+
+    return 0;
+}