chore(CPlusPlus): add detecting a cycle in a graph (#862)

* Add files via upload

* Delete Detecting a cycle in a graph (Using three color mechanism).cpp

* Create detecting-cycle-in-a-graph-using-three-color-mechanism.cpp

* Update detecting-cycle-in-a-graph-using-three-color-mechanism.cpp

* Update detecting-cycle-in-a-graph-using-three-color-mechanism.cpp

* Update README.md

algorithms/CPlusPlus/Graphs/detecting-cycle-in-a-graph-using-three-color-mechanism.cpp

@@ -0,0 +1,127 @@
+// A DFS based approach to find if there is a cycle
+// in a directed graph. 
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+// Declaring an enum of three colors
+enum Color {WHITE, GRAY, BLACK};
+
+// Class Graph
+// Graph class represents a directed graph using
+// adjacency list representation
+
+class Graph
+{
+	int V;  // No. of vertices
+	list<int>* adj; // adjacency list
+
+	//  DFS traversal of the vertices reachable from v
+    	bool DFSUtil(int v, int color[]);
+	
+public:
+
+	Graph(int V); // The Constructor
+
+  // Function to add an edge to graph
+	void addEdge(int v, int w);
+ // Function to check whether graph is cyclic or not
+	bool isCyclic();
+};
+
+// Constructor
+Graph::Graph(int V)
+{
+	this->V = V;
+	adj = new list<int>[V];
+}
+
+// Utility function to add an edge
+void Graph::addEdge(int v, int w)
+{
+	adj[v].push_back(w); // Add w to v's list.
+}
+
+// Recursive function to find if there is back edge
+// in DFS subtree tree rooted with 'u'
+
+bool Graph::DFSUtil(int u, int color[])
+{
+	// GRAY : This vertex is being processed (DFS
+	//		 for this vertex has started, but not
+	//		 ended (or this vertex is in function
+	//		 call stack)
+	
+	color[u] = GRAY;
+
+	// Iterate through all adjacent vertices
+	
+	list<int>::iterator i;
+	for (i = adj[u].begin(); i != adj[u].end(); ++i)
+	{
+		int v = *i; // An adjacent of u
+
+		// If there is Gray 
+		if (color[v] == GRAY)
+		return true;
+
+		// If v is not processed and there is a back
+		// edge in subtree rooted with v Call DFSUtil and check accordingly
+		if (color[v] == WHITE && DFSUtil(v, color))
+		return true;
+	}
+
+	// Mark this vertex as processed
+	color[u] = BLACK;
+
+	return false;
+}
+
+// Returns true if there is a cycle in graph
+bool Graph::isCyclic()
+{
+	// Initialize color of all vertices as WHITE
+	int *color = new int[V];
+	for (int i = 0; i < V; i++)
+		color[i] = WHITE;
+
+	// Do a DFS traversal beginning with all
+	// vertices
+	for (int i = 0; i < V; i++)
+		if (color[i] == WHITE)
+		if (DFSUtil(i, color) == true)
+			return true;
+
+	return false;
+}
+
+// Driver code to test above
+int main()
+{
+	  /*
+  
+           0--->1--->2--->3--->3
+  
+           2<---->0
+  
+           total 6 edges
+  
+          */
+	
+	// Create a graph given in the above diagram
+	Graph g(4);
+	g.addEdge(0, 1);
+	g.addEdge(0, 2);
+	g.addEdge(1, 2);
+	g.addEdge(2, 0);
+	g.addEdge(2, 3);
+	g.addEdge(3, 3);
+
+	if (g.isCyclic())
+		cout << "Graph contains cycle";
+	else
+		cout << "Graph doesn't contain cycle";
+
+	return 0;
+}

algorithms/CPlusPlus/README.md

@@ -56,6 +56,9 @@
 - [Cycle Detection](Graphs/cycle-detection.cpp)
 - [Prim's Algorithm](Graphs/prim's_algorithm.cpp)
 - [Floyd Warshall](Graphs/floyd-warshall.cpp)
+- [Detecting Cycle in Directed graph using three colors](Graphs/detecting-cycle-in-a-graph-using-three-color-mechanism.cpp)
+
+
 
 ## Multiplication
 
@@ -207,4 +210,4 @@
 
 ## Backtracking
 
-- [N-Queens Problem](Backtracking/n-queens.cpp)
+- [N-Queens Problem](Backtracking/n-queens.cpp)