add Bipartite Graph Check

Bipartite_Graph.cpp

@@ -0,0 +1,79 @@
+// Bipartite Graph
+// ---------------
+// You can divide all the vertices of graph in 2 sets
+// such that all edges of the graph are from set1 to set2
+
+// Two Coloring
+
+
+/// How  to flip colors between 1 and 2 ?
+// Use 3-color
+//   3-2 = 1    and   3-1 = 2
+
+#include <iostream>
+#include <vector>
+using namespace std;
+
+bool dfs_helper(vector<int> graph[], int node, int visited[], int parent, int color){
+	// come to node and assign the color
+	visited[node] = color;    // 1 or 2 -- both means visited
+	for(auto nbr: graph[node]){
+		// Many possibilities
+		if(visited[nbr] == 0){
+			int subprob = dfs_helper(graph, nbr, visited, node, 3-color);
+			if(subprob == false){
+				return false;
+			}
+		}
+		else if(nbr != parent and color == visited[nbr]){
+			return false;
+		}
+	}
+	return true;	
+}
+
+// Yes or No, whether graph is Bipartite or Not
+bool dfs(vector<int> graph[], int N){
+	// Visited array states :
+	// 0 -> Not visited
+	// 1 -> Color 1
+	// 2 -> Color 2
+	int visited[N];
+	for(int i=0; i<=N; i++){
+		visited[i] = 0;
+	}
+
+	int color = 1;
+	int ans = dfs_helper(graph,0,visited,-1, color);
+
+	for(int i=0; i<N; i++){
+		cout << i << "->" << visited[i] << "\n";
+	}
+
+	return ans;
+}
+
+int main(){
+
+	int N, M;
+	cin >> N >> M;
+
+	vector<int> graph[N];
+
+	while(M--){
+		int x, y;
+		cin >> x >> y;
+		graph[x].push_back(y);
+		graph[y].push_back(x);
+	}	
+
+	// By DFS, coloring the nodes at each step 
+	// Current node -> color 1
+	// Neighbouring nodes -> color 2
+	if(dfs(graph, N)){
+		cout << "Yes, its bipartite..\n";
+	}
+	else{
+		cout << "No, its not bipartite..\n";
+	}
+}