Added is_graph_bipartite.cpp

graph/is_graph_bipartite.cpp

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+/**
+ *  @file is_graph_bipartite
+ *
+ *	@brief Algorithm to check whether a graph is bipartite
+ *
+ *	@details
+ *	A graph is a collection of nodes also called vertices and these vertices
+ *	are connected by edges.A bipartite graph is a graph whose vertices can be
+ * 	divided into two disjoint and independent sets U and V such that every edge 
+ *	connects a vertex in U to one in V. 	
+ *	(https://en.wikipedia.org/wiki/Bipartite_graph)
+ *	The given Algorithm will determine whether the given graph is bipartite or not
+ *
+ *
+ * 	Example - Here is a graph g1 with 5 vertices and is bipartite
+ *
+ *		1   4
+ *	   / \ / \
+ *	  2   3   5
+ *	
+ *	Example - Here is a graph G2 with 3 vertices and is not bipartite
+ *
+ *		1 --- 2
+ *		 \   /
+ *		   3
+ *
+ *	
+ *	@author [Akshat Vaya](https://github.com/AkVaya)
+ *		
+ */
+#include <iostream>
+#include <vector>
+#include <queue>
+
+using std::vector;
+using std::queue;
+
+const int nax = 5e5 + 1;
+/**
+ * Class for representing graph as an adjacency list.
+ */
+class graph {
+ 	private: 
+ 		int n;						/// size of the graph
+
+    	vector<vector <int> > adj;	/// adj stores the graph as an adjacency list
+
+    	vector<int> side;			///stores the side of the vertex
+
+ 	public:
+    /**
+     * @brief Constructor that initializes the graph on creation
+     */
+    graph(int size = nax){
+    	n = size;
+    	adj.resize(n);
+    	side.resize(n,-1);
+    }
+
+    void addEdge(int u, int v);     /// function to add edges to our graph
+
+	bool is_bipartite();    	/// function to check whether the graph is bipartite or not
+
+};
+/**
+ * @brief Function that add an edge between two nodes or vertices of graph
+ *
+ * @param u is a node or vertex of graph
+ * @param v is a node or vertex of graph
+ */
+void graph::addEdge(int u, int v) {
+    adj[u-1].push_back(v-1);
+    adj[v-1].push_back(u-1);
+}
+/**
+ *	@brief function that checks whether the graph is bipartite or not
+ */
+bool graph::is_bipartite(){
+	n = adj.size();
+	side.resize(n,-1);
+	bool check = true;
+	queue<int> q;
+	for (int current_edge = 0; current_edge < n; ++current_edge)
+	{
+		if(side[current_edge] == -1){
+			q.push(current_edge);
+			side[current_edge] = 0;
+			while(q.size()){
+				int current = q.front();
+				q.pop();
+				for(auto neighbour : adj[current]){
+					if(side[neighbour] == -1){
+						side[neighbour] = (1 ^ side[current]);
+						q.push(neighbour);
+					}
+					else{
+						check &= (side[neighbour] != side[current]);
+					}
+				}
+			}
+		}
+	}
+	return check;
+}
+/**
+ * main funtion
+ */
+int main(){
+	graph G1(5);	/// creating graph G1 with 5 vertices
+	/// adding edges to the graphs as per the illustrated example
+	G1.addEdge(1,2);
+	G1.addEdge(1,3);
+	G1.addEdge(3,4);
+	G1.addEdge(4,5);
+
+	graph G2(3);	/// creating graph G2 with 3 vertices
+	/// adding edges to the graphs as per the illustrated example
+	G2.addEdge(1,2);
+	G2.addEdge(1,3);
+	G2.addEdge(2,3);
+	/// checking whether the graphs are bipartite or not
+	if(G1.is_bipartite()){
+		std::cout<<"The given graph G1 is a bipartite graph\n";
+	} 
+	else{
+		std::cout<<"The given graph G1 is not a bipartite graph\n";
+	}
+	if(G2.is_bipartite()){
+		std::cout<<"The given graph G2 is a bipartite graph\n";
+	} 
+	else{
+		std::cout<<"The given graph G2 is not a bipartite graph\n";
+	}
+	return 0;
+}