/**
 *  @file
 *
 *	@brief Algorithm to check whether a graph is [bipartite](https://en.wikipedia.org/wiki/Bipartite_graph)
 *	
 *	@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. 	
 *	
 *	The given Algorithm will determine whether the given graph is bipartite or not
 *	
 *	<pre>
 * 	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
 *	
 *	</pre>
 *
 *	@author [Akshat Vaya](https://github.com/AkVaya)
 *		
 */
#include <iostream>
#include <vector>
#include <queue>

/**
 * @namespace graph
 * @brief Graph algorithms
 */
namespace graph{
	/**
	 * @namespace is_graph_bipartite
	 * @brief Functions for checking whether a graph is bipartite or not
	 */
	namespace is_graph_bipartite{
		/**
		 * @brief Class for representing graph as an adjacency list.
		 */
		class Graph {
 			private: 
 				int n;						/// size of the graph

	    		std::vector<std::vector <int> > adj;	/// adj stores the graph as an adjacency list

		    	std::vector<int> side;			///stores the side of the vertex

				static const int nax = 5e5 + 1;


	 		public:
	    		/**
    			 * @brief Constructor that initializes the graph on creation
    			 */
	    		explicit 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
		 *	the function returns true if the graph is a bipartite graph
		 *	the function returns false if the graph is not a bipartite graph
		 *
		 *	@details
		 *	Here, side refers to the two disjoint subsets of the bipartite graph.
		 *	Initially, the values of side are set to -1 which is an unassigned state. A for loop is run for every vertex of the graph.
		 *	If the current edge has no side assigned to it, then a Breadth First Search operation is performed.
		 *	If two neighbours have the same side then the graph will not be bipartite and the value of check becomes false.
		 *	If and only if each pair of neighbours have different sides, the value of check will be true and hence the graph bipartite.
		 * 
		 */
		bool Graph::is_bipartite(){
			bool check = true;
			std::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;
		}
	} /// namespace is_graph_bipartite
} /// namespace graph
/**
 * 	Function to test the above algorithm
 *	@returns none
 */
static void test(){
	graph::is_graph_bipartite::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::is_graph_bipartite::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";
	}
}
/**
 * Main function
 */
int main(){
	test();  ///Testing
	return 0;
}