diff --git a/graph/is_graph_bipartite.cpp b/graph/is_graph_bipartite.cpp new file mode 100644 index 000000000..7d6df310d --- /dev/null +++ b/graph/is_graph_bipartite.cpp @@ -0,0 +1,135 @@ +/** + * @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 +#include +#include + +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 > adj; /// adj stores the graph as an adjacency list + + vector 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 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; +} \ No newline at end of file