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Merge branch 'is_graph_bipartite' into fix_clang

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Krishna Vedala 2020-08-26 10:04:37 -04:00
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graph/is_graph_bipartite.cpp
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/** /**
* @file * @file
* *
* @brief Algorithm to check whether a graph is [bipartite](https://en.wikipedia.org/wiki/Bipartite_graph) * @brief Algorithm to check whether a graph is [bipartite](https://en.wikipedia.org/wiki/Bipartite_graph)
* *
* @details * @details
* A graph is a collection of nodes also called vertices and these vertices * 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 * 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 * divided into two disjoint and independent sets U and V such that every edge
* connects a vertex in U to one in V. * connects a vertex in U to one in V.
* *
* The given Algorithm will determine whether the given graph is bipartite or not * The given Algorithm will determine whether the given graph is bipartite or not
* *
* <pre> * <pre>
* Example - Here is a graph g1 with 5 vertices and is bipartite * Example - Here is a graph g1 with 5 vertices and is bipartite
* *
* 1 4 * 1 4
* / \ / \ * / \ / \
* 2 3 5 * 2 3 5
* *
* Example - Here is a graph G2 with 3 vertices and is not bipartite * Example - Here is a graph G2 with 3 vertices and is not bipartite
* *
* 1 --- 2 * 1 --- 2
* \ / * \ /
* 3 * 3
* *
* </pre> * </pre>
*
* @author [Akshat Vaya](https://github.com/AkVaya)
* *
* @author [Akshat Vaya](https://github.com/AkVaya)
*
*/ */
#include <iostream> #include <iostream>
#include <vector> #include <vector>
@ -37,127 +37,124 @@
* @namespace graph * @namespace graph
* @brief Graph algorithms * @brief Graph algorithms
*/ */
namespace graph{ namespace graph {
/** /**
* @namespace is_graph_bipartite * @namespace is_graph_bipartite
* @brief Functions for checking whether a graph is bipartite or not * @brief Functions for checking whether a graph is bipartite or not
*/ */
namespace is_graph_bipartite{ namespace is_graph_bipartite {
/** /**
* @brief Class for representing graph as an adjacency list. * @brief Class for representing graph as an adjacency list.
*/ */
class Graph { class Graph {
private: private:
int n; /// size of the graph int n; /// size of the graph
std::vector<std::vector <int> > adj; /// adj stores the graph as an adjacency list std::vector< std::vector<int> > adj; /// adj stores the graph as an adjacency list
std::vector<int> side; ///stores the side of the vertex std::vector<int> side; ///stores the side of the vertex
static const int nax = 5e5 + 1; 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);
}
public: void addEdge(int u, int v); /// function to add edges to our graph
/**
* @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
};
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
* @brief Function that add an edge between two nodes or vertices of graph * @param v is a node or vertex of graph
* */
* @param u is a node or vertex of graph void Graph::addEdge(int u, int v) {
* @param v is a node or vertex of graph adj[u - 1].push_back(v - 1);
*/ adj[v - 1].push_back(u - 1);
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
* @brief function that checks whether the graph is bipartite or not *
* the function returns true if the graph is a bipartite graph * @details
* the function returns false if the graph is not a bipartite graph * 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.
* @details * If the current edge has no side assigned to it, then a Breadth First Search operation is performed.
* Here, side refers to the two disjoint subsets of the bipartite graph. * If two neighbours have the same side then the graph will not be bipartite and the value of check becomes false.
* 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 and only if each pair of neighbours have different sides, the value of check will be true and hence the graph bipartite.
* 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;
bool Graph::is_bipartite(){ for (int current_edge = 0; current_edge < n; ++current_edge) {
bool check = true; if (side[current_edge] == -1){
std::queue<int> q; q.push(current_edge);
for (int current_edge = 0; current_edge < n; ++current_edge) side[current_edge] = 0;
{ while (q.size()) {
if(side[current_edge] == -1){ int current = q.front();
q.push(current_edge); q.pop();
side[current_edge] = 0; for (auto neighbour : adj[current]) {
while(q.size()){ if (side[neighbour] == -1) {
int current = q.front(); side[neighbour] = (1 ^ side[current]);
q.pop(); q.push(neighbour);
for(auto neighbour : adj[current]){ }
if(side[neighbour] == -1){ else {
side[neighbour] = (1 ^ side[current]); check &= (side[neighbour] != side[current]);
q.push(neighbour); }
} }
else{ }
check &= (side[neighbour] != side[current]); }
} }
} return check;
} }
} } // namespace is_graph_bipartite
} } // namespace graph
return check;
}
} /// namespace is_graph_bipartite
} /// namespace graph
/** /**
* Function to test the above algorithm * Function to test the above algorithm
* @returns none * @returns none
*/ */
static void test(){ static void test(){
graph::is_graph_bipartite::Graph G1(5); /// creating graph G1 with 5 vertices graph::is_graph_bipartite::Graph G1(5); /// creating graph G1 with 5 vertices
/// adding edges to the graphs as per the illustrated example /// adding edges to the graphs as per the illustrated example
G1.addEdge(1,2); G1.addEdge(1, 2);
G1.addEdge(1,3); G1.addEdge(1, 3);
G1.addEdge(3,4); G1.addEdge(3, 4);
G1.addEdge(4,5); G1.addEdge(4, 5);
graph::is_graph_bipartite::Graph G2(3); /// creating graph G2 with 3 vertices graph::is_graph_bipartite::Graph G2(3); /// creating graph G2 with 3 vertices
/// adding edges to the graphs as per the illustrated example /// adding edges to the graphs as per the illustrated example
G2.addEdge(1,2); G2.addEdge(1, 2);
G2.addEdge(1,3); G2.addEdge(1, 3);
G2.addEdge(2,3); G2.addEdge(2, 3);
/// checking whether the graphs are bipartite or not /// checking whether the graphs are bipartite or not
if(G1.is_bipartite()){ if (G1.is_bipartite()) {
std::cout<<"The given graph G1 is a bipartite graph\n"; std::cout<<"The given graph G1 is a bipartite graph\n";
} }
else{ else {
std::cout<<"The given graph G1 is not a bipartite graph\n"; std::cout<<"The given graph G1 is not a bipartite graph\n";
} }
if(G2.is_bipartite()){ if (G2.is_bipartite()) {
std::cout<<"The given graph G2 is a bipartite graph\n"; std::cout<<"The given graph G2 is a bipartite graph\n";
} }
else{ else {
std::cout<<"The given graph G2 is not a bipartite graph\n"; std::cout<<"The given graph G2 is not a bipartite graph\n";
} }
} }
/** /**
* Main function * Main function
*/ */
int main(){ int main() {
test(); ///Testing test(); ///Testing
return 0; return 0;
} }