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fix: linter and spacing for is_graph_bipartite. (#1037)

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* fix: linter and spacing for is_graph_bipartite.

* updating DIRECTORY.md

* clang-tidy fixes for a49ec9b8d7

* clang-format and clang-tidy fixes for 40a56d2f

* Address reviewer's comments.

* Fix docs wording.

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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 graph is bipartite if its 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 algorithm implemented in this file determines 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 <queue> #include <queue>
#include <vector>
/** /**
* @namespace graph * @namespace graph
* @brief Graph algorithms * @brief Graph algorithms
*/ */
namespace graph{ 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 * @namespace is_graph_bipartite
* @returns none * @brief Functions for checking whether a graph is bipartite or not
*/ */
static void test(){ namespace is_graph_bipartite {
graph::is_graph_bipartite::Graph G1(5); /// creating graph G1 with 5 vertices /**
/// adding edges to the graphs as per the illustrated example * @brief Class for representing graph as an adjacency list.
G1.addEdge(1,2); */
G1.addEdge(1,3); class Graph {
G1.addEdge(3,4); private:
G1.addEdge(4,5); int n; ///< size of the graph
graph::is_graph_bipartite::Graph G2(3); /// creating graph G2 with 3 vertices std::vector<std::vector<int> >
/// adding edges to the graphs as per the illustrated example adj; ///< adj stores the graph as an adjacency list
G2.addEdge(1,2);
G2.addEdge(1,3);
G2.addEdge(2,3);
/// checking whether the graphs are bipartite or not std::vector<int> side; ///< stores the side of the vertex
if(G1.is_bipartite()){
std::cout<<"The given graph G1 is a bipartite graph\n"; public:
} /**
else{ * @brief Constructor that initializes the graph on creation
std::cout<<"The given graph G1 is not a bipartite graph\n"; * @param size number of vertices of the graph
} */
if(G2.is_bipartite()){ explicit Graph(int size) {
std::cout<<"The given graph G2 is a bipartite graph\n"; n = size;
} adj.resize(n);
else{ side.resize(n, -1);
std::cout<<"The given graph G2 is not a bipartite graph\n"; }
}
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.
*
* @returns `true` if th graph is bipartite
* @returns `false` otherwise
*/
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 * Main function
*/ */
int main(){ int main() {
test(); ///Testing test(); /// Testing
return 0; return 0;
} }