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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.

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
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graph/is_graph_bipartite.cpp
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@ -1,15 +1,17 @@
/** /**
* @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
@ -30,88 +32,92 @@
* *
*/ */
#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 * @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
static const int nax = 5e5 + 1;
std::vector<int> side; ///< stores the side of the vertex
public: public:
/** /**
* @brief Constructor that initializes the graph on creation * @brief Constructor that initializes the graph on creation
* @param size number of vertices of the graph
*/ */
explicit Graph(int size = nax){ explicit Graph(int size) {
n = size; n = size;
adj.resize(n); adj.resize(n);
side.resize(n,-1); side.resize(n, -1);
} }
void addEdge(int u, int v); /// function to add edges to our graph 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 * @brief Function that add an edge between two nodes or vertices of graph
* *
* @param u is a node or vertex of graph * @param u is a node or vertex of graph
* @param v is a node or vertex of graph * @param v is a node or vertex of graph
*/ */
void Graph::addEdge(int u, int v) { void Graph::addEdge(int u, int v) {
adj[u-1].push_back(v-1); adj[u - 1].push_back(v - 1);
adj[v-1].push_back(u-1); adj[v - 1].push_back(u - 1);
} }
/**
/**
* @brief function that checks whether the graph is bipartite or not * @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 true if the graph is a bipartite graph
* the function returns false if the graph is not a bipartite graph * the function returns false if the graph is not a bipartite graph
* *
* @details * @details
* Here, side refers to the two disjoint subsets of the 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. * Initially, the values of side are set to -1 which is an unassigned state. A
* If the current edge has no side assigned to it, then a Breadth First Search operation is performed. * for loop is run for every vertex of the graph. If the current edge has no
* If two neighbours have the same side then the graph will not be bipartite and the value of check becomes false. * side assigned to it, then a Breadth First Search operation is performed. If
* If and only if each pair of neighbours have different sides, the value of check will be true and hence the graph bipartite. * 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 Graph::is_bipartite() {
bool check = true; bool check = true;
std::queue<int> q; std::queue<int> q;
for (int current_edge = 0; current_edge < n; ++current_edge) for (int current_edge = 0; current_edge < n; ++current_edge) {
{ if (side[current_edge] == -1) {
if(side[current_edge] == -1){
q.push(current_edge); q.push(current_edge);
side[current_edge] = 0; side[current_edge] = 0;
while(q.size()){ while (q.size()) {
int current = q.front(); int current = q.front();
q.pop(); q.pop();
for(auto neighbour : adj[current]){ for (auto neighbour : adj[current]) {
if(side[neighbour] == -1){ if (side[neighbour] == -1) {
side[neighbour] = (1 ^ side[current]); side[neighbour] = (1 ^ side[current]);
q.push(neighbour); q.push(neighbour);
} } else {
else{
check &= (side[neighbour] != side[current]); check &= (side[neighbour] != side[current]);
} }
} }
@ -119,45 +125,47 @@ namespace graph{
} }
} }
return check; return check;
} }
} /// namespace is_graph_bipartite } // namespace is_graph_bipartite
} /// namespace graph } // 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 {
std::cout << "The given graph G1 is not a bipartite graph\n";
} }
else{ if (G2.is_bipartite()) {
std::cout<<"The given graph G1 is not a bipartite graph\n"; std::cout << "The given graph G2 is a bipartite graph\n";
} } else {
if(G2.is_bipartite()){ std::cout << "The given graph G2 is not a bipartite graph\n";
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;
} }