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

* 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>

graph/is_graph_bipartite.cpp

@@ -1,15 +1,17 @@
 /**
  * @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
  * 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
  * 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>
  *  Example - Here is a graph g1 with 5 vertices and is bipartite
@@ -30,8 +32,8 @@
  *
  */
 #include <iostream>
-#include <vector>
 #include <queue>
+#include <vector>
 
 /**
  * @namespace graph
@@ -48,20 +50,19 @@ namespace graph{
  */
 class Graph {
  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:
     /**
      * @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;
         adj.resize(n);
         side.resize(n, -1);
@@ -69,9 +70,10 @@ namespace 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
  *
@@ -82,6 +84,7 @@ namespace graph{
     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
@@ -89,17 +92,21 @@ namespace 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.
+ * 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 check = true;
     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) {
             q.push(current_edge);
             side[current_edge] = 0;
@@ -110,8 +117,7 @@ namespace graph{
                     if (side[neighbour] == -1) {
                         side[neighbour] = (1 ^ side[current]);
                         q.push(neighbour);
-							}
+                    } else {
-							else{
                         check &= (side[neighbour] != side[current]);
                     }
                 }
@@ -120,21 +126,24 @@ namespace graph{
     }
     return check;
 }
-	} /// namespace is_graph_bipartite
+}  // namespace is_graph_bipartite
-} /// namespace graph
+}  // 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
+    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
+    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);
@@ -143,17 +152,16 @@ static void test(){
     /// checking whether the graphs are bipartite or not
     if (G1.is_bipartite()) {
         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";
     }
     if (G2.is_bipartite()) {
         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";
     }
 }
+
 /**
  * Main function
  */