2色アルゴリズムを使用してグラフが2部グラフであるかどうかを確認するC++プログラム

2部グラフは、グラフの彩色が2つの色を使用して可能である場合にグラフです。セット内の頂点は同じ色で色付けされます。これは、2色アルゴリズムを使用してグラフが2部グラフであるかどうかを確認するC++プログラムです。

関数と擬似コード

Begin
   1. Develop function isSafe() to check if the current color assignment
      is safe for vertex v, i.e. checks whether the edge exists or not.
      If it exists, then next check whether the color to be filled in
      the new vertex is already used by its adjacent vertices.
   2. function graphColoringtil(bool g[V][V], int k, int col[], int v) :
      g[V][V] = It is a 2D array where V is the number of vertices in graph
      k = maximum number of colors that can be used.
      col[] = an color array that should have numbers from 1 to m.
      if v == V
      return true
      For c = 1 to k
      if (isSafe(v, g, col, c))
         col[v] = c
         if (graphColoringtil (g, k, col, v+1) == true)
            return true
         col[v] = 0
      return false
   3.function graphColoring(bool g[V][V], int k):
   for i = 0 to V-1
      color[i] = 0
      if (graphColoringtil(g, k, color, 0) == false)
   return false
return true

例

#include <iostream>
#include <cstdio>
#define V 4
using namespace std;
bool isSafe (int v, bool g[V][V], int col[], int C) //to solve m coloring //problem
{
   for (int i = 0; i < V; i++)
      if (g[v][i] && C == col[i])
      return false;
   return true;
}
bool graphColoringtil(bool g[V][V], int k, int col[], int v)
{
   if (v == V) //If all vertices are assigned a color then
   return true;
   for (int c = 1; c <= k; c++) //Consider this vertex v and try different colors
   {
      if (isSafe(v, g, col, c)) //Check if assignment of color c to v is fine
      {
         col[v] = c;
         if (graphColoringtil (g, k, col, v+1) == true) //recur to assign colors to rest of the vertices
         return true;
         col[v] = 0; //If assigning color c doesn't lead to a solution then remove it
      }
   }
   return false;
}

出力

The graph is Bipartite