使用 2 色演算法檢查圖是否為二分圖的 C++ 程式


如果一個圖可以用兩種顏色進行著色即圖的著色是可能的,則該圖是二分圖(例如:一組中頂點的顏色相同)。這是一個使用 2 色演算法檢查圖是否為二分圖的 C++ 程式。

函式和虛擬碼

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

示例

#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;
}

輸出

The graph is Bipartite

更新於: 30-Jul-2019

232 次瀏覽

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