4색 문제의 구현을 보여주는 C++ 프로그램

4색 문제의 구현을 보여주는 C++ 프로그램입니다.

알고리즘

Begin
   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.
End
Begin
   Function graphColoringtil(bool graph[V][V], int m, int col[], int v)
   solve 4 coloring problem:
   Here,
   g[V][V] = It is a 2D array where V is the number of vertices in graph
   m = 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 m
      if (isSafe(v, g, col, c))
         col[v] = c
         if (graphColoringtil (g, k, col, v+1) == true)
            return true
         col[v] = 0
   return false
End

Begin
   function graphColor():
      It mainly uses graphColoringUtil() to solve the problem.
         It returns false if the m colors cannot be assigned,
            otherwise return true.
End

예시

#include <iostream>
#include <cstdio>
#define V 5
using namespace std;
bool isSafe (int v, bool graph[V][V], int col[], int C) {
   for (int i = 0; i < V; i++)
   if (graph[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;
}
void solution(int color[]) {
   cout<<"The assigned colors are: \n";
   for (int i = 0; i < V; i++)
      cout<<color[i];
   cout<<"\n";
}
bool graphColor(bool graph[V][V], int k) {
   int *color = new int[V];
   //initialize all colors value as 0
   for (int i = 0; i < V; i++)
   color[i] = 0;
   if (graphColoringtil(graph, k, color, 0) == false) {
      cout<<"Solution does not exist";
      return false;
   }
   solution(color);
   return true;
}
int main() {
   bool g[V][V] = {
      {0, 0, 1, 0,1},
      {1, 1, 1, 0,0},
      {1, 1, 0, 0,1},
      {0, 1, 1, 0,0}
   };
   int k= 4;
   graphColor(g, k);
   return 0;
}

출력

The assigned colors are:
1 2 3 1 1