TheAlgorithms-C-Plus-Plus/Backtracking/Graph Coloring.cpp

#include<stdio.h>
 
// Number of vertices in the graph
#define V 4
 
void printSolution(int color[]);
 
/* A utility function to check if the current color assignment
   is safe for vertex v */
bool isSafe (int v, bool graph[V][V], int color[], int c)
{
    for (int i = 0; i < V; i++)
        if (graph[v][i] && c == color[i])
            return false;
    return true;
}
 
/* A recursive utility function to solve m coloring problem */
void graphColoring(bool graph[V][V], int m, int color[], int v)
{
    /* base case: If all vertices are assigned a color then
       return true */
    if (v == V){
    	printSolution(color);
        return;
    }
 
    /* Consider this vertex v and try different colors */
    for (int c = 1; c <= m; c++)
    {
        /* Check if assignment of color c to v is fine*/
        if (isSafe(v, graph, color, c))
        {
           color[v] = c;
 
           /* recur to assign colors to rest of the vertices */
           graphColoring (graph, m, color, v+1);
            
 
            /* If assigning color c doesn't lead to a solution
               then remove it */
           color[v] = 0;
        }
    }
 
}

/* A utility function to print solution */
void printSolution(int color[])
{
    printf(" Following are the assigned colors \n");
    for (int i = 0; i < V; i++)
      printf(" %d ", color[i]);
    printf("\n");
}
 
// driver program to test above function
int main()
{
    /* Create following graph and test whether it is 3 colorable
      (3)---(2)
       |   / |
       |  /  |
       | /   |
      (0)---(1)
    */
    bool graph[V][V] = {{0, 1, 1, 1},
        {1, 0, 1, 0},
        {1, 1, 0, 1},
        {1, 0, 1, 0},
    };
    int m = 3; // Number of colors

	int color[V];

	for (int i = 0; i < V; i++)
        color[i] = 0;
    
    graphColoring(graph, m, color, 0);
    return 0;
}