m-coloring.cpp

#include<bits/stdc++.h>
using namespace std;
// Number of vertices in the graph
#define V 25
int num;
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 < num; i++)
        if (graph[v][i] && c == color[i])
            return false;
    return true;
}

/* A recursive utility function to solve m coloring problem */
bool graphColoringUtil(bool graph[V][V], int m, int color[], int v)
{
    /* base case: If all vertices are assigned a color then
       return true */
    if (v == num)
        return true;

    /* 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 */
           if (graphColoringUtil (graph, m, color, v+1) == true)
             return true;

            /* If assigning color c doesn't lead to a solution
               then remove it */
           color[v] = 0;
        }
    }

    /* If no color can be assigned to this vertex then return false */
    return false;
}

/* This function solves the m Coloring problem using Backtracking. It mainly uses graphColoringUtil() to solve the problem. It returns
  false if the m colors cannot be assigned, otherwise return true and prints assignments of colors to all vertices. Please note that there
  may be more than one solutions, this function prints one of the feasible solutions.*/
bool graphColoring(bool graph[V][V], int m)
{
    // Initialize all color values as 0. This initialization is needed
    // correct functioning of isSafe()
    int *color = new int[num];
    for (int i = 0; i < num; i++)
       color[i] = 0;

    // Call graphColoringUtil() for vertex 0
    if (graphColoringUtil(graph, m, color, 0) == false)
    {
      printf("Solution does not exist");
      return false;
    }

    // Print the solution
    printSolution(color);
    return true;
}

/* A utility function to print solution */
void printSolution(int color[])
{
    printf("Solution Exists:"
            " Following are the assigned colors \n");
    for (int i = 0; i < num; i++)
      printf(" %d ", color[i]);
    printf("\n");
}

// driver program to test above function
int main()
{
    cout<<"Enter number of row and column :"<<endl;
    cin>>num;
    /* 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},
    };*/
    cout<<"Enter the adjacency matrix for graph (enter 0 for no edge /enter 1 for edge) :"<<endl;
    for(int i=0;i<num;i++)
        for(int j=0;j<num;j++)
            cin>>graph[i][j];
    cout<<"Enter number of colors available :"<<endl;
    int m ;/*= 3; */
    cin>>m;
    graphColoring (graph, m);
    return 0;
}