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Using Java write a program that implements a backtracking algorithm that solves

ID: 3819913 • Letter: U

Question

Using Java write a program that implements a backtracking algorithm that solves the m-Coloring Problem as presented in class and given in your text. Your program should conform to the following specifications.

Write the pre and post condition.

Prompt the user for the number of vertices in the graph.

Prompt the user to enter the adjacency matrix of the graph one row at a time.

Print the adjacency matrix of the graph.

Prompt the user for the maximum number of colors to be used.

Print the first solution and ask the user if they want the rest of the solutions.

If the user indicates they want the rest of the solutions, print them without any additional prompts.

Explanation / Answer

public class GrColor{

/*G is graph's adjacency matrix and x is solution vector */

    private int G[ ][ ], x[ ], n, m, soln;

public void mColoring(int k){ //backtracking function

        for (int i=1; i<=n; i++) {

           next_color(k); //coloring kth vertex

           if (x[k] == 0)

              return; //if unsuccessful then backtrack

           if(k==n) //if all colored then show

              write( );

           else

              mColoring(k+1); /* successful but still left to color */

        }

   }

private void next_color(int k) {

      do{

           int i=1;

         x[k] = (x[k]+1) % (m+1);

         if (x[k] == 0)

           return;

         for (i=1; i<=n; i++)

            if (G[i] [k] != 0 && x[k] == x[i]) /* checking adjacency and not same color */

               break;

         if (i == n+1)   return; //new color found

      } while(true);

   }

private void write( ) {

      System.out.print( " Coloring(V C) # "+(++soln)+"-->");

      for (int i=1; i<=n; i++)

          System.out.print(" ("+i+" "+x[i]+")"); //solution vector

   }

public void input( ) {

         java.util.Scanner sc = new java.util.Scanner(System.in);

         System.out.print ("Enter no. of vertices : ");

         n = sc.nextInt();

         G = new int[n+1][n+1];

         x = new int[n+1];

         System.out.print ("Enter no. of colors : ");

         m = sc.nextInt();

        System.out.println("Enter adjacency matrix-->");

        for (int i=1; i<=n; i++)

           for (int j=1; j<=n; j++)

               G[i] [j] = sc.nextInt( );

   }

public static void main (String[ ] args) {

GrColor obj = new GrColor( );

        obj.input( );

        obj.mColoring(1);

        if (obj.soln == 0)

           System.out.println (" Need more than "+obj.m+" colors");

        else

           System.out.print (" TOTAL SOLN : "+obj.soln);

   }

}

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