public class Coins_dp
{
    static int M[];    // M[j] = min # coins used to make change for $j


    /* =============================================================
       make_M(v, M): make the M[] array

	   v[] = values of each type of coin
	   M[j] = min # coins used to make change for $j

       Return: the value M[C] (which is the min # coins used 
		to make change for $C
       ============================================================= */
    static int make_M(int[] v, int M[])
    {
       int sol;
       int j, k, min;


       /* ---------------------------
	  Base cases
	  --------------------------- */
       M[0] = 0;	// 0 coins needed to make change for $0

       /* ---------------------------------------------------
	  The other cases (starting from 1 to M.length - 1)
	  --------------------------------------------------- */
       for ( j = 1; j < M.length; j++ )
       {

          if ( M.length < 20 )
             System.out.println("\nComputing M[" + j + "]");

          /* ==========================================================
             When for any value j, we have the solutions for:

		M[0] M[1] ... M[j-1]

			M[x] = min # coins used to make change for $x

	     We can compute M[i] as:

	        M[j] = min( M[j - v[k]] + 1 )  k = 0, 1, 2, ..., i-1
	     ========================================================== */

          sol = M[j - v[0]];    // Try one coin of denomination 0
				// with value v[0] = 1
          min = sol + 1;	// Best solution so far...

          if ( M.length < 20 )
             System.out.println("     " + (sol+1) );

          for ( k = 1; k < v.length; k++ )
          {
             /* --------------------------------------------
	        Check if we can use the k-th denomination
	        -------------------------------------------- */
             if ( v[k] <= j )
             {
                /* ------------------------
	           Divide step
	           ------------------------ */
                sol = M[j - v[k]];    // Try one coin of denomination k
				      // with value v[k]

                if ( M.length < 20 )
                   System.out.println("     " + (sol+1) );

	        /* ---------------------------------------
	           Conquer: solve original problem using
	           solution from smaller problems
	           --------------------------------------- */
	        if ( sol + 1 < min )
	           min = sol + 1;	// New best solution so far
             }
          }

	  M[j] = min;

          if ( M.length < 20 )
             System.out.println("=====> M[" + j + "] = " + M[j]);
       }

       return( M[M.length-1] );
   }


   public static void main(String[] args)
   {
//       int[] v = {1, 5, 10, 25, 50, 100, 500};
       int[] v = {1, 3, 9, 19, 26 };

       int C, r, i;


       C = 65;                  // Around 53 it starts to slow...

       M = new int[ C + 1 ];

       r = make_M(v, M);

/*
       for (i = 0; i <= C; i ++)
          System.out.println("M[" + i + "] = " + M[i]);
*/

       System.out.println("Min # coins to make change for " + C + " = " + r);
   }

}