/* Java class that includes a method for computing the product of
** two integers using repeated addition.  The point is to illustrate
** the development of a loop that conforms to a proposed loop invariant.
**
** Authors: R. McCloskey and < STUDENTS' NAMES >
*/
public class Multiply {

   /* Given two integers (the first necessarily nonnegative), returns their 
   ** product.  Using the multiplication operator is forbidden (except in
   ** assert statements).
   ** The intended solution is to be based upon the fact that multiplication
   ** is repeated addition.  That is, the product of k and m is the sum
   ** m + m + m + ... + m, where m occurs k times.
   ** pre: k >= 0 
   ** post: value returned is k*m
   */
   public static int productOf(int k, int m) {
      int result = ??;
      int i = ??;
      assert result == i*m;    // Loop invariant verification (after initialization)
      while (i != k) {
         result = ??
         i = i+1;
         assert result == i*m;  // verify the loop invariant at end of each iteration
      }
      // Verify that, upon termination of the loop, 'result' has the 
      // value that is intended to be returned (namely the product k*m).
      assert result == k*m;
      return result;
   }

   /* This method expects to receive two arguments, both describing
   ** integers, the first being nonnegative.  It calls the productOf()
   ** method to compute their product and reports the results.
   */
   public static void main(String[] args) {
      // Translate the two arguments from Strings into values of type int.
      int first = Integer.parseInt(args[0]);
      int second = Integer.parseInt(args[1]);

      // Call productOf() to compute the product and then report the result.
      int product = productOf(first, second);
      System.out.printf("productOf(%d,%d) evaluates to %d\n", 
                        first, second, product);
   }

}