/* Programmer: Bill Marion
   Date: 1/23/06
   Modified: 2/16/06   
*/
 
/* Import the simple standard I/O classes developed by Prof. Greg Hume. */ 

import hsa.*;

/* Given n >= 1 stones in a pile, split the pile into two smaller piles.
   Continue to split each pile into two smaller piles until there are n
   piles of size one. At each splitting compute the product of the size 
   of the two smaller piles. Once there are n piles sum all the products
   computed. The result will always be the same no matter how each of the
   piles is split into two smaller piles. The sum of products is a function
   of n. (Rosen, 2003; Tanton, 2004) */
   
/* This computational solution generates a recursive process and splits
   the piles randomly into k and n-k piles until there are n piles of
   size 1. A runing total of the sum of products is computed. */
    
class PilesOfStones
{
  static void stones(int numStones)
  {
    int sum = 0; 
    sum = stonesSumOfProducts(sum, numStones);
    
    Stdout.println();
    Stdout.print("Given ");
    Stdout.print(numStones);
    Stdout.print(" stones in a pile, the sum of products is: ");
    Stdout.println(sum);
    Stdout.println();
    
  } // end stones
  
  static int stonesSumOfProducts(int sum, int numStones)
  {
    
    int sizePileOne = 1 + (int) (Math.random() * (numStones - 1));
    int sizePileTwo = numStones - sizePileOne;
    sum = sum + sizePileOne * sizePileTwo;
    
    if (sizePileOne != 1)
      sum = stonesSumOfProducts(sum,sizePileOne);
      
    if (sizePileTwo != 1)
      sum = stonesSumOfProducts(sum,sizePileTwo);
      
      
    return sum;
      
  } // end stonesSumOfProducts
  
  static public void main(String[] args)
  {
    Stdout.println();
    Stdout.println("Enter the number of stones in the pile-- enter 0 to stop");
    int numStones = Stdin.readInt();
    
    while (numStones >= 1)
    {
      if (numStones == 1) 
      { 
        Stdout.println();
        Stdout.print("Given ");
        Stdout.print(numStones);
        Stdout.print(" stone in a pile, the sum of products is: ");
        Stdout.println(numStones - 1);
        Stdout.println(); 
      }
      else
        stones(numStones);
        
      Stdout.print("Enter the number of stones in the pile-- enter 0");
      Stdout.println(" to stop");
      numStones = Stdin.readInt();
    }
    
    Stdout.println();
  } // end main
  
} // end PilesOfStones