/**
 * Binomial number and Pascal's triangle
 * 
 * @author (Stefan Edelkamp) 
 * @version (2013)
 */
public class Binomial
{
    /**
     * Computes Binomial numbers
     * 
     * @param  n   the top number ~ different elements in a urn
     * @param  k   the bottom number ~ elements to be chosen, no replacement
     * @return     n choose k    
     */
     private int choose(int n, int k) { 
       return (k == 0) ? 1 : (n * choose(n-1,k-1)) / k; 
     } 

     /**
     * Prints Pascal's triangle from top row 0 to row m-1
     * 
     * @param  m   row of Pascal's triangle
     * @return      
     */
    public void triangle(int m) {
      int n,k;
      for (n=0;n<m;n++) {
        for (k=0;k<=n;k++) {
          System.out.print("("+m+","+k+")="+choose(n,k));
        }
        System.out.println();
      }
    }
}