import java.util.Scanner;

public class SpockFast {
	
	/**
	 * Recursive computation of n choose k
	 * @param n >= 0
	 * @param k <= n
	 * @return the number of possible combinations of
     * k out of n
	 */
	public int combRec(int n, int k){
		// pre: 0 <= k <= n
		// 	n < 0
		// post:  return the number of possible combinations of
		// k out of n
		if (n==k || k==0) return 1;
		else // n>k and k>0
			return combRec(n-1,k-1) + combRec(n-1,k);
		
	}
	
	/*
	 * Fast Spock
	 */
	public long combFast(int n, int k, long[][] A) {
		// pre: 0 <= k <= n
		// 	n < 0
		// post:  return the number of possible combinations of
		// k out of n
		if (A[n][k] > 0) return A[n][k];
		else if (n==k || k==0) return 1;
		else {
			A[n][k] = combFast(n-1,k-1, A) + combFast(n-1,k, A);
			return A[n][k];
		}
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner Input = new Scanner(System.in);
		int n;
		long start, finish, res;
		SpockFast S = new SpockFast();
		do{
		System.out.println("Enter set size n>0  (0 to finish)");
		n = Input.nextInt();
		long A[][] = new long[n+1][n+1];
		if(n>0 && n<=33) {

			for(int k = 0; k<=n; k++){ 
			   start = System.currentTimeMillis();
			   res = S.combRec(n, k);
			   finish = System.currentTimeMillis();
		    	   System.out.println("Number of combinations (slow): (" +
		    		            n + " choose " +k+ ")  =  " + res + ", time = " + 
					    (finish-start) + "  milliseconds");
			   start = System.currentTimeMillis();
			   res = S.combFast(n, k, A);
			   finish = System.currentTimeMillis();
		     	   System.out.println("Number of combinations (fast): (" +
		    		            n + " choose " +k+ ")  =  " + res + " time = " + 
					    (finish-start) + "  milliseconds\n");
			}
		 } 
		if (n > 33) System.out.println ("n > 33 will cause overflow");
		} while (n>0);
		System.out.println("goodbye Spock");
	}

}