/****************************************************************************** * Compilation: javac SlowBinomial.java * Execution: java SlowBinomial 56 3 * * Reads in two command-line arguments n and k and print the corresponding * binomial coefficient n choose k using Pascal's indentity. * * binomial(n, k) = binomial(n-1, k-1) + binomial(n-1, k) * * % java Binomial 10 2 * 45 * * % java Binomial 20 0 * 1 * * % java Binomial 0 0 * 1 // by definition * * % java Binomial 50 20 * [ takes a really really really long time ] * * * % java Binomial 100 15 * [ takes a really really really long time ] * * * Remark * ------------ * This program is to slow to be useful in practice. * See Binomial.java, which uses dynamic programming. * ******************************************************************************/ public class SlowBinomial { public static long binomial(long n, long k) { if (k == 0) return 1; if (n == 0) return 0; if (k == n) return 1; return binomial(n-1, k-1) + binomial(n-1, k); } public static void main(String[] args) { int n = Integer.parseInt(args[0]); int k = Integer.parseInt(args[1]); StdOut.println(binomial(n, k)); for (int i = 0; true; i++) { long result = binomial(4*i, i); StdOut.println(i + " " + result); } } }