001package algs11; 002import stdlib.*; 003/* *********************************************************************** 004 * Compilation: javac Binomial.java 005 * Execution: java Binomial N k p 006 * Dependencies: StdOut.java 007 * 008 * Reads in N, k, and p as command-line arguments and prints out 009 * (N choose k) p^k (1-p)^N-k. 010 * 011 * % java Binomial 5 2 .25 012 * 0.263671875 013 * 0.263671875 014 * 015 * % java Binomial 5 3 .25 016 * 0.087890625 017 * 0.087890625 018 * 019 * % java Binomial 5 0 .25 020 * 0.2373046875 021 * 0.2373046875 022 * 023 * % java Binomial 5 5 .25 024 * 9.765625E-4 025 * 9.765625E-4 026 * 027 *************************************************************************/ 028 029public class XBinomial { 030 031 // slow 032 public static double binomial1(int N, int k, double p) { 033 if (N == 0 && k == 0) return 1.0; 034 if (N < 0 || k < 0) return 0.0; 035 return (1.0 - p) *binomial1(N-1, k, p) + p*binomial1(N-1, k-1, p); 036 } 037 038 // memoization 039 public static double binomial2(int N, int k, double p) { 040 double[][] b = new double[N+1][k+1]; 041 042 // base cases 043 for (int i = 0; i <= N; i++) 044 b[i][0] = Math.pow(1.0 - p, i); 045 b[0][0] = 1.0; 046 047 // recursive formula 048 for (int i = 1; i <= N; i++) { 049 for (int j = 1; j <= k; j++) { 050 b[i][j] = p * b[i-1][j-1] + (1.0 - p) *b[i-1][j]; 051 } 052 } 053 return b[N][k]; 054 } 055 056 public static void main(String[] args) { 057 args = new String[] { "5", "2", ".25" }; 058 //args = new String[] { "5", "3", ".25" }; 059 //args = new String[] { "5", "0", ".25" }; 060 //args = new String[] { "5", "5", ".25" }; 061 062 int N = Integer.parseInt(args[0]); 063 int k = Integer.parseInt(args[1]); 064 double p = Double.parseDouble(args[2]); 065 StdOut.println(binomial1(N, k, p)); 066 StdOut.println(binomial2(N, k, p)); 067 } 068 069}