``` 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 ``` ```package algs11; import stdlib.*; /* *********************************************************************** * Compilation: javac Binomial.java * Execution: java Binomial N k p * Dependencies: StdOut.java * * Reads in N, k, and p as command-line arguments and prints out * (N choose k) p^k (1-p)^N-k. * * % java Binomial 5 2 .25 * 0.263671875 * 0.263671875 * * % java Binomial 5 3 .25 * 0.087890625 * 0.087890625 * * % java Binomial 5 0 .25 * 0.2373046875 * 0.2373046875 * * % java Binomial 5 5 .25 * 9.765625E-4 * 9.765625E-4 * *************************************************************************/ public class XBinomial { // slow public static double binomial1(int N, int k, double p) { if (N == 0 && k == 0) return 1.0; if (N < 0 || k < 0) return 0.0; return (1.0 - p) *binomial1(N-1, k, p) + p*binomial1(N-1, k-1, p); } // memoization public static double binomial2(int N, int k, double p) { double[][] b = new double[N+1][k+1]; // base cases for (int i = 0; i <= N; i++) b[i][0] = Math.pow(1.0 - p, i); b[0][0] = 1.0; // recursive formula for (int i = 1; i <= N; i++) { for (int j = 1; j <= k; j++) { b[i][j] = p * b[i-1][j-1] + (1.0 - p) *b[i-1][j]; } } return b[N][k]; } public static void main(String[] args) { args = new String[] { "5", "2", ".25" }; //args = new String[] { "5", "3", ".25" }; //args = new String[] { "5", "0", ".25" }; //args = new String[] { "5", "5", ".25" }; int N = Integer.parseInt(args[0]); int k = Integer.parseInt(args[1]); double p = Double.parseDouble(args[2]); StdOut.println(binomial1(N, k, p)); StdOut.println(binomial2(N, k, p)); } } ```