BinomialDistribution.java

Below is the syntax highlighted version of BinomialDistribution.java from §1.4 Arrays.

/******************************************************************************
 *  Compilation:  javac BinomialDistribution.java
 *  Execution:    java BinomialDistribution n
 *
 *  Prints out binomial coefficients such that such that a[n][k] contains
 *  the probability that you get exactly k heads when you toss a
 *  coin n times.
 *
 *  See also https://introcs.cs.princeton.edu/java/14array/BinomialCoefficients.java
 *
 *  % java BinomialDistribution 7
 *  1/1
 *  1/2 1/2
 *  1/4 2/4 1/4
 *  1/8 3/8 3/8 1/8
 *  1/16 4/16 6/16 4/16 1/16
 *  1/32 5/32 10/32 10/32 5/32 1/32
 *  1/64 6/64 15/64 20/64 15/64 6/64 1/64
 *
 ******************************************************************************/

public class BinomialDistribution {
    public static void main(String[] args) {
        int n = Integer.parseInt(args[0]);

        double[][] binomial = new double[n+1][];

        // initialize first row
        binomial[1] = new double[1 + 2];
        binomial[1][1] = 1.0;

        // fill in coefficients of binomial distribution
        for (int i = 2; i <= n; i++) {
            binomial[i] = new double[i+2];
            for (int k = 1; k < binomial[i].length - 1; k++)
                binomial[i][k] = 0.5 * (binomial[i-1][k-1] + binomial[i-1][k]);
        }

        // print binomial coefficients
        for (int i = 1; i <= n; i++) {
            for (int k = 1; k < binomial[i].length - 1; k++) {
                System.out.print(binomial[i][k] + " ");
            }
            System.out.println();
        }
    }

}