Binomial.java

Below is the syntax highlighted version of Binomial.java from §1.1 Programming Model.

```/******************************************************************************
*  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 Binomial {

// 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) {
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));
}

}
```