/******************************************************************************
 *  Compilation:  javac Flip.java
 *  Execution:    java Flip n
 *  Dependencies: StdDraw.java
 *
 *  Each experiment consists of flipping n fair coins. Plots (in real time)
 *  a histogram of the number of times exactly i of the n coins are heads.
 *
 *  % java Flip 32
 *
 *  % java Flip 64
 *
 *  % java Flip 128
 *
 ******************************************************************************/


public class Flip {


    // number of heads when flipping n coins, each with prob p of heads
    public static int binomial(int n, double p)  {
        int heads = 0;
        for (int j = 0; j < n; j++)
            if (StdRandom.bernoulli(p)) heads++;
        return heads;
    }


    public static void main(String[] args) {
        int n = Integer.parseInt(args[0]);   // number of coins to flip
        int[] freq = new int[n+1];           // freq[i] = # times you get i heads

        StdDraw.setCanvasSize(1000, 600);
        StdDraw.enableDoubleBuffering();
        StdDraw.setXscale(0, n);
        StdDraw.setYscale(0, Math.sqrt(1.0 / n));


        int count = 0;
        while (true) {
            // flip n coins and tabulate the results
            for (int j = 0; j < n; j++) {
                int heads = binomial(n, 0.5);
                freq[heads]++;
                count++;
            }

            StdDraw.clear();

            // plot histogram
            StdDraw.setPenRadius(1.0 / n);
            for (int i = 0; i <= n; i++) {
                StdDraw.line(i, 0, i, 1.0 * freq[i] / count);
            }

            // plot hypothesis
            StdDraw.resetPenRadius();
            double mean = 0.5 * n;
            double var  = 0.25 * n;
            for (double i = 0.0; i < n; i += n/1000.0)
                StdDraw.point(i, Gaussian.pdf(i, mean, Math.sqrt(var)));
            StdDraw.show();
            StdDraw.pause(50);
        }
    }
}