/*******************************************************************************
 *  Name:    T. Shy
 *  Login:   jsshy
 *  Precept: P00
 *
 *  Compilation:  javac PlotTukey.java
 *  Execution:    java PlotTukey N
 *  Dependencies: StdDraw.java
 *
 *  Draws Tukey plots for N random doubles in the range [0., 1.).  
 *  N is the first command-line argument to the program.
 *
 ******************************************************************************/

public class PlotTukey
{

    //calculate the mean of a[0..n]
    public static double mean(double[] a, int n) {
        double sum = 0.0;
        for (int i = 0; i <= n; i++) sum += a[i];
        return sum/(n + 1);
    }

    //calculate the std. err. of the mean of a[0..n]
    public static double sigma(double[] a, int n) {
        double mean = mean(a, n);
        double var = 0.0;

        //one point case
        if (n <= 0) return 0.0;

        for (int i = 0; i <= n; i++) {
            double d = mean - a[i];
            var += d*d;
        }
        var /= n;

        return Math.sqrt(var/(n + 1));
    }

    public static void main(String[] args) {
        int N = Integer.parseInt(args[0]);
        final double PEN_RADIUS = 0.5/N;
        double[] a = new double[N];

        //initialize "a" with random double values
        for (int i = 0; i < N; i++) {
            a[i] = Math.random();
        }

        StdDraw.setXscale(0, N-1);
	if (N > 0) StdDraw.setPenRadius(PEN_RADIUS);

        for (int i = 0; i < N; i++) {
            double mean = mean(a, i);
            double sig = sigma(a, i);

            StdDraw.setPenColor(StdDraw.BLACK);
            StdDraw.point(i, a[i]);
            //draw the std. dev. lines
            StdDraw.line(i, mean + sig, i, mean + 2*sig);
            StdDraw.line(i, mean - sig, i, mean - 2*sig);

            StdDraw.setPenColor(StdDraw.RED);
            StdDraw.point(i, mean);
        }
    }
}