// quincunx simulation

import java.awt.*;
import javax.swing.*;


public class NormalQuincunx  {   

    public static void main (String[] args) {
        int bins;
        int balls;
        double biasSD, binSize;
        String input;
        
        input = JOptionPane.showInputDialog("Number of bins","31");
        bins = Integer.parseInt(input);
        
        input = JOptionPane.showInputDialog("Number of balls","1000");
        balls = Integer.parseInt(input);
        
        input = JOptionPane.showInputDialog("0 < Bias to middle < 1", "0.5");
        biasSD = Double.parseDouble(input);    // how to get this to change the standard deviation????

        int[] B = new int[bins];
        
        for (int ball=0; ball<balls; ball++) {   //each ball
            int pluses=0;
            if (Math.random() >= .5) {    //row 0: top peg falls to right
            	pluses++;
            }
            for (int row=1; row<bins-1; row++)   //each row of pegs
            	if (row%2 == 0 && pluses==row/2) {   //even numbered row->odd number of pegs And at center peg
            	    if (Math.random() >= .5)
            	    	pluses++;   //fall to right
            	}
            	else if (pluses <= row/2) {   //in left half
               	    if (Math.random() < biasSD)    //falls toward center
            	        pluses++;
            	}
                else                         //in right half
               	    if (Math.random() > biasSD)    //falls away from center
            	        pluses++;
            B[pluses]++;    //lands in this bin
        }
        
        System.out.println("Frequency histogram");
        for (int bin=0; bin<bins; bin++)
            System.out.print(" "+B[bin]);
        System.out.println();
        
        //input = JOptionPane.showInputDialog("Bin size (interval length)", "1.0");
        //binSize = Double.parseDouble(input);
	binSize = 1.0/bins;   //area under standard normal curve is 1
	
        double sum=0, areaSum=0;
        int d;
        for (int bin=0; bin<bins; bin++) {
	    d = bin - bins/2;    //#bins from center mu
	    areaSum += B[bin] / (double)balls;
            sum += B[bin]* ((d*binSize)*(d*binSize));    //f_i * x_i^2
        }
         System.out.println("area = "+(areaSum)+"   sd= "+Math.sqrt(sum/balls)+
         	            "  at mu=0 h="+(B[bins/2]/(double)balls));      //mu=0
//doesn't appear to be standard normal distribution...         
   }
    
}