//-----------------------------------------------------------------------
// Miranda Moore
// COS488/MAT474
// Problem Set 7, Q2
//-----------------------------------------------------------------------
// The command "java Ehrenfest k t"
// simulates t trials of the Ehrenfest model with 1000 balls and 10^k 
// steps, and plots a histogram of the distribution of the number of 
// balls in chamber A at the end of each trial.
// The resulting histogram has its x-axis ranging from 0 to 1000,
// and the heights of the bars show the relative likelihood of each 
// outcome.
//-----------------------------------------------------------------------


public class Ehrenfest { 
    
    public static final int N = 1000;               // number of balls
    
 
    // adapted from StdStats.java
    // plots a histogram of the data
    public static void histogram(double[] a, int trials) {
        StdDraw.setCanvasSize(700, 100);
        StdDraw.setXscale(0, N+1);
        StdDraw.setYscale(0, .06);
        for (int i = 0; i <= N ; i++) {
            StdDraw.filledRectangle(i+.5, a[i]/(2*trials), 
                                    0.5, a[i]/(2*trials));
        }
    }
        
    
    // simulate one trial with n steps
    public static int trial(int n) { 
        
        int a = N;                                // # balls in urn A
        int b = 0;                                // # balls in urn B
        int i;                                    // a random integer
        
        // simulate the n steps.
        // at each step, we choose a random integer, 
        // and move the corresponding ball
        for (int l = 0; l < n; l++) {
            i = StdRandom.uniform(N);
            if (i < a) {a--; b++;}
            else       {b--; a++;}
        }

       // return the number of balls in urn A at the end of n steps
       return a;
    }
    
    
    public static void main(String[] args) {
        int pow = Integer.parseInt(args[0]); 
        int n = (int) Math.pow(10, pow);         // number of steps
        
        // array keeping track of the frequency of each result
        double[] freq = new double[N+1];    
        
        int trials = Integer.parseInt(args[1]);  // number of trials
        
        for (int k = 0; k < trials; k++) {
            freq[trial(n)]++;
        }
     
        histogram(freq, trials);
    }
    
}