/******************************************************************************
 *  Compilation:  javac Random2DWalk.java
 *  Execution:    java Random2DWalk n
 *
 *  Simulates a random walk on a 2 dimensional grid. At each step you
 *  either move left, right, up, or down 1 unit. Prints out how far
 *  away from the origin you end up after n steps.
 *
 *  Sample execution:
 *
 *     % java Random2DWalk 1000000
 *      Arrives at (817, 435) after 1000000 steps.
 *      Distance from origin = 925.5884614665418
 *
 *  Remark: on average, after n steps you are sqrt(n) units from origin.
 *
 ******************************************************************************/

public class Random2DWalk {

    public static void main(String[] args) {

        int n = Integer.parseInt(args[0]);         // number of steps
        int x = 0, y = 0;                          // current location

        for (int i = 0; i < n; i++) {
            double r = Math.random();               // between 0.0 and 1.0
            if      (r < 0.25) x++;
            else if (r < 0.50) x--;
            else if (r < 0.75) y++;
            else               y--;
        }

        System.out.println("Arrives at (" + x + ", " + y + ") after " + n + " steps.");
        System.out.println("Distance from origin = " + Math.sqrt(x * x + y * y));
    }
}