/******************************************************************************
 *  Compilation:  javac Laplace.java
 *  Execution:    java Laplace N x y
 *  
 *  Estimate the potential of a point (x, y) in an N-by-N region where
 *  the horizontal boundaries have potential 10 and the vertical boundaries
 *  have potential 5.
 *
 *  Simulate 1,000,000 random walks until they reach the boundary and use
 *  the average potential to estimate the potential at (x, y).
 *
 *  java Laplace 10 5 8
 *  Potential of (5, 8) = 6.5365
 *
 *  java Laplace 10 5 8
 *  Potential of (5, 8) = 6.53945
 *
 *  java Laplace 10 5 8
 *  Potential of (5, 8) = 6.5378
 *
 ******************************************************************************/

public class Laplace {

   public static void main(String[] args) { 
      int TRIALS = 100000;                   // number of trials
      int N = Integer.parseInt(args[0]);     // number of steps
      int X = Integer.parseInt(args[1]);     // starting x value
      int Y = Integer.parseInt(args[2]);     // starting y value
      int potential = 0;                     // sum of potentials

      for (int i = 0; i < TRIALS; i++) {
         int x = X, y = Y;
         while (x > 0 && x < N && y > 0 && y < N) {
            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--;
         }
         if (x == 0 || x == N) potential += 10;
         else potential +=  5;
       
      }

      StdOut.println("Potential of (" + X + ", " + Y + ") = " + 1.0 * potential / TRIALS);
   }
}