// CSE 142 Lecture 12
// Random, boolean
// Calculates Pi using Random numbers.

// Picture a circle of radius 1 inside of a square. The circle has area Pi * radius^2.
// Since our circle has radius 1, it has area Pi. The square has area 4.
// If we pick a bunch of random points in the square, we can calculate Pi
// by using the ratio of points that fall inside the circle to the number of points we picked.

import java.util.*; // for Random
import java.awt.*; // for Graphics, Color

public class Pi {
	// How far away from actual Pi our calculation is allowed to be.
	public static final double ERROR = 0.00000001;
	// The size to draw the representation of our calculations at
	public static final int SIZE = 400;

	public static void main(String[] args) {
		DrawingPanel p = new DrawingPanel(SIZE, SIZE);
		Graphics g = p.getGraphics();
		Random r = new Random(1342425406762L); // ~66K points
		//Random r = new Random(1342424639929L); // ~1.3M points
		//Random r = new Random(1342425440783L); // ~8M points
		//Random r = new Random(1342425511441L); // ~350M points (this will take a long time)
		double pi = 0;
		int n = 0;
		int inside = 0;
		
		// Keep going until the difference between Pi and our calculation is less than
		// than or equal to the acceptable error.
		while (Math.abs(Math.PI - pi) > ERROR) {
			// We're only going to use the upper right quarter of the circle and square
			// described earlier. Symmetry makes this work out.
			// Pick a random point in a 1 by 1 square.
			double x = r.nextDouble();
			double y = r.nextDouble();
			// See if this point would be within a radius 1 circle.
			if (Math.sqrt(x * x + y * y) <= 1) {
				inside++;
				g.setColor(Color.BLUE);
			} else {
				g.setColor(Color.RED);
			}
			g.drawRect((int)(x * SIZE), (int)(y * SIZE), 1, 1);
			n++;
			// Pi is the ratio of points inside the circle to points inside the square.
			pi = 4.0 * inside / n;
			
			// Limit the amount of printing because it slows down the computation.
			if (n % 1000 == 0) {
				System.out.println("Step " + n + ", Pi = " + pi);
			}
		}
		
		System.out.println("Step " + n + ", Pi = " + pi);
		System.out.println();
		System.out.println("We calculated Pi = " + pi);
		System.out.println("Pi actually      = " + Math.PI);
		System.out.println("Error            = " + Math.abs(Math.PI - pi));
	}
}