# Monte Carlo method of computing pi
# Toss darts at a dart board (2x2, centered at (0,0)
# The ratio of the darts in the unit circle to all darts is pi/4
# (see problem 10, chapter 9 of book)
# ECS 10, May 11, 2009
# Matt Bishop
import random
import math

# Generate a landing position for a dart tossed at
# a 2x2 square with center at (0,0)
# returns: (x, y) co-ordinates of toss
def gentoss():
    x = 2*random.random() - 1
    y = 2*random.random() - 1
    return x, y

# if x^2 + y^2 <= 1, they are in the unit circle
def inunitcircle(x, y):
    return x ** 2 + y ** 2 <= 1

# function to read and vet user selection
# returns: n, the number of tosses
# NOTE: n must be positive; return -1 to quit
def getinput():
    # loop until we get good input
    while True:
        try:
            # get the input and check the type here
            n = input("Enter the number of tosses: ")
            n += 0;
        except EOFError:        # user wants to quit, so help her
            n = -1
            break
                                # oops! let error check below do the work
                                # so set v to something illegal (not 0-3)
        except (SyntaxError, NameError, TypeError):
            n = -1
        # now check the value we read/were given
        if n > 0:
            break
        # this is bad, so say so
        print "You have to enter a positive number"

    # it's non-negative to continue, -1 to quit
    return n

# main routine: pull it all together
def main():
    # get number of tosses
    n = getinput()
    if n > 0:
        # number of darts in unit circle
        # nothing thrown yet
        h = 0
        # now start throwing
        for i in range(n):
            # toss
            x, y = gentoss()
            # is it in the circle?
            if inunitcircle(x, y):
                h += 1
        # done! see how well you did ...
        print "approximation:", 4.0 * h / n, "actual", math.pi

main()