# 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
#

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

# for point x, y, if x^2 + y^2 <= 1, they are in the unit circle
# parameters: x, y: co-ordinates of point
# returns True if so, False if not
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 = int(input("number of tosses (EOF to quit): "))
        except EOFError:        # user wants to quit, so help
            n = -1
            break
        except ValueError:      # user didn't enter a number
            print("You have to enter a positive n or EOF")
            continue
        # got an integer
        # now check the value we read/were given
        if n > 0:
            break
        # this is bad input, so say so
        print("You have to enter a positive n or EOF")

    # it's positve 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("   number of throws: %8d\t\tapproximation to pi: %9.7f" % (n, 4.0 * h / n))
        print("     number of hits: %8d\t\t actual value of pi: %9.7f" % (h, math.pi))
        print("              ratio: %8.6f\t\t              error: %9.7f" % (h/n, abs(4.0 * h / n - math.pi)))

#
# run the simulation
#
main()