import argparse # See https://docs.python.org/3/library/argparse.html
import random
from math import pi

def sample_pi(n):
    """ Perform n steps of Monte Carlo simulation for estimating Pi/4.
        Returns the number of sucesses."""
    s = 0
    for i in range(n):
        x = random.random()
        y = random.random()
        if x**2 + y**2 <= 1.0:
            s += 1
    return s


def compute_pi(args):
    random.seed(1)

    n_total  = args.steps
    s_total = sample_pi(n_total)
    pi_est = (4.0*s_total)/n_total
    print(" Steps\tSuccess\tPi est.\tError")
    print("%6d\t%7d\t%1.5f\t%1.5f" % (n_total, s_total, pi_est, pi-pi_est))


if __name__ == "__main__":
    parser = argparse.ArgumentParser(description='Compute Pi using Monte Carlo simulation.')
    parser.add_argument('--steps', '-s',
                        default='1000',
                        type = int,
                        help='Number of steps in the Monte Carlo simulation')
    args = parser.parse_args()
    compute_pi(args)