birthday.py

# Birthday paradox simulation. https://en.wikipedia.org/wiki/Birthday_problem
from argparse import ArgumentParser
from random import randint
from typing import Set
from math import factorial

DAYS_IN_YEAR = 365


def main():
    parser = ArgumentParser(prog="birthday", description="Birthday Paradox Simulator")
    parser.add_argument("-s", "--size", dest="size", help="the group size", default=23, type=int)
    parser.add_argument("-e", "--experiments", dest="experiments", help="number of experiments to run", default=1000,
                        type=int)
    args = parser.parse_args()
    size = args.size
    experiments = args.experiments
    print(f'Simulating Birthday Paradox with group size {size}, {experiments} experiments')
    print(f'Computed: {compute(size)}')
    print(f'Simulated: {simulate(experiments, size)}')


# Generates `num` random uniformly distributed birthdays.
# Returns the set of unique birthdays
def generate_birthdays(num: int) -> Set[int]:
    days: Set[int] = set()
    for _ in range(num):
        days.add(randint(1, DAYS_IN_YEAR))
    return days


def simulate(experiments: int, size: int) -> float:
    dupes = 0
    for _ in range(experiments):
        if len(generate_birthdays(size)) < size:
            dupes = dupes + 1
    return dupes / experiments


# Computes the probability of a duplicate birthday for the group of the given `size`
def compute(size: int):
    return 1 - factorial(DAYS_IN_YEAR) / (DAYS_IN_YEAR ** size * factorial(DAYS_IN_YEAR - size))


if __name__ == '__main__':
    main()