Coupon Collector's Problem applied to Birthdays

birthdays.py

# This is not the actual Birthday Paradox Problem.
# This is something similar suggested by Taylor Smith.
#
# How many people do you need in a room to have a 50%
# chance of having every possible birthday represented
# within the room?
#
# After typing all of this out, I realized that it's
# the same as the Coupon Collector's Problem.

import random

def main():
    # Total possible birthdays
    BIRTHDAYS = 365

    # Number of trials to perform
    TRIALS = 1000

    # Total number of people across all trials.
    total_people = 0

    # Keep track of the number of completed trials
    i = 0

    while i < TRIALS:
        # This is our tally of recorded birthdays
        calendar = [0] * BIRTHDAYS

        # Total number of unique birthdays for this trial
        unique_birthdays = 0

        # Number of people in the room
        people_this_trial = 0

        while unique_birthdays < BIRTHDAYS:
            # Allow 1 person in the room. Ask them their birthday.
            people_this_trial += 1
            my_birthday = random.randint(0, BIRTHDAYS-1)

            # Check for a unique birthday. If unique, record it.
            if calendar[my_birthday] == 0:
                calendar[my_birthday] += 1
                unique_birthdays += 1

        # Finished with 1 trial. Add the people_this_trial to total_people
        total_people += people_this_trial
        i += 1

    # Finally, calculate the average number of people per trial
    # for the solution
    average_per_trial = total_people / float(TRIALS)
    print average_per_trial

if __name__ == '__main__':
    main()