bdayParadox.py

"""Birthday Paradox Simulation, by Al Sweigart al@invent withpython.com
Explore the suprising probabilites of the "Birthday Paradox".
 More info at https://en.wikipedia.org/wiki/Birthday_problem
 View this code at https://nostarch.com/big-book-small-python-projects
 Tags: short, math, simulation """

import datetime, random


def getBirthdays(numberOfBirthdays):
    """Returns a list of number random date objects for birthdays."""
    birthdays = []
    for i in range(numberOfBirthdays):
        #the year is unimportant for the simulation, as long as all
        #birthdays have the same year.
        startOfYear = datetime.date(2001, 1, 1)

        #get a random day into the year:
        randomNumberOfDays = datetime.timedelta(random.randint(0,364))
        birthday = startOfYear + randomNumberOfDays
        birthdays.append(birthday)
    return birthdays


def getMatch(birthdays):
    """Returns the date object of a birthday that occurs more than once 
    in the birthdays list."""
    if len(birthdays) == len(set(birthdays)):
        return None # all birthdays are unique, so return None.

    #Compare ach birthday to every other birthday:
    for a, birthdayA in enumerate(birthdays):
        for b, birthdayB in enumerate(birthdays[a + 1 :]):
            if birthdayA == birthdayB:
                return birthdayA #return the matching birthday.


#Display the intro:
print('''Birthday Paradox, by AlSweigart al@incentwithpython.com

The Birthday Paradox shows us that in a group of N people, the odds
 that two of them have matching birthdays is suprisingly large. 
 This program does a Monte Carlo simulation (that is, repeated random
 simulations) to explore this concept.
 
 (It's not actually a paradox, it's just a suprising reult.)
 ''')

#set up a tuple of month names in order:
MONTHS = ('Jan','Feb','Mar','Apr','May','Jun',
          'Jul','Aug','Sep','Oct','Nov','Dec')

while True: #keep asking until the user enters a valid amount.
    print('How many birthdays shall I generate? (Max 1000)')
    response = input('>')
    if response.isdecimal() and (0 < int(response) <= 1000):
        numBdays = int(response)
        break # User has entered a valid amount.
print()

# Generate and display the birthdays:
print('Here are', numBdays, 'birthdays:')
birthdays = getBirthdays(numBdays)
for i, birthday in enumerate(birthdays):
    if i != 0:
        #Display a coma for each birthday after the first birthday.
        print(',', end='')
        monthName = MONTHS[birthday.month -1]
        dateText = '{} {}'.format(monthName, birthday.day)
        print(dateText, end='')
print()
print()

#determine if there are two birthdays that match.
match = getMatch(birthdays) 

#display the results
print('In this simulatioin, ', end='')
if match != None:
    monthName = MONTHS[match.month -1]
    dateText = '{} {}'.format(monthName, match.day)
    print('multiple people have a birthday on', dateText)
else:
    print('there are no matching birthdays.')
print()

#Run through 100,000:
print('Generating', numBdays, 'random birthdays 1000,000 times...')
input('Press Enter to begin...')

print('Let\s run another 100,000 simulation.')
simMatch = 0 #How many simulations had matching birthdays in them.
for i in range(100_000):
    #Report  on the progress every 10,000 simulations:
    if i % 10_000 == 0:
        print(i, 'simulations run...')
    birthdays = getBirthdays(numBdays)
    if getMatch(birthdays) != None:
        simMatch = simMatch + 1
print('100,000 simulations run.')

#display simulation results:
probability = round(simMatch / 100_000 * 100, 2)
print('Out of 100,000 simulations of', numBdays, 'people, there was a')
print('matching birthday in that group', simMatch, 'times. This means')
print('that', numBdays, 'people have a', probability, '% chance of')
print('having a matching birthday in their group.')
print('That\'s probably more than you would think!')