112 lines
3.9 KiB
Python
112 lines
3.9 KiB
Python
"""Birthday Paradox Simulation, by Al Sweigart al@inventwithpython.com
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Explore the surprising possibilities of the "Birthday Paradox".
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More info at https://en.wikipedia.org/wiki/Birthday_problem
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View this code at https://nostarch.com/big-book-small-python-projects
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Tags: short, math, simulation"""
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import datetime, random
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def getBirthdays(numberOfBirthdays):
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"""Returns a list of number random date objects for birthdays."""
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birthdays = []
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for i in range(numberOfBirthdays):
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# The year is unimportant for our simulation, as long as all
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# birthdays have the same year.
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startOfYear = datetime.date(2001, 1, 1)
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# Get a random day into the year:
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randomNumberOfDays = datetime.timedelta(random.randint(0, 364))
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birthday = startOfYear + randomNumberOfDays
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birthdays.append(birthday)
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return birthdays
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def getMatch(birthdays):
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"""Returns the date object of a birthday that occurs more than once
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in the birthdays list."""
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if len(birthdays) == len(set(birthdays)):
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return None #All birthdays are unique, so return None.
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# Compare each birthday to every other birthday:
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for a, birthdayA in enumerate(birthdays):
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for b, birthdayB in enumerate(birthdays[a + 1 :]):
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if birthdayA == birthdayB:
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return birthdayA # Return the matching birthday
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# Display the intro:
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print('''Birthday Paradox, by Al Sweigart al@inventwithpython.com
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The Birthday Paradox shows us that in a group of N people, the odds
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that two of them have matching birthdays is surprisingly large.
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This program does a Monte Carlo simulation (that is, repeated random
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simulations) to explore this concept.
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(It's not actually a paradox, it's just a surprising result.)
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''')
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# Set up a tuple of month names in order:
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MONTHS = ('Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun',
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'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec')
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while True: # Keep asking until the user enters a valid amount.
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print('How many birthdays shall I generate (Max 100)')
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response = input('> ')
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if response.isdecimal() and (0 < int(response) <= 100):
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numBDays = int(response)
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break # User has entered a valid amount
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print()
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# Generate and display birthdays:
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print('Here are', numBDays, 'birthdays:')
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birthdays = getBirthdays(numBDays)
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for i, birthday in enumerate(birthdays):
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if i != 0:
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# Display a comma for each birthday after the first birthday.
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print(', ', end='')
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monthName = MONTHS[birthday.month - 1]
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dateText = '{} {}'.format(monthName, birthday.day)
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print(dateText, end='')
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print()
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print()
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# Determine if there are two birthdays that match.
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match = getMatch(birthdays)
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# Display the results:
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print('In this simulation, ', end='')
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if match != None:
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monthName = MONTHS[match.month - 1]
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dateText = '{} {}'.format(monthName, match.day)
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print('multiple people have a birthday on', dateText)
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else:
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print('there are no matching birthdays.')
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print()
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# Run through 100,000 simulations:
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print('Generating', numBDays, 'random birthdays 100,000 times...')
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input('Press Enter to begin...')
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print('Let\'s run another 100,000 simulations.')
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simMatch = 0 # How many simulations had matching birthdays in them.
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for i in range(100_000):
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# Report on the progress every 10,000 simulations:
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if i % 1000 == 0:
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print(i, 'simulations run...')
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birthdays = getBirthdays(numBDays)
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if getMatch(birthdays) != None:
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simMatch = simMatch + 1
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print('100,000 simulations run.')
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# Display simulation results:
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probability = round(simMatch / 100_000 * 100, 2)
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print('Out of 100,000 simulations of', numBDays, 'people, there was a a')
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print('matching birthday in that group', simMatch, 'times. This means')
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print('that', numBDays, 'people have a', probability, '% chance of')
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print('having a matching birthday in their group.')
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print('That\'s probably more than you would think!')
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#if __name__ == '__main__':
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