Birthday Paradox Simulation

Birthday-Paradox/birthdayparadox.py

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+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 our 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 each 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 Al Sweigart al@inventwithpython.com
+
+The birthday paradox shows us that in a group of N people, the odds
+that two of them have matching birthdays is surprisingly 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 surprising result.)
+''')
+
+# 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 100)')
+    response = input('> ')
+    if response.isdecimal() and (0 < int(response) <= 100):
+        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 comma 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 simulation, ', 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 simulations:
+print('Generating', numBDays, 'random birthdays 100,000 times...')
+input('Press Enter to begin...')
+
+print('Let\'s run another 100,000 simulations.')
+simMatch = 0  # How many simulations had matching birthdays in them.
+for i in range(100000):
+    # Report on the progress every 10,000 simulations:
+    if i % 10000 == 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 / 100000 * 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!')