Skip to content

Instantly share code, notes, and snippets.

Embed
What would you like to do?
"Birthday problem" calculator in Python
"""Calculate the probability of generating a duplicate random number after
generating "n" random numbers in the range "d".
Usage: python birthday_probability.py n [d=365]
Each value can either be an integer directly, or in the format "2**x", where
x is the number of bits in the value.
For example, to calculate the probability that two people will have the same
birthday in a room with 23 people:
$ python birthday_probability.py 23
Probability is 0.5155095380615168, or about 1 in 2
Or to calculate the probability of a collision with 1,000,000 items and a
range of 2**48:
$ python birthday_probability.py 1000000 2**48
Probability is 0.001774780051374103, or about 1 in 563
"""
from __future__ import division
import math
import sys
def birthday_probability(n, d):
"""Calculate the probability of generating a duplicate random number after
generating "n" random numbers in the range "d".
"""
# Formula taken from: https://en.wikipedia.org/wiki/Birthday_problem
return 1 - math.e ** (-n**2 / (2 * d))
if __name__ == '__main__':
def error(message):
sys.stderr.write(message)
sys.exit(1)
def convert(s):
if s.startswith('2**'):
return 2 ** int(s[3:])
else:
return int(s)
if len(sys.argv) < 2:
error(__doc__)
try:
n = convert(sys.argv[1])
d = convert(sys.argv[2]) if len(sys.argv) > 2 else 365
except ValueError:
error('ERROR: "n" and "d" must be integers or in the form "2**x"\n')
probability = birthday_probability(n, d)
print('Probability is {}, or about 1 in {:,d}'.format(
probability, int(round(1 / probability))))
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
You can’t perform that action at this time.