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#!/usr/bin/env python

# Sebastian Raschka 2014

# Functions to calculate factorial, combinations, and permutations

# bundled in an simple command line interface.

def factorial(n):

if n == 0:

return 1

else:

return n * factorial(n-1)

def combinations(n, r):

numerator = factorial(n)

denominator = factorial(r) * factorial(n-r)

return int(numerator/denominator)

def permutations(n, r):

numerator = factorial(n)

denominator = factorial(n-r)

return int(numerator/denominator)

assert(factorial(3) == 6)

assert(combinations(20, 8) == 125970)

assert(permutations(30, 3) == 24360)

if __name__ == '__main__':

import argparse

parser = argparse.ArgumentParser(

description='Script to calculate the number of combinations or permutations ("n choose r")',

formatter_class=argparse.RawTextHelpFormatter,

prog='Combinations',

epilog='Example: ./combinations.py -c 20 3'

)

parser.add_argument('-c', '--combinations', type=int, metavar='NUMBER', nargs=2,

help='Combinations: Number of ways to combine n items with sequence length r where the item order does not matter.')

parser.add_argument('-p', '--permutations', type=int, metavar='NUMBER', nargs=2,

help='Permutations: Number of ways to combine n items with sequence length r where the item order does not matter.')

parser.add_argument('-f', '--factorial', type=int, metavar='NUMBER', help='n! e.g., 5! = 5*4*3*2*1 = 120.')

parser.add_argument('--version', action='version', version='%(prog)s 1.0')

args = parser.parse_args()

if not any((args.combinations, args.permutations, args.factorial)):

parser.print_help()

quit()

if args.factorial:

print(factorial(args.factorial))

if args.combinations:

print(combinations(args.combinations[0], args.combinations[1]))

if args.permutations:

print(permutations(args.permutations[0], args.permutations[1]))

if args.factorial:

print(factorial(args.factorial))