Possible Duplicates:
Statistics: combinations in Python
counting combinations and permutations efficiently
Project euler problem in python (problem 53)
I'm looking to see if built in with the math library in python is the nCr (n Choose r) function:
I understand that this can be programmed but I thought that I'd check to see if it's already built in before I do.
The answer is
The following program calculates nCr in an efficient manner (compared to calculating factorials etc.)
import operator as op
from functools import reduce
def ncr(n, r):
r = min(r, n-r)
numer = reduce(op.mul, range(n, n-r, -1), 1)
denom = reduce(op.mul, range(1, r+1), 1)
return numer // denom # or / in Python 2
As of Python 3.8, binomial coefficients are available in the standard library as math.comb:
>>> from math import comb
>>> comb(10,3)
120
Do you want iteration? itertools.combinations. Common usage:
>>> import itertools
>>> itertools.combinations('abcd',2)
<itertools.combinations object at 0x01348F30>
>>> list(itertools.combinations('abcd',2))
[('a', 'b'), ('a', 'c'), ('a', 'd'), ('b', 'c'), ('b', 'd'), ('c', 'd')]
>>> [''.join(x) for x in itertools.combinations('abcd',2)]
['ab', 'ac', 'ad', 'bc', 'bd', 'cd']
If you just need to compute the formula, use math.factorial:
import math
def nCr(n,r):
f = math.factorial
return f(n) / f(r) / f(n-r)
if __name__ == '__main__':
print nCr(4,2)
In Python 3, use the integer division // instead of / to avoid overflows:
return f(n) // f(r) // f(n-r)
Output
6
Source: Stackoverflow.com