Function for factorial in Python

How do I go about computing a factorial of an integer in Python?

Solution 1:

The easiest way is to use math.factorial (available in Python 2.6 and above):

import math
math.factorial(1000)

If you want/have to write it yourself, you can use an iterative approach:

def factorial(n):
    fact = 1
    for num in range(2, n + 1):
        fact *= num
    return fact

or a recursive approach:

def factorial(n):
    if n < 2:
        return 1
    else:
        return n * factorial(n-1)

Note that the factorial function is only defined for positive integers, so you should also check that n >= 0 and that isinstance(n, int). If it's not, raise a ValueError or a TypeError respectively. math.factorial will take care of this for you.

Solution 2:

On Python 2.6 and up, try:

import math
math.factorial(n)

Solution 3:

Existing solution

The shortest and probably the fastest solution is:

from math import factorial
print factorial(1000)

Building your own

You can also build your own solution. Generally you have two approaches. The one that suits me best is:

from itertools import imap
def factorial(x):
    return reduce(long.__mul__, imap(long, xrange(1, x + 1)))

print factorial(1000)

(it works also for bigger numbers, when the result becomes long)

The second way of achieving the same is:

def factorial(x):
    result = 1
    for i in xrange(2, x + 1):
        result *= i
    return result

print factorial(1000)

Solution 4:

def factorial(n):
    if n < 2:
        return 1
    return n * factorial(n - 1)

Solution 5:

If you are using Python 2.5 or older, try

from operator import mul

def factorial(n):
    return reduce(mul, range(1, n+1))

For newer versions of Python, there is factorial in the math module as given in other answers here.