阶乘巨大数Python

Question

I am trying to make a program that can compute the factorial of 987654321, but I can't find a way to do it.

def range_prod(lo,hi):
    if lo+1 < hi:
        mid = (hi+lo)//2
        return range_prod(lo,mid) * range_prod(mid+1,hi)
    if lo == hi:
        return lo
    return lo*hi

def treefactorial(n):
    if n < 2:
        return 1
    return range_prod(1,n)
print(treefactorial(987654321))

Answer 1

The proposed approaches will take a very long time to compute. If you're OK with losing some precision, you can get an approximate value quickly using the LogGamma function, for example

math.exp(scipy.special.gammaln(3+1))
=> 6.0

scipy.special.gammaln(987654322)
=> 19467499583.824226

so 987654321! is approximately exp(19467499583.824226) you can convert to log 10 base to find the number of digits...

ps. It will have more than 8 billion digits.

Answer 2

You can use builtin math.factorial

import math
math.factorial(n)

Or you can use reduce function to calculate factorial

from operator import mul

for Python 2.7

factorial = lambda n: reduce(mul, xrange(1, n+1))

for Python 3

factorial = lambda n: reduce(mul, range(1, n+1))

>>> factorial(987654321)