# [BangPypers] Implementing a fast factorial function in python

Amit Saha lists.amitsaha at gmail.com
Mon Sep 14 18:36:36 CEST 2009

```Shashwat Anand wrote:
> How do we calculate last 5-digits of 10**12 ignoring trailing zeros. The
> code i wrote works good until 10**8 and after that take ages.
> The source of problem is Project Euler :
> http://projecteuler.net/index.php?section=problems&id=160

You might consider using the Stirling's Approximation
(http://en.wikipedia.org/wiki/Stirling%27s_approximation) to calculate
the factorial of a large N. You will still have to figure out a good way
to find the trailing zeros, ofcourse.

HTH
-Amit
>
> The code is pasted here : http://paste.pocoo.org/show/139745/
>
>  1 '''
>
>
>   2 For any N, let f(N) be the last five digits before the trailing zeroes
> in N!.
>   3 For example,
>   4
>   5 9! = 362880 so f(9)=36288
>   6 10! = 3628800 so f(10)=36288
>   7 20! = 2432902008176640000 so f(20)=17664
>   8
>   9 Find f(1,000,000,000,000)
>  10 '''
>  11 def f(n):
>  12     fac = 1
>  13     i = 1
>  14     #for i in range(1, n+1):
>  15     while i < n + 1:
>  16         fac = int(str(fac * i).strip('0')) % 100000
>  17         i += 1
>  18     return fac
>  19
>  20 print f(1000000000000)
>
> PS. hope posting algorithmic doubts will not be considered spamming :)
>
>
>
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