[Python-Dev] a note in random.shuffle.__doc__ ...

Josiah Carlson jcarlson at uci.edu
Sat Jun 10 21:52:05 CEST 2006

Alex Martelli <aleaxit at gmail.com> wrote:
> ...claims:
> Note that for even rather small len(x), the total number of
> permutations of x is larger than the period of most random number
> generators; this implies that "most" permutations of a long
> sequence can never be generated.
> I suspect that the note is just a fossil from a time when the default  
> random number generator was Whichman-Hill, with a much shorter  
> period.  Should this note just be removed, or instead somehow  
> reworded to point out that this is not in fact a problem for the  
> module's current default random number generator?  Opinions welcome!

I'm recovering from a migraine, but here are my thoughts on the topic...

The number of permutations of n items is n!, which is > (n/2)^(n/2).
Solve:  2**19997 < (n/2)^(n/2)
        log_2(2**19997) < log_2((n/2)^(n/2))
        19997 < (n/2)*log(n/2)

Certainly with n >= 4096, the above holds (2048 * 11 = 22528)

 - Josiah

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