[Python-Dev] a note in random.shuffle.__doc__ ...
jcarlson at uci.edu
Sat Jun 10 21:52:05 CEST 2006
Alex Martelli <aleaxit at gmail.com> wrote:
> 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)
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