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### Re: Generate uniform random partitions of a number

 on Sep 25, 2008 at 20:45 UTC ( #713741=note: print w/replies, xml ) Need Help??

Nice. I wonder if there is a more direct way to sample the distribution, instead of computing the number of partitions for each of the possible first choices (this appears to be what you do, although the code is too golfed for me to really parse). For this application, you don't need the actual number of such partitions, just their ratios.

BTW, did you have in mind a cool application of uniformly sampling partitions, or was this just "because it's there"? ;)

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Re^2: Generate uniform random partitions of a number
by ambrus (Abbot) on Sep 25, 2008 at 22:08 UTC

I'm holding a programming course and one of the homeworks I'm setting requries a partition of an integer as input. It's not really important that it's uniformly random, but I wanted to generate some sample inputs (and corresponding outputs) so the students can test their solutions on, and then I thought of this.

It's a bit of an overkill because it needs like an hour to generate a partition of 5000, and the homework problem would work just as well if I just generated random partitions of any other distribution as test input, but the task carried me over. I posted it in case me or someone else really needs a uniformly random partition at one point. I'd have written it by hand for the challenge even if I knew of a pre-written function that can generate a random partition. If you know of such a function in any library (not necessarily perl), please tell, because it seems so obvious it must exist, yet I can't find any right now. Even mathematica doesn't seem to have a function that gives you the kth partitioning of the integer n or anything similar.

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