number generator

[Paul Rubin]

Steven D'Aprano <steve at REMOVEME.cybersource.com.au> writes:
> If you generate all the possible sets of five numbers between 1 and 50,
> there are 50**5 of them, not 2611.

Yes, the idea is generate only the sets that add up to 50.

> unique_partitions(60, 6) takes 0.8 seconds; unique_partitions(80, 8)
> takes about 25 seconds; unique_partitions(80, 10) takes about 80 seconds,
> and unique_partitions(81, 10) takes over 90 seconds.

Hmm, interesting.  Maybe some more optimization is possible.

> (E.g. unique_partitions(80, 10) returns 533,975 unique lists.
> _partitions(80, 10) gives 3,233,568 non-unique lists.)

Well that's just 6x "inflation" due to duplicates, so I dunno what
else can be done for exhaustive enumeration.  Maybe another approach
to generating the k'th partition is possible.  I'll try to think about
this.