Try: {x. e.g.
{ 8 9;0;3 4;1 2;5
┌─────────┬─────────┐
│8 0 3 1 5│8 0 3 2 5│
├─────────┼─────────┤
│8 0 4 1 5│8 0 4 2 5│
└─────────┴─────────┘
┌─────────┬─────────┐
│9 0 3 1 5│9 0 3 2 5│
├─────────┼─────────┤
│9 0 4 1 5│9 0 4 2 5│
└─────────┴─────────┘
cperm 8 9;0;3 4;1 2;5
┌─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┐
│8 0 3 1 5│8 0 3 2 5│8 0 4 1 5│8 0 4 2 5│9 0 3 1 5│9 0 3 2 5│9 0 4 1 5│9 0
4 2 5│
└─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┘
On Thu, May 8, 2014 at 10:53 AM, 'Pascal Jasmin' via Programming <
[email protected]> wrote:
> cperm =: [: , [: < "1 [: > [: ,"0 1/ each/ (_2&}. , [: ,"0 0/ each/ _2&{.)
>
> this creates constrained permutations where each position in the list can
> only be drawn from its own set:
>
> cperm 3 4 ; 1 2
> ┌───┬───┬───┬───┐
> │3 1│3 2│4 1│4 2│
> └───┴───┴───┴───┘
>
> cperm 0 ; 3 4 ; 1 2; 5
> ┌───────┬───────┬───────┬───────┐
> │0 3 1 5│0 3 2 5│0 4 1 5│0 4 2 5│
> └───────┴───────┴───────┴───────┘
>
> cperm 8 9 ;0 ; 3 4 ; 1 2; 5
>
> ┌─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┬─────────┐
> │8 0 3 1 5│8 0 3 2 5│8 0 4 1 5│8 0 4 2 5│9 0 3 1 5│9 0 3 2 5│9 0 4 1 5│9 0
> 4 2 5│
>
> └─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┴─────────┘
>
> The rightmost part (_2&}. , [: ,"0 0/ each/ _2&{.) of the verb is just
> there to deal with edge cases of joining the last 2 boxes.
>
> The core is: (,"0 1/ each/)
>
> I thought it was pretty cool to use / twice.
>
> This was useful in solving this problem in sufficiently elegant fashion:
>
>
> http://www.reddit.com/r/dailyprogrammer/comments/24ypno/572014_challenge_161_medium_appointing_workers/
>
> often the constrained permutation list has overlapping allowable values in
> each slot, and in the above resource allocation problem, those happen to
> indicate the invalid permutations, and are fairly easily eliminated with ~.
>
> It could also be used ( a bit of a stretch) for games where the first few
> moves have been played and are known, but you wish to know the permutations
> for a select number of future moves.
> ----------------------------------------------------------------------
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