I want to generate all-length subsets of a vector, always starting from the
left-most integer:
We need to define a verb f, that does the following:
f 1 2 3 4 5 6
┌─┬───┬─────┬───────┬─────────┬───────────┐
│1│1 2│1 2 3│1 2 3 4│1 2 3 4 5│1 2 3 4 5 6│
└─┴───┴─────┴───────┴─────────┴───────────┘
It would be handy if it took a left argument as an option (partition count
for each partition), but that's not critical if that is too complex,
2 4 5 f 1 2 3 4 5 6
┌───┬───────┬─────────┐
│1 2│1 2 3 4│1 2 3 4 5│
└───┴───────┴─────────┘
More importantly, f needs to work on rank 2 arrays:
]n=.>:perm 3
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
f"1 n
┌─┬───┬─────┐
│1│1 2│1 2 3│
├─┼───┼─────┤
│1│1 3│1 3 2│
├─┼───┼─────┤
│2│2 1│2 1 3│
├─┼───┼─────┤
│2│2 3│2 3 1│
├─┼───┼─────┤
│3│3 1│3 1 2│
├─┼───┼─────┤
│3│3 2│3 2 1│
└─┴───┴─────┘
I know I can do this by brute force:
Build dyadic verb t that takes the first x elements from y & boxes them:
t=.4 :'x {."1 ea {y'
(1 t n),.(2 t n),.(3 t n)
┌─┬───┬─────┐
│1│1 2│1 2 3│
├─┼───┼─────┤
│1│1 3│1 3 2│
├─┼───┼─────┤
│2│2 1│2 1 3│
├─┼───┼─────┤
│2│2 3│2 3 1│
├─┼───┼─────┤
│3│3 1│3 1 2│
├─┼───┼─────┤
│3│3 2│3 2 1│
└─┴───┴─────┘
Is there a more elegant (and efficient) way to do this?
Skip
Skip Cave
Cave Consulting LLC
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