Hello everybody,
I stumbled across an interesting little problem. I would like to generate all
possible combinations of taking ⍺ things from a total of ⍵. The number of
possible combinations is consequently ⍺!⍵.
Here's a straight-forward "brute force" solution:
Perm ← {(X/⍨⍺=+/¨X←(⊂2⍴⍨⍵)⊤¨⍳2*⍵) /¨ ⊂⍳⍵; X}
2 Perm 4
3 4 2 4 2 3 1 4 1 3 1 2
3 Perm 4
2 3 4 1 3 4 1 2 4 1 2 3
Unfortunately the algorithm has O(2^⍵) time and space complexity. Which is okay
for what I am using it, but I was still curious of how this could be solved
recursively in a lambda. I feel that simple things like this should have elegant
solutions in GNU APL. Unfortunately this is the best I could come up with:
Perm ← {⍎∊('↑,/X,¨¨X+(⍺-1) Perm¨⍵-X' 'X')[1+⍺≤1] ⊣ X←⍳1+⍵-⍺; X}
At this point I was really feeling the limitations of lambdas in GNU APL. There
apparently aren't enough means of control flow. At least I couldn't find a way
to utilize one of APL's operators elegantly for this purpose, so I fell back to
a computed ⍎, which feels really clumsy and is probably quite slow as well.
Or you write a traditional ∇ function with →... I mean you could also write your
own ⍶IfElse⍹ operator, but due to the lack of lexical scoping this would be
pretty useless for recursion, unless you pass in your context as ⍺ or ⍵ which is
again very clumsy.
I would therefore claim that we are either lacking lexical scoping and/or
built-in structured If-Else constructs. Or lambdas should simply be allowed to
contain ⋄, new lines and →. Or I am missing something obvious. I am not sure.
But IMHO something fundamental is missing in the language.
I am interested in hearing your thoughts.
Yours sincerely,
Robin
PS: I am not saying "I want it like in Dyalog!!!11". GNU APL is great for what
it is and I am not ready to switch over to Dyalog yet. I particularly like two
things about GNU APL: 1) It's FREE software. 2.) It's more conservatively
designed than Dyalog.