@ngn I feel confident that you can shorten this significantly.

@Adám Hey, I was looking at the answer you linked there and I was wondering if you could tell me why ↑∪↓⍉(⍋∘⍋⍴⌸⊢) works for the Word Icicle challenge. My answer there is very convoluted.

@J.Sallé Well, it is just taken from ngn, but I can try to explain it.

@J.Sallé Remember last lesson, how we substituted functions with non-computing functions that just report what they would do?

@J.Sallé So remember that ⍋⍋ gives you the cardinal numbers, i.e. the positions that the letters will occupy when sorted:

⍞←⍋⍋'Word Icicle!'

@Adám 4 11 12 7 1 3 5 9 6 10 8 2

W will be the 4th, o the 11th, etc. Now since we need to remove them in sort order, W will be the 4th to go, o the 11th to go, etc. This also means that there will be 4 Ws in its column, 11 os in its column, etc.

Now look at the arguments to ⌸'s operand:

⎕←(⍋∘⍋{⍺,'⍴''',⍵,''''}⌸⊢) 'Word Icicle!'

@Adám
 4 ⍴'W'
11 ⍴'o'
12 ⍴'r'
 7 ⍴'d'
 1 ⍴' '
 3 ⍴'I'
 5 ⍴'c'
 9 ⍴'i'
 6 ⍴'c'
10 ⍴'l'
 8 ⍴'e'
 2 ⍴'!'

So that gives:

⎕←(⍋∘⍋{⍺⍴⍵}⌸⊢) 'Word Icicle!'

@Adám
WWWW
ooooooooooo
rrrrrrrrrrrr
ddddddd

III
ccccc
iiiiiiiii
cccccc
llllllllll
eeeeeeee
!!

And now we just need to transpose and remove duplicates:

⎕←∪↓⍉(⍋∘⍋{⍺⍴⍵}⌸⊢) 'Word Icicle!'

@Adám
┌────────────┬────────────┬────────────┬────────────┬────────────┬────────────┬────────────┬────────────┬────────────┬────────────┬────────────┐
│Word Icicle!│Word Icicle │Word  cicle │ ord  cicle │ ord   icle │ ord   i le │ or    i le │ or    i l  │ or      l  │ or         │  r         │
└────────────┴────────────┴────────────┴────────────┴────────────┴────────────┴────────────┴────────────┴────────────┴────────────┴────────────┘

And of course mix back together for nicer display:

⎕←↑∪↓⍉(⍋∘⍋{⍺⍴⍵}⌸⊢) 'Word Icicle!'

@Adám
Word Icicle!
Word Icicle
Word  cicle
 ord  cicle
 ord   icle
 ord   i le
 or    i le
 or    i l
 or      l
 or
  r

Btw, in 17.0, ∪ works on major cells, so ngn can save 2 bytes: ∪∘⍉⍋∘⍋⍴⌸⊢

@J.Sallé Clear?

@Adám Perfectly, thanks!

Sorry I wasn't responding, I was having lunch with my boss :p

@Adám Another question, is there a way to give multiple arguments to ⌽ so it would rotate the argument multiple times? i.e. something like 1 2⌽'123' yielding 231 312 (I know that doesn't work like that, btw)

I'm trying to use ⍣ but it'll only yield the last result

@J.Sallé want to answer the challenge?

@EriktheOutgolfer yes

@Adám thank you :)

@J.Sallé Like these?

⎕←1 2⌽¨⊂'123' ⋄ ⎕←1 2⌽⍤0 1⊢'123'

@Adám
┌───┬───┐
│231│312│
└───┴───┘
231
312

@Adám Aaaaah, the right argument needs to be enclosed!

That's what I was missing. Thanks a lot!

@J.Sallé Yes, remember APL's scalar extension. If the left is a vector and the right a scalar, the scalar is extended. ⊂ makes anything into a scalar.

Yeah, I see it now

@J.Sallé Here is a more array oriented way to do it:

⎕←1 2⌽2⌿⍉⍪'123'

@Adám
231
312

I sometimes think of some arguments as a bunch of scalars instead of vectors >.>

@ngn Feel free to rework into an explanation for your post.

⎕←(+/⍎¨∘((⍳∘≢⊢)⌽¨⊂)÷∘≢⊢)'123'

@J.Sallé
222

Any golfing suggestions?

@J.Sallé (⍳∘≢⊢) ‽

@Adám that's supposed to rotate the argument ⍳≢ times

@J.Sallé Right, but you clearly converted this from a dfn, right?

Nope, did it from scratch

@J.Sallé Oh, my bad. Then how did you end up with (⍳∘≢⊢)? It is the monadic function ⍳∘≢ atop the no-op ⊢!

@Adám honestly? Trial and error. That was the only way that didn't throw a domain or length error

I guess I didn't change it as I built the function over it (that was the first thing I did)

@J.Sallé OK, and you've got the same issue with ≢⊢.

@Adám the rightmost one?

⎕←(+/⍎¨∘((⍳∘≢)⌽¨⊂)÷∘≢)'123'

@J.Sallé
DOMAIN ERROR

@J.Sallé You have a stray ∘ between ÷ and ≢.

Ah, I see

@J.Sallé You can remove the parens around ⍳∘≢ now that it is a single (derived) function.

I think I used ÷∘≢ reflexively and just added the ⊢ when it threw the error

⎕←⎕←(+/⍎¨∘(⍳∘≢⌽¨⊂)÷≢)'123'

@J.Sallé
222
222

lol doubled the ⎕←

Sounds good though

@J.Sallé Well, the good thing is that you're building up so much APL experience that you're doing things reflexively. APL becomes a way of thinking rather than coding.

@Adám yeah, that's kind of what I'm doing. I built this function really fast after you gave me the tip about rotating stuff

@J.Sallé Remember, any time you have (ParenthesisedExpression) Function SingleToken you can save a byte with SingleToken Function⍨ ParenthesisedExpression.

@Adám Oh, let me see

@Adám I can't actually see how that applies there though >.>

@J.Sallé (⍳∘≢⌽¨⊂)÷≢ → ≢÷⍨⍳∘≢⌽¨⊂

@Adám oh, I tried doing that with ÷≢ instead of ≢÷

but it does make sense that you'd need to swap the tokens there

I think I broke something though

⎕←(+/⍎¨∘≢÷⍨⍳∘≢⌽¨⊂)'123'

@J.Sallé Yeah, the execute part.

@J.Sallé
DOMAIN ERROR

@J.Sallé Now it tries to execute each of the length.

And I can't just do the same thing and swap arguments can I?

@J.Sallé No. because then you need parens again: (+/≢÷⍨⍎¨∘(⍳∘≢⌽¨⊂)) But I'll teach you a trick for this one.

Oooooooh I like tricks :D

The problem here is that you want to call ⍎ monadically on each one. Since you need the ¨, you can't do +/∘⍎¨ as that would require +/∘(⍎¨) to limit the ¨ to ⍎ and not +/. But since you're only evaluating numbers, remember that numbers have the same value in every namespace, so you can use dyadic ⍎ to evaluate them in a specific scalar (so that it distributes to each rotation vector) 1-char namespace: #⍎¨. Now you can write +/#≢÷⍨⍎¨⍳∘≢⌽¨⊂.

@Adám oh cool

I've never seen # used in APL before, I think?

Something seems to be broken though

@J.Sallé Lesson 16.

⎕←(+/#≢÷⍨⍎¨⍳∘≢⌽¨⊂)'123'

@J.Sallé
DOMAIN ERROR

@J.Sallé Yeah, I made a typo. Should be +/≢÷⍨#⍎¨⍳∘≢⌽¨⊂.

Ah, okay

How do I explain the # on my post though?

Do I just say it's the root namespace?

@J.Sallé You don't need to. Notice the double loop?

@Adám not really? You mean the two ¨?

@J.Sallé Yeah.

Okay, then yes :p

@J.Sallé That's too much "pepper" (looks like pepper dots). You can fuse the loops: +/≢÷⍨#⍎¨⍳∘≢⌽¨⊂ → +/≢÷⍨⍳∘≢(⍎⌽)¨⊂. Since it costs you 2 (parens) and saves you 2 (# and ¨) it is free.

@Adám geez that's a brain knot right there

Looks very simple, but it's doing a lot

I'll post it that version then!

@J.Sallé I hope it was a learning experience.

@Adám indeed it was