L€€CH€$! D€AṬH ỊṢ ṢOOṄ! (Length Mapping)

Question

_{The title is valid Jelly Code which has the same output as L€€ except printed twice.}

Background

^{You can skip this section without losing ability to complete the challenge}

Some operations in Jelly try to convert its argument to a list first before applying the operation. One example is €, the mapping quick. This sometimes leads to unintended output.

For the program L€ and input 5, the Jelly interpreter tries to find the length of every element of the list 5. Since 5 is not a list, Jelly converts it to the list [1,2,3,4,5]. Then the length of every element is output: [1,1,1,1,1]. Note that every integer has length 1. If e.g. 10 was present, it would become 1, not 2 (the length in digits).

For the program L€€ and input 5, the Jelly interpreter tries to find the length of every element of every element of the list 5. Since 5 is not a list, Jelly converts it to the list [1,2,3,4,5]. Now the interpreter tries to find the length of every element of every element of the list [1,2,3,4,5]. Every element is not a list, so Jelly converts them to lists in the same manner: [[1],[1,2],[1,2,3],[1,2,3,4],[1,2,3,4,5]]. The length of every sub-element is output as [[1],[1,1],[1,1,1],[1,1,1,1],[1,1,1,1,1]]

Task

Your task is to find the output of the Jelly program L followed by € repeated a times, with input b, where a and b are positive integers equal to your program/function's inputs.

A way to do this is:

Starting with the input b, do the following a times:

• For every integer that the program sees, replace it with the range of the integer (where range(x) := [1,2,3,...,x-1,x])

Finally, replace every integer with 1.

Test Cases

a
b
output
- - - - -
1
1
[1]
- - - - -
1
2
[1, 1]
- - - - -
1
3
[1, 1, 1]
- - - - -
1
4
[1, 1, 1, 1]
- - - - -
1
5
[1, 1, 1, 1, 1]
- - - - -
1
6
[1, 1, 1, 1, 1, 1]
- - - - -
2
1
[[1]]
- - - - -
2
2
[[1], [1, 1]]
- - - - -
2
3
[[1], [1, 1], [1, 1, 1]]
- - - - -
2
4
[[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]
- - - - -
2
5
[[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]
- - - - -
2
6
[[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]
- - - - -
3
1
[[[1]]]
- - - - -
3
2
[[[1]], [[1], [1, 1]]]
- - - - -
3
3
[[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]
- - - - -
3
4
[[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]
- - - - -
3
5
[[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]]
- - - - -
3
6
[[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]]
- - - - -
4
1
[[[[1]]]]
- - - - -
4
2
[[[[1]]], [[[1]], [[1], [1, 1]]]]
- - - - -
4
3
[[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]]
- - - - -
4
4
[[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]]
- - - - -
4
5
[[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]]]
- - - - -
4
6
[[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]]]
- - - - -
5
1
[[[[[1]]]]]
- - - - -
5
2
[[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]]]
- - - - -
5
3
[[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]]]
- - - - -
5
4
[[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]]]
- - - - -
5
5
[[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]]]]
- - - - -
5
6
[[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]]]]
- - - - -
6
1
[[[[[[1]]]]]]
- - - - -
6
2
[[[[[[1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]]]]
- - - - -
6
3
[[[[[[1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]]]]
- - - - -
6
4
[[[[[[1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]]]]
- - - - -
6
5
[[[[[[1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]]]]]
- - - - -
6
6
[[[[[[1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]]]], [[[[[1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]]], [[[[1]]], [[[1]], [[1], [1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]]], [[[1]], [[1], [1, 1]], [[1], [1, 1], [1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1]], [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]]]]]

Rules

• a and b are restricted to positive integers
• Your program or function may take a and b in any order and in any standard input format
• The output should be a depth-a list or string representation of such a list
• The output should be returned through any standard output format.
• This is code-golf, so shortest code in each language wins!

Answer 1

Jelly, 3 bytes

R¡Ṡ

Try it online!

Takes input in reverse order.
-2 bytes thanks to fireflame.
-1 byte thanks to Dennis

Explanation

R¡Ṡ  Main link
 ¡   Repeat <first argument> times
R    Range (generates range, and vectorizes on lists)
  Ṡ  Sign (converts all numbers to 1 because they are all positive)

Answer 2

Python 2, 49 bytes

^{-1 thanks to Jonathan Allan}

f=lambda a,b:1>>a or[0]*b and f(a,b-1)+[f(a-1,b)]

Try it online!

This problem seemed like it could be written in the form of a doubly recursive function, subtracting one from each parameter. The key idea is that the sequence can be related as follows:

f(0,b) = 1
f(a,0) = []
f(a,b) = f(a,b-1) + [f(a-1,b)]

However writing a recursive function like this is pretty tricky, since 1 is a truthy value and [] is a falsy value, so we need two short-circuiting keywords (and and or).

A less golfed version might look like:

lambda a,b:int(a<1)or[1,[]][b<1]and f(a,b-1)+[f(a-1,b)]

However we can use the trick that 1>>a gives 1 if a is zero, and 0 otherwise, and that we can return a truthy value if b>0 and an empty list otherwise by doing [0]*b.

Answer 3

Mathematica, 17 bytes

1^Range~Nest~##&

Takes b then a.

Try it on Wolfram Sandbox

How?

1^Range~Nest~##&

  Range             (* Range function; generates {1..<input>} *)
       ~Nest~##     (* Apply it on <input 1> <input 2> times *)
                    (* Mathematica automatically maps Range onto integers *)
1^                  (* Raise those to the exponent of 1; make everything 1 *)

Usage

1^Range~Nest~##&[4, 2]

{{1}, {1, 1}, {1, 1, 1}, {1, 1, 1, 1}}

Answer 4

Gaia, 7 bytes

ẏ¦”@)⊃e

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ẏ¦ does just about the same thing here as L€ in Jelly. ẏ is "is positive?" and ¦ is map, which also implicitly casts an integer to the range 1 .. n before mapping. And since we're dealing with only integers >= 1, ẏ will result in 1 for each.

ẏ¦”      Push the string "ẏ¦"
   @)    Push the first input+1
     ⊃   Repeat the last character of the string until it's input+1 characters long.
      e  Eval it.

Answer 5

Python 2, 57 55 bytes

^{-1 byte thanks to Jakob
-1 byte thanks to notjagan}

f=lambda a,b:[1]*b*(a<2)or[f(a-1,i+1)for i in range(b)]

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Answer 6

PHP, 134 bytes

for($r=[$argv[2]];$argv[1]--;)($w=array_walk_recursive)($r,function(&$n){$n=range(1,$n);});$w($r,function(&$n){$n=1;});print_r($r[0]);

There may be a shorter approach than the literal one ... but it´s working at least.

Run with -nr and provide a and b as arguments or try it online.

---

For output as in the examples, use echo strtr(preg_replace('#"\d":#','',json_encode($r[0],JSON_NUMERIC_CHECK)),"{}","[]"); (as I do in the TiO) instead of print_r($r[0]);.

Answer 7

JavaScript (ES6), 95 bytes

f=(a,b,r=/\d+/g)=>a--?f(a,b.replace(r,s=>`[${[...Array(+s)].map((_,i)=>++i)}]`)):b.replace(r,1)

<div oninput=o.textContent=f(a.value,b.value)><input type=number min=0 value=0 id=a><input type=number min=0 value=0 id=b><pre wrap id=o>1

I/O is with strings. The best I could do nonrecursively was 100 bytes:

(a,b)=>[...Array(-~a)].reduce(r=>r.replace(/\d+/g,a--?s=>`[${[...Array(+s)].map((_,i)=>++i)}]`:1),b)

Answer 8

Brachylog, 21 bytes

,1{t+₁I&⟦₁ᵐ⁾;I}ⁱ⁽ṡᵐ⁾c

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Conceptually simple, but keeping track of the right level to map the 'range' ⟦ predicate at, takes up almost half the bytes. :(

                 % Implicit input, list [a, b]
,1               % Append iteration index 1 to the list
{           }ⁱ⁽  % Do this iteratively a times, with [b, i] as the initial input
 t+₁I            % Increment iteration index, let this be I
     &⟦₁ᵐ⁾       % Map the "range from 1 to input" predicate on the first part of input
                 %   (b in the first iteration), at depth given by (old) iteration index
          ;I     % Append the incremented index to this, this is the input to next iteration
ṡᵐ⁾              % Take the sign of each element, mapped at depth given by final I
c                % "Concatenate" to remove extra surrounding array

And a recursive solution, just for the heck of it:

24 bytes

{t0&hṡᵐ|t-₁L&h⟦₁ᵐ;Lz↰ᵐ}c

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Answer 9

Jelly, 12 bytes

⁴Ṿ;”L;”€ẋ³¤V

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Just to get things started. I'm pretty sure it would be shorter if I actually did it the way I'm supposed to, so I'm working on that (inb4 ninja'd by someone)

Explanation

⁴Ṿ;”L;”€ẋ³¤V  Main link
 Ṿ            Generate Jelly code that will evaluate to
⁴             The second input
  ;           Concatenate with
   ”L         "L"
     ;        Concatenate with
      ”€ẋ³¤   Niladic Expression
      ”€      "€"
        ẋ     Repeated                times
         ³             <first input>
           V  Jelly-eval it