Is this a Permutation of 1..n

Question

Input a non-empty array with \$n\$ positive integers. Test if the input array contains every integer in \$1\cdots n\$.

In case you prefer 0-indexed numbers, you may choose to input an array of non-negative integers, and test if the input array contains every integer in \$0\cdots (n-1)\$ instead. All testcases and formula listed below use 1-index. You may need to adjust them if you choose this option.

Input / Output

Input is an array \$A\$ with \$n\$ positive integers:

$$ A = \left[A_1,\dots,A_n\right] $$ $$ \forall i \in \left[1,\dots,n\right]: A_i>0 $$

Output if input \$A\$ satisfies:

$$ \forall i \in \left[1,\dots,n\right]: i \in A $$

Output would be two distinct values, or truthy vs falsy values (swap meaning of truthy / falsy is allowed).

Rules

• This is code-golf, shortest code wins. And since this is code-golf, don't worry about time / memory complexity of your code. You may even timeout on TIO as long as your program works when giving it more time to run.

Testcases

Truthy

1
1,2
2,1
1,3,2
3,1,2
1,2,3,4,5,6,7,8,9,10,11,12
12,11,10,9,8,7,6,5,4,3,2,1
6,3,8,12,1,10,4,2,7,9,5,11
16,37,14,15,23,8,29,35,21,6,5,34,38,9,36,26,24,32,28,7,20,33,39,12,30,27,40,22,11,41,42,1,10,19,2,25,17,13,3,18,31,4

Falsy

2
12
1,1
1,3
2,3
3,3
2,1,3,2
1,4,3,1
4,1,2,4
1,2,2,5,5
1,3,3,3,5
8,7,5,3,4,1,6
5,7,1,4,6,1,8,3
6,3,5,4,7,1,8,1,2
6,5,3,8,2,7,9,4
1,1,1,1,1,1,1,1
1,5,9,13,11,7,3
14,6,12,4,10,8,16,2
34,33,38,17,35,11,36,31,28,14,6,15,18,2,19,40,29,41,9,1,27,23,20,32,26,25,37,8,13,30,39,7,5,3,21,4,11,16,10,22,12,24
38,27,20,23,31,6,2,24,21,31,33,7,26,12,14,17,3,2,28,31,5,23,28,27,37,32,7,39,22,6,35,42,19,3,35,17,35,40,22,13,27,7

Answer 1

Lua, 64 bytes

load't=...table.sort(t)for i=1,#t do b=b or i~=t[i]end return b'

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Truthy and falsy values are swapped.

Answer 2

Pascal, 134 Bytes

This function requires a processor supporting Extended Pascal as defined by ISO standard 10206 (level 1).

type Z=integer;function f(A:array[p..q:Z]of Z):Boolean;var S:set of Z;i:Z;begin S:=[];for i:=p to q do S:=S+[A[i]];f:=S=[1..q-p+1]end;

Ungolfed:

function f(A: array[minimum..maximum: integer] of integer): Boolean;
var
    members: set of integer value [];
    i: integer;
begin
    { transform an ordered `array` into an unordered `set` }
    for i := minimum to maximum do
    begin
        { form the union of two sets }
        members := members + [A[i]]
    end;
    { analyze: compare `members` to a set of `[1..n]` }
    f := members = [1..(maximum - minimum + 1)]
end;

Evidently, the implementation is index-insensitive.

Answer 3

Kamilalisp, 28 bytes

[≡ $(+ 1)∘⍳∘⍴ ⊼]

Determines whether the sorted vector is equal to the range [1, length(input)].

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Kamilalisp, 24 bytes

[≡ #0 ⍋@⍋]@$(^- 1)

A port of the APL answer.

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Answer 4

C (clang), 47 bytes

Input is a null-terminated array of positive integers

i;f(*a){return!a[i++]?i=0,1:!wcschr(a,i)<f(a);}

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---

C (gcc) -m32, 35 bytes

Requires that you also pass the length

f(a,n){n=!n||wcschr(a,n)*f(a,n-1);}

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Answer 5

Scala 3, 36 30 bytes

l=>l.toSet==(1to l.size).toSet

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Answer 6

RAD, 5 bytes

<≡⍳∘⍴

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 ≡       - Check equality between ...
<        - ... the input vector ...
  ⍳∘     - ... and 1 through ...
   ⍴     - ... the length of the input vector.
   

Answer 7

Arturo, 22 bytes

$[a][=sort a 1..max a]

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Checks whether the input sorted is equal to \$[1..\mathrm{max}(input)]\$.