# Finding the period of a recurring element in an array [closed]

Given an array A of integers, there exists at least one positive integer p such that A[i] == A[j] for all i and j for which i % p == j % p == 0. Find the smallest p.

Examples:

• Input array: [1, _, 1, _, 1, _, 1, _, 1]. Output: 2
• Input array: [1, _, _, 1, _, _, 1, _, _]. Output: 3.
• Input array: [1, _, _, _, 1, _, _, _, 1]. Output: 4

## closed as unclear what you're asking by xnor, O.O.Balance, Peter Taylor, Ian Miller, Sriotchilism O'ZaicNov 23 '18 at 17:33

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• Since the only problem is the lack of objective winning criterion, this seems like a good fit for the code-golf tag. – lirtosiast Nov 20 '18 at 17:59
• wha are the _? – Jonah Nov 20 '18 at 19:14
• I take it that _ stands for any entry that isn't 1? And that the array is zero-indexed? – xnor Nov 23 '18 at 3:57
• I was really hopeful that it would be i % p == j % p == N instead, which I think would have been a more interesting challenge – Sparr Nov 23 '18 at 5:31
• This could use more clarity on the quantifiers: I assume that "for all i and j for which" should be "for all i and j which are valid indexes into A and for which". The examples are missing some important corner cases: the empty array, a one-element array, an array of more than one element without repeats. But most importantly, and the reason that I'm voting to close as unclear, either the test suite or the spec is wrong for languages with 1-based indexing. – Peter Taylor Nov 23 '18 at 13:40

# Python 3, 47 bytes

f=lambda l,d=1:f(l,d+1)if~-len({*l[::d]})else d


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# Python 3, 43 bytes

f=lambda l,n=1:2>len({*l[::n]})or-~f(l,n+1)


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Assumes the list is non-empy. Outputs True as 1, though for 1 byte this can be fixed by changing 2> to 1//.

44 bytes:

f=lambda l,n=1:{l[0]}=={*l[::n]}or-~f(l,n+1)


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f=lambda l,n=1:l[:-n:n]==l[n::n]or-~f(l,n+1)


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# Jelly, 6 bytes

Assuming this is meant to be for now.

mJE€TḢ


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• Or mJE€i1. Does posting before the question is clarifed get you the win for tiebreaking purposes? I was hesitant to. – lirtosiast Nov 20 '18 at 19:18
• For me it just means I got to post from a computer rather than a mobile. Most wont upvote until the winning criteria is given anyway. – Jonathan Allan Nov 20 '18 at 19:57

# Pyth, 7 bytes

f!t{%TQ


Try it here. Pyth is at a disadvantage because it uses only printable ASCII; optimally encoded this would be $$\7 * \log_{256} 95 = 5.749\$$ bytes.

f             Find the first positive integer T such that
!t           there is only one element in
{          the list obtained by taking unique elements
%TQ       of every Tth element of the input.


# Java 8, 85 bytes

A lambda from a primitive array type to int.

l->{for(int d=0,i;;)for(i=++d;;i+=d){if(i>=l.length)return d;if(l[i]!=l[i-d])break;}}


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## Ungolfed

l -> {
for (int d = 0, i; ;)
for (i = ++d; ; i += d) {
if (i >= l.length)
return d;
if (l[i] != l[i - d])
break;
}
}


# Japt, 10 bytes

@ëX â ÊÉ}f


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Explanation:

@       }f    :Get the first integer X which returns 0 from:
ëX           : Get every Xth item in the input
â         : Get the unique values of that list
Ê       : Count how many there are
É      : Subtract 1


# Powershell, 82 bytes

(($a=$args)|%{($i++)}|?{"$a"-match"^(\d+)(( -?\d+){$_} \1)*( -?\d+){0,$_}$"})[0]+1  Test script: $f = {

(($a=$args)|%{($i++)}|?{"$a"-match"^(\d+)(( -?\d+){$_} \1)*( -?\d+){0,$_}$"})[0]+1 } @( ,(1 , 1,1,1,1,1) ,(2 , 1,-2,1,3,1,-4,1,5) ,(2 , 1,-2,1,3,1,-4,1,5,1) ,(3 , 1,-2,1,1,3, 4,1,5,1) # 1 may be in place '_' ,(4 , 1,-2,3,4,1, 5,1,6,1) ,(5 , 1,2,3,4,5,1) ) | % {$expected, $a =$_
$result = &$f @a
"$($result-eq$expected):$result"

}


Explanation:

Regexp match on array.toString() which equivalent array.join(' ').

# Python 3, 64 Bytes

A recursive approach.

f=lambda x,s=1:s if x[::s].count(x[0])==len(x[::s])else f(x,s+1)


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# Python 3, 82 81 Bytes

-1 byte thanks to Jakob!

lambda x:[x[::i].count(x[0])==len(x[::i])for i in range(1,len(x)+1)].index(1>0)+1


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• How about 1>0 instead of True? – Jakob Nov 23 '18 at 4:13
• For the recursive approach, you need to initialize s=1 as an optional argument so that the function runs without taking an extra input. – xnor Nov 23 '18 at 5:38

# Japt, 6 bytes

I think this is right, the spec isn't all that clear. Assumes, as the spec would seem to suggest, that the number we're looking for will always appear first in the array and the _s must all be different from that number.

ð¶Ug)æ


Try it

           :Implicit input of array U
ð          :0-based indices of elements
¥         :  Equal to
Ug       :  First element of U
)      :End indexing
æ     :First truthy (non-zero) element