Are the lists divisible?

Question

Inspired (with the explanation stolen from) this

Background

Say you have two lists A = [a_1, a_2, ..., a_n] and B = [b_1, b_2, ..., b_n] of integers. We say A is potentially-divisible by B if there is a permutation of B that makes a_i divisible by b_i for all i. The problem is then: is it possible to reorder (i.e. permute) B so that a_i is divisible by b_i for all i? For example, if you have

A = [6, 12, 8]
B = [3, 4, 6]

Then the answer would be True, as B can be reordered to be B = [3, 6, 4] and then we would have that a_1 / b_1 = 2, a_2 / b_2 = 2, and a_3 / b_3 = 2, all of which are integers, so A is potentially-divisible by B.

As an example which should output False, we could have:

A = [10, 12, 6, 5, 21, 25]
B = [2, 7, 5, 3, 12, 3]

The reason this is False is that we can't reorder B as 25 and 5 are in A, but the only divisor in B would be 5, so one would be left out.

Your task

Your task is, obviously, to determine whether two lists (given as input) are potentially divisible. You may take input in any accepted manner, as with output.

Duplicates in the lists are a possibility, and the only size restrictions on the integers are your language. All integers in both lists will be larger than 0, and both lists will be of equal size.

As with all decision-problems the output values must be 2 distinct values that represent true and false.

This is a code-golf so shortest code wins!

Test cases

Input, input => output

[6, 12, 8], [3, 4, 6] => True
[10, 5, 7], [1, 5, 100] => False
[14, 10053, 6, 9] [1,1,1,1] => True
[12] [7] => False
[0, 6, 19, 1, 3] [2, 3, 4, 5, 6] => undefined

Answer 1

Jelly, 5 bytes

Œ!%ḄẠ

Returns 0 for True, 1 for False.

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How it works

Œ!%ḄẠ  Main link. Arguments: A, B (arrays)

Œ!     Generate all permutations of A.
  %    Take each permutation modulo B (element-wise).
   Ḅ   Convert all resulting arrays from binary to integer.
       This yields 0 iff the permutation is divisible by B.
    Ạ  All; yield 0 if the result contains a 0, 1 otherwise.

Answer 2

Husk, 7 6 5 bytes

Saved 2 bytes thanks to @Zgarb

▼▲‡¦P

Takes argents in reverse order and returns 1 for True and 0 for False.

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Explanation

    P     -- Permutations of the first argument
  ‡       -- Deep zip (vectorises function) with second argument
   ¦      --   Does x divide y
 ▲        -- Get the maximum of that list, returns [1,1...1] if present
▼         -- Get the minimum of that list, will return 0 unless the list is all 1s

Answer 3

05AB1E, 7 bytes

Input: takes lists B and A (reversed order)
Output: 1 when true, 0 otherwise

œvIyÖPM

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Explanations:

œvIyÖPM    Complete program
œ          Pushes all permutations of B as a list
 v         For each permutation
  I        Pushes last input on top of the stack
   yÖ      Computes a % b == 0 for each element of A and B
     P     Pushes the total product of the list
      M    Pushes the largest number on top of the stack

Answer 4

MATL, 8 7 6 bytes

1 byte off using an idea from Dennis' Jelly answer

Y@\!aA

Inputs are B, then A. Output is 0 if divisible or 1 if not.

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Explanation

Y@     % Implicit input: row vector B. Matrix of all permutations, each on a row
\      % Implicit input: row vector A. Modulo, element-wise with broadcast. Gives
       % a matrix in which each row contains the moduli of each permutation of B
       % with respect to A
!a     % True for rows that contain at least a nonzero value
A      % True if all values are true. Implicit display

Answer 5

Mathematica, 52 bytes

Cases[Permutations@#2,p_/;And@@IntegerQ/@(#/p)]!={}& 

thanks @ngenisis for -5 bytes

Answer 6

JavaScript (ES6), 67 63 bytes

Returns a boolean.

f=([x,...a],b)=>!x||b.some((y,i)=>x%y?0:f(a,c=[...b],c[i]=1/0))

Test cases

f=([x,...a],b)=>!x||b.some((y,i)=>x%y?0:f(a,c=[...b],c[i]=1/0))

console.log(f([6, 12, 8],[3, 4, 6]))        // true
console.log(f([10, 5, 7],[1, 5, 100]))      // false
console.log(f([14, 10053, 6, 9],[1,1,1,1])) // true
console.log(f([12],[7]))                    // false

Answer 7

Haskell, 79 74 68 62 61 bytes

import Data.List
f a=any((<1).sum.zipWith rem a).permutations

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Saved 1 byte thanks to @nimi

Answer 8

R + combinat, 69 66 58 bytes

-3 bytes thanks to Jarko Dubbeldam

another -8 bytes thanks to Jarko

function(a,b)any(combinat::permn(b,function(x)all(!a%%x)))

oddly, R doesn't have a builtin for generating all permutations. Returns a boolean.

Additionally, with Jarko's second improvement, any coerces the list to a vector of logical with a warning.

Try it online! (r-fiddle)

Answer 9

Mathematica, 42 bytes

MemberQ[Permutations@#2,a_/;And@@(a∣#)]&

Answer 10

C (gcc), 191 bytes

#define F(v)for(i=0;i<v;++i){
#define X if(f(s,n,a,b))return 1
j;f(s,n,a,b,i)int*a,*b;{if(--n){F(n)X;j=i*(n%2);b[j]^=b[n];b[n]^=b[j];b[j]^=b[n];}X;}else{F(s)if(a[i]%b[i])return 0;}return 1;}}

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Usage: f(int size, int size, int *a, int *b)

returns 1 if divisable, 0 otherwise. See example usage on TIO.

(Gotta do permutations the hard way in C, so this is hardly competitive)

Answer 11

Brachylog, 6 bytes

pᵐz%ᵛ0

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The predicate succeeds if the two lists are potentially divisible and fails if they are not.

pᵐ        For some pair of permutations of the two input lists,
  z       for each pair of corresponding elements
   %ᵛ0    the first mod the second is always zero.

Answer 12

Jelly, 7 bytes

Œ!ọẠ€1e

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Factorial complexity in the length of the list.

Answer 13

Pyth - 11 bytes

sm!s%Vdvz.p

Test Suite.

Answer 14

J, 27 bytes

0=[:*/(A.~i.@!@#)@]+/@:|"1[

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Takes the first list as the left argument and the second list as the right.

Answer 15

CJam, 20 17 bytes

:A;e!{A\.%:+!}#W>

Test Version

Function that takes array B as the first argument and array A as the second argument. Note that in the test version I switch the order to A then B.

Answer 16

JavaScript (ES6), 100 bytes

f=(a,b)=>!a[0]||a.some((c,i)=>b.some((d,j)=>c%d<1&f(e=[...a],d=[...b],e.splice(i,1),d.splice(j,1))))

Somewhat inefficient; an extra & would speed it up.

Answer 17

Python 2, 90 bytes

lambda a,b:any(sum(map(int.__mod__,a,p))<1for p in permutations(b))
from itertools import*

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Answer 18

PHP, 112 180 178 bytes

I was thinking too short.

function($a,$b){for($p=array_keys($b);++$i<count($b);){foreach($b as$k=>$x)$f|=$a[$k]%$x;if($f=!$f)return 1;$p[$i]?[$b[$j],$b[$i],$i]=[$b[$i],$b[$j=$i%2*--$p[$i]],0]:$p[$i]=$i;}}

anonymous function takes two arrays, returns NULL for falsy and 1 for truthy.
Throws an error if second array contains 0.

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Answer 19

Perl 6, 38 bytes

Actually @nwellnhof's answer seems to be too much readable, so I set out to follow the fine Perl tradition of write-only code :—).

1 byte saved thanks to @nwellnhof.

{min max (@^a,) XZ%% @^b.permutations}

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What does it do: It's an anonymous function that takes two list arguments. When we say @^a, we mean the first one, when @^b, it's the second one.

(@^a,) is a list containing the list @^a. @^b.permutations is the list of all the permutations of @^b. The "XZ%%" operator makes all possible pairs of that one list on the left and all the permutations on the right, and uses the operator "Z%%" on them, which is the standard "zip" operation using the divisibility operator %%.

The max operator gives the largest element of the list (in this case, it's the list that has the most True's in it). We then reduce it using the logical AND operator to see if all elements of that "most true" list are true, and that's the result. It's nearly exact copy of what @nwellnhof wrote, just using obscure operators to shave off bytes.

Answer 20

Factor + math.combinatorics math.unicode, 49 bytes

[ <permutations> [ v/ [ ratio? ] ∄ ] with ∃ ]

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• <permutations> [ ... ] with ∃ Is there any permutation of the second input where...
• v/ ...the quotient of the first input and the permutation...
• [ ratio? ] ∄ ...contains no ratios? (In other words, are they all integers?)

Answer 21

Vyxal, 7 bytes

Ṗ$vḊvAa

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Answer 22

Python 2, 92 bytes

lambda a,b:any(all(x%y<1for x,y in zip(a,p))for p in permutations(b))
from itertools import*

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Yer basic implementation.

Answer 23

Ruby, 56 bytes

->x,y{x.permutation.any?{|p|p.zip(y).all?{|a,b|a%b==0}}}

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Fairly straightforward, exploits the fact that permutation exists.

Answer 24

Scala, 60 Bytes

Golfed:

a=>b=>b.permutations exists(a zip _ forall(p=>p._1%p._2==0))

Ungolfed:

a=>b=>         // Function literal taking 2 lists of integers, a and b.
b.permutations // All permutations of b.
exists(        // Whether the given function is true for any element.
a zip _        // Zips a and the current permutation of b into a list of pairs.
forall(        // Whether the given function is true for all elements.
p=>            // Function literal taking a pair of integers.
p._1%p._2==0)) // If the remainder of integer division between the members of the pair is 0.

Answer 25

Japt, 12 11 bytes

Outputs true or false.

Vá de@gY vX

Test it

---

Explanation

Implicit input of arrays U & V (A & B, respectively)

Vá

Generate an array of all permutations of V.

d

Check if any of the elements (sub-arrays) return true.

e@

Check if every element in the current sub-array returns true when passed through the following function, with X being the current element and Y the current index.

gY

Get the element in U at index Y.

vX

Check if it's divisible by X.