Generate permutations of multi array

Question

I would like to generate all permutations of elements in a multi array in javascript (or the algorithm):

Input:

[
  ['a', 'b', 'c', 'd'],
  ['e', 'f', 'g'],
  ['h', 'i']
]

Output:

[
  ['a', 'e', 'h'],
  ['a', 'e', 'i'],
  ['a', 'f', 'h'],
  ...
  ['d', 'g', 'i']
]

Note: I don't want the permutations of ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'] because i don't want results like: ['a', 'b', 'c'].

Note2: I'm only interested in solutions that support input of N-dimension array.

Thanks!

Answer 1

If you like functional programming, you can use lift on Array type. In my case, I've used RamdaJS for the sake of simplicity:

const input = [
  ['a', 'b', 'c', 'd'],
  ['e', 'f', 'g'],
  ['h', 'i']
]

const output = R.lift ( ( x, y, z ) => [ x, y, z ] ) ( ...input )

console.log( output )

<script src="https://cdnjs.cloudflare.com/ajax/libs/ramda/0.25.0/ramda.min.js"></script>

Here's a vanilla JavaScript lift3 implementation:

const input = [
  ['a', 'b', 'c', 'd'],
  ['e', 'f', 'g'],
  ['h', 'i']
]

const flatten = array => [].concat.apply ( [], array )

// Array#flatMap please! ;-)
const ap = funs => array => flatten ( funs.map ( f => array.map ( f ) ) )

const lift3 = f => array1 => array2 => array3 => 
                ap ( ap ( array1.map ( f ) ) ( array2 ) ) ( array3 )

const output = lift3 ( x => y => z => [ x, y, z ] ) ( input[0] ) ( input[1] ) ( input[2] )

console.log( output )