get nth permutation of a string

nth-permutation.js

// (as: Array[Array[A]]) => Array[A]
function flatten (as) {
  return as.reduce((a, b) => a.concat(b), [])
}

// (as: Array[A], a: A) => Array[A]
function without (as, a) {
  const bs = as.slice(0)
  bs.splice(as.indexOf(a), 1)
  return bs
}

// (as: Array[A]) => Array[A]
function permute (as) {
  switch (as.length) {
    case 0: return []
    case 1: return as
    default: return flatten(as.map(a => permute(without(as, a)).map(b => a.concat(b))))
  }
}

// (String) => Array[String]
const permuteString = _ => permute(_.split(''))

// (a: String, n: Number) => String
const nthPermutation = (a, n) => permuteString(a)[n]

console.assert(permuteString(''), [])
console.assert(permuteString('a'), ['a'])
console.assert(permuteString('ab'), ['ab', 'ba'])
console.assert(permuteString('abc'), ['abc', 'acb', 'bac', 'bca', 'cab', 'cba'])

console.assert(nthPermutation('abcd', 6), 'bacd')