Trying to generate all permutations from array but only getting a small subset

Question

EDIT: I will try to be more clear in this question:

I have this array [1,2,3] and I want to generate all permutations like this:

1,2,3 | 1,3,2 | 3,2,1 | 3,1,2 | 2,3,1 | 2,1,3 | 1 | 1,2 | 1,3 | 2 | 2,3 | 2,1 | 3 | 3,1 | 3,2

Do note that we also want single and double digit permutations, which is not addressed in the proposed duplicate.

I tried to adapt Python code to JavaScript:

function my_permutations(lst) {
if (lst.length == 0) {
    return []
}
if (lst.length == 1) {
    return [lst]
}
var l = []
var m;
var remLst;
for (var i = 0; i < lst.length; i++) {
    m = lst[i]
    remLst = lst.slice(0, i).concat(lst.slice(i + 1))
    my_permutations(remLst).forEach(function(element) {
        l.push([m].concat(element))
    });
}
return l
}

console.log(JSON.stringify(my_permutations([1, 2, 3])))

With the new edit in the code I can get all combination of triplet ! But I want more, I want combination with pairs and singletons. How can I do that ?

So not all possible combinations are generated.

How can I fix this?

Answer 1

Here's a solution

This almost does what you want. The problem is that it contains an empty array :(

function my_permutations(lst) {
  var l = [[]]
  var m;
  var remLst;
  for(var i = 0; i < lst.length; i++) {
    m = lst[i]
    remLst = lst.slice(0, i).concat(lst.slice(i + 1))
    my_permutations(remLst).forEach(function(element){
      l.push([m].concat(element))
    })
  }
  return l
}

console.log(my_permutations([1, 2, 3]))

Here's another way to do it

It's definitely not efficient and uses a lot of new javascript features but I think it's slick.

const rotations = ([l, ...ls], right=[]) =>
  l ? [[l, ...ls, ...right], ...rotations(ls, [...right, l])] : []

const permutations = ([x, ...xs]) =>
  x ? permutations(xs).flatMap((p) => rotations([x, ...p])) : [[]]

const powerset = (xs) =>
  xs.reduce((ys, x) => [...ys, ...ys.map((y) => [x, ...y])], [[]])

const powerPermutations = (xs) =>
  powerset(xs).flatMap(permutations)

console.log(powerPermutations([1, 2, 3]))