Generate permutations of JavaScript array

Question

I have an array of n different elements in javascript, I know there are n! possible ways to order these elements. I want to know what's the most effective (fastest) algorithm to generate all possible orderings of this array?

I have this code:

var swap = function(array, frstElm, scndElm) {

    var temp = array[frstElm];
    array[frstElm] = array[scndElm];
    array[scndElm] = temp;
}

var permutation = function(array, leftIndex, size) {

    var x;

    if(leftIndex === size) {

        temp = "";

        for (var i = 0; i < array.length; i++) {
            temp += array[i] + " ";
        }

        console.log("---------------> " + temp);

    } else {

        for(x = leftIndex; x < size; x++) {
            swap(array, leftIndex, x);
            permutation(array, leftIndex + 1, size);
            swap(array, leftIndex, x);
        }
    }
}

arrCities = ["Sidney", "Melbourne", "Queenstown"];
permutation(arrCities, 0, arrCities.length);

And it works, but I guess swapping every item to get the combinations is a bit expensive memory wise, I thought a good way of doing it is just focusing on the indexes of the array and getting all the permutations of the numbers, I'm wondering if there's a way of computing all of them without having to switch elements within the array? I guess recursively is possible to get all of them, I need help to do so.

So for example if I have:

arrCities = ["Sidney", "Melbourne", "Queenstown"];

I want the output to be:

[[012],[021],[102],[120],[201],[210]]

or:

[[0,1,2],
 [0,2,1],
 [1,0,2],
 [1,2,0],
 [2,0,1],
 [2,1,0]]

I'm reading this: http://en.wikipedia.org/wiki/Permutation#Algorithms_to_generate_permutations

But Wikipedia has never been good at explaining. I don't understand much of it, I have to say my math level isn't the best.

Answer 1

This function, perm(xs), returns all the permutations of a given array:

function perm(xs) {
  let ret = [];

  for (let i = 0; i < xs.length; i = i + 1) {
    let rest = perm(xs.slice(0, i).concat(xs.slice(i + 1)));

    if(!rest.length) {
      ret.push([xs[i]])
    } else {
      for(let j = 0; j < rest.length; j = j + 1) {
        ret.push([xs[i]].concat(rest[j]))
      }
    }
  }
  return ret;
}

console.log(perm([1,2,3]).join("\n"));