Get permutation from the index of the permutation.

permutation2.js

var x=[1,2,3,4,5,6];

function factorial(i) {
  if (!factorial.memorize[i]) {
    factorial.memorize[i] = i * factorial(i-1);
  }
  return factorial.memorize[i];
}
factorial.memorize = {0:1};

function perm(arr, index) {
  for(var start = 0; start<arr.length; ++start) {
    var fac = factorial(arr.length - start  -1),
        swapIndex = Math.floor( index / fac );
    var swapElement = arr.splice( swapIndex + start , 1)[0];
    arr.splice(start, 0 , swapElement);
    index = index % fac;
  }
}

perm(x,0);  // x keeps [1,2,3,4,5,6]
perm(x,719); // x changed to [6,5,4,3,2,1]