How can I sort only the integers in this Javascript array of strings and integers?

There are a few possible strategies.

Use an array of indices so that you have a layer of indirection -- create an array [0, 1, 2, 3, 4, 5, ...] and sort that with a custom comparator that dereferences 3 to array[3]. The dereferencing comparator might not obey the transitive property though so you run into undefined behavior. O(n) extra memory required.

var array = [6, 3, 18, 'four', 8, 'five', 6, 'nineteen', 'eight', 'two'];

// Create an array of indices.
var indices = [];
for (var i = array.length; --i >= 0;) { indices[i] = i; }
// indices is [0, 1, 2, 3, 4, 5, 6, 7, 8, 9];

// Sort the indices, comparing by number of corresponding element iff
// corresponding elements are both numbers.
indices.sort(function (i, j) {
  var a = array[i], b = array[j];  // dereference
  if (a === (a | 0) && b === (b | 0)) {
    return a === b ? 0 : a < b ? -1 : 1;
  } else {
    return i - j;
  }
});

var newArray = [];
for (var i = array.length; --i >= 0;) { newArray[i] = array[indices[i]; }

array = newArray;

The other class of solutions is to extract the numbers, sort, and then replace which requires O(n) extra memory worst-case.

var array = [6, 3, 18, 'four', 8, 'five', 6, 'nineteen', 'eight', 'two'];

var integers = array.filter(function (x) { return x === (x | 0); });
integers.sort();

for (var i = 0, k = 0; k < integers.length; ++i) {
  if (array[i] === (array[i] | 0)) { array[i] = integers[k++]; }
}

Well, this question was pretty confusing, but after some thought, it seems to me that it's not possible to sort the array the way I was hoping to.

The best solution I came up with is to sort the items as they are added to the list, maintaining a valid array at every step in the process instead of trying to sort after the fact.

Feel free to post other answers. I'd love to see what people come up with. It's an interesting problem.

You can use isNaN(). If it is a true number (3) instead of a string of a number ("3") then it will return true.

Then you can just place them in separate arrays or whatever way you would prefer to perform the sorting.