Quicksort - conditions that makes it stable

Question

A sorting algorithm is stable if it preserves the relative order of any two elements with equals keys. Under which conditions is quicksort stable?

Quick

Answer 1

Well, it is quite easy to make a stable quicksort that uses O(N) space rather than the O(log N) that an in-place, unstable implementation uses. Of course, a quicksort that uses O(N) space doesn't have to be stable, but it can be made to be so.

I've read that it is possible to make an in-place quicksort that uses O(log N) memory, but it ends up being significantly slower (and the details of the implementation are kind of beastly).

Of course, you can always just go through the array being sorted and add an extra key that is its place in the original array. Then the quicksort will be stable and you just go through and remove the extra key at the end.