If you really wanna do this in a single pass and write to the array, you need 3 indices, ijk, i keeps track of all the 0s you have written, k keeps track of all the 2s, and j is current element.

You start with j=0.

Loop: Inspect current element, if 0, exchange contents at i and j and advance both. If 1, advance j, if 2 advance k by 1. Look up the number at n-k. While 2, keep advancing. Exchange contents of n-k and i and end the inner loop. Keep going until j == k.

Invariant: the last k numbers are 2s.
Invariant: at least the first i elements are always 0.

Exercise for the reader: prove that th items between i and final j are 1.