Quicksort's asymptotic performance for array of [50,...,50,100,...100] Let's have an array where first half are of value 50 and the second half 100. What would be the asymptotic performance when sorting using Quicksort.

I think it it should be $O(n^2)$ as for array of same elements the complexity is $O(n^2)$ and this particular problem could be rewritten as sorting the first half + sorting the second hald $O(2*(\frac{n}{2})^2 + n)$ which is still $O(n^2)$.

But my schoolmates claim it should be $O(n log(n))$.. so which one is correct?
That depends very much on exactly what quicksort variant you use. Perhaps you should take a peek at Sedgewick "Quicksort with equal keys", SIAM J. Comp 6:2 (jun 1977), pp 240-267 (get it here) or Bentley, McIllroy "Engineering a sort function", Software: Practice &amp; Experience 23:11 (nov 1993), pp 1249-1265.