Consider a sequence $s$ of $n$ integers (let's ignore the specifics of their representation and just suppose we can read, write and compare them in O(1) time with arbitrary positions). What's known about the worst-case time complexity of producing a sequence of all distinct elements in $s$, in any order?
By randomized hashing, one can do this in expected $O(n)$. On the upper bound side, one may sort the elements, then produce the output in a single pass by only copying elements which differ from their predecessors to the output - for a total time of $O(n \log(n))$.
But can one do better than $O(n \log(n) )$ deterministically?
Note: This is sort-of a "remove duplicates" problem, but since the order is not preserved I'm not sure it should be called that.