Depending on how the pivot is picked, Quicksort can actually be implemented in O(n lg n) worst-case time.
EDIT: I was going to link a proof for this but it's surprisingly hard to find. IIRC, the idea is to use the median of medians algorithm ([1]) to pick the median for the pivot, and deal with values equal to the pivot by alternatingly placing them in the left and right partition, or alternatively just keep them in a third partition in the middle.
EDIT: I was going to link a proof for this but it's surprisingly hard to find. IIRC, the idea is to use the median of medians algorithm ([1]) to pick the median for the pivot, and deal with values equal to the pivot by alternatingly placing them in the left and right partition, or alternatively just keep them in a third partition in the middle.
[1] https://en.wikipedia.org/wiki/Median_of_medians