What is the worst case scenario for quicksort?

Question

When does the quicksort algorithm take O(n^2) time?

Answer 1

Quicksort works by taking a pivot, then putting all the elements lower than that pivot on one side and all the higher elements on the other; it then recursively sorts the two sub groups in the same way (all the way down until everything is sorted.) Now if you pick the worst pivot each time (the highest or lowest element in the list) you'll only have one group to sort, with everything in that group other than the original pivot that you picked. This in essence gives you n groups that each need to be iterated through n times, hence the O(n^2) complexity.

The most common reason for this occurring is if the pivot is chosen to be the first or last element in the list in the quicksort implementation. For unsorted lists this is just as valid as any other, however for sorted or nearly sorted lists (which occur quite commonly in practice) this is very likely to give you the worst case scenario. This is why all half-decent implementations tend to take a pivot from the centre of the list.

There are modifications to the standard quicksort algorithm to avoid this edge case - one example is the dual-pivot quicksort that was integrated into Java 7.