# choose pivotswap a[1,rand(1,n)]# 2-way partitionk = 1 for i = 2:n, if a[i] < a[1], swap a[++k,i] swap a[1,k]→ invariant: a[1..k-1] < a[k] <= a[k+1..n]# recursive sortssort a[1..k-1] sort a[k+1,n]

- Not stable
- O(lg(n)) extra space (see discussion)
- O(n
^{2}) time, but typically O(n·lg(n)) time - Not adaptive

When carefully implemented, quick sort is robust and has low overhead. When a stable sort is not needed, quick sort is an excellent general-purpose sort -- although the 3-way partitioning version should always be used instead.

The 2-way partitioning code shown above is written for clarity rather than optimal
performance; it exhibits poor locality, and, critically, exhibits
O(n^{2}) time when there are few unique keys.
A more efficient and robust 2-way partitioning method is given in
Quicksort is Optimal
by Robert Sedgewick and Jon Bentley. The robust partitioning produces
balanced recursion when there are many values equal to the pivot,
yielding probabilistic guarantees of O(n·lg(n))
time and O(lg(n)) space for all inputs.

With both sub-sorts performed recursively, quick sort
requires O(n) extra space for the recursion stack
in the worst case when recursion is not balanced. This is exceedingly unlikely to occur, but it can be avoided
by sorting the *smaller* sub-array recursively first; the second sub-array sort is a tail
recursive call, which may be done with iteration instead. With this optimization,
the algorithm uses O(lg(n)) extra space in the worst case.

- Black values are sorted.
- Gray values are unsorted.
- Dark gray values denote the current interval.
- A pair of red triangles mark k and i (see the code).