Sorting an array that consists of a small number of unique keys is common in practice. One would like an algorithm that adapts to O(n) time when the number of unique keys is O(1). In this example, there are 4 unique keys.

The traditional 2-way partitioning quicksort exhibits its
worse-case O(n^{2})
behavior here. For this reason, any quicksort
implementation should use 3-way partitioning, where the
array is partitioned into values less than, equal, and greater
than the pivot. Because the pivot values need not be sorted
recursively, 3-way quick sort adapts to O(n) time in this case.

Shell sort also adapts to few unique keys, though I do not know its time complexity in this case.

- Black values are sorted.
- Gray values are unsorted.
- A red triangle marks the algorithm position.
- Dark gray values denote the current interval (shell, merge, quick).
- A pair of red triangles marks the left and right pointers (quick).