## Discussion

A random initial order is often used to evaluate sorting algorithms
in order to elucidate the "typical" case and to facilitate
mathematical analysis. For some applications, however, this does
not represent the typical case, so conclusions drawn here do not
generalize.

Here we see the vast difference in speed between the O(n^{2})
elementary sorting algorithms (insert, selection, bubble) and
the more advanced algorithms.

## Key

- 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).