Analysis of Red-Black Balancing Rule - GNU libavl 2.0.3
Author: Ben Pfaff

6.1.1 Analysis |

As we were for AVL trees, we're interested in what the red-black balancing rule guarantees about performance. Again, we'll simply state the results:

> A red-black tree with n nodes has height at least log2 (n + 1) but no more than 2 * log2 (n + 1). A red-black tree with height h has at least pow (2, h / 2) - 1 nodes but no more than pow (2, h) - 1.

> For comparison, an optimally balanced BST with n nodes has height ceil (log2 (n + 1)). An optimally balanced BST with height h has between pow (2, h - 1) and pow (2, h) - 1 nodes.

See also: [Cormen 1990], lemma 14.1; [Sedgewick 1998], property 13.8.