A note on the largest number of red nodes in red-black trees

In this paper, we are interested in the number of red nodes in red-black trees. We first present an O(n2log⁡n) time dynamic programming solution for computing r(n), the largest number of red internal nodes in a red-black tree on n keys. Then the algorithm is improved to some O(log⁡n) time recursive and nonrecursive algorithms. Based on these improved algorithms we finally find a closed-form solution of r(n).