In this paper, we are interested in the number of red nodes in red-black
trees. We first present an O(n2logn) 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(logn) time recursive
and nonrecursive algorithms. Based on these improved algorithms we finally find
a closed-form solution of r(n)