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

Abstract In this paper, we are interested in the number of red nodes in red-black trees. We first present an O ( n 2 log ⁡ 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 ) .