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).
@article{arxiv.1406.3092,
title = {A note on the largest number of red nodes in red-black trees},
author = {Yingjie Wu and Daxin Zhu and Lei Wang and Xiaodong Wang},
journal= {arXiv preprint arXiv:1406.3092},
year = {2014}
}