A note on the largest number of red nodes in red-black trees
Yingjie Wu, Daxin Zhu, Lei Wang, Xiaodong Wang

TL;DR
This paper investigates the maximum number of red nodes in red-black trees, developing efficient algorithms and a closed-form formula to compute this maximum for any number of keys.
Contribution
It introduces improved algorithms and derives a closed-form expression for the maximum red nodes in red-black trees, advancing understanding of their structure.
Findings
Developed an $O(n^2 \log n)$ dynamic programming solution.
Created $O(\log n)$ time recursive and nonrecursive algorithms.
Derived a closed-form formula for the maximum number of red nodes.
Abstract
In this paper, we are interested in the number of red nodes in red-black trees. We first present an time dynamic programming solution for computing , the largest number of red internal nodes in a red-black tree on keys. Then the algorithm is improved to some time recursive and nonrecursive algorithms. Based on these improved algorithms we finally find a closed-form solution of .
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Taxonomy
TopicsAdvanced Graph Theory Research · Algorithms and Data Compression
