A Pedagogically Sound yet Efficient Deletion algorithm for Red-Black Trees: The Parity-Seeking Delete Algorithm

Red-black (RB) trees are one of the most efficient variants of balanced binary search trees. However, they have always been blamed for being too complicated, hard to explain, and not suitable for pedagogical purposes. Sedgewick (2008) proposed left-leaning red-black (LLRB) trees in which red links are restricted to left children, and proposed recursive concise insert and delete algorithms. However, the top-down deletion algorithm of LLRB is still very complicated and highly inefficient. In this paper, we first consider 2-3 red-black trees in which both children cannot be red. We propose a parity-seeking delete algorithm with the basic idea of making the deficient subtree on a par with its sibling: either by fixing the deficient subtree or by making the sibling deficient, as well, ascending deficiency to the parent node. This is the first pedagogically sound algorithm for the delete operation in red-black trees. Then, we amend our algorithm and propose a parity-seeking delete algorithm for classical RB trees. Our experiments show that, despite having more rotations, 2-3 RB trees are almost as efficient as RB trees and twice faster than LLRB trees. Besides, RB trees with the proposed parity-seeking delete algorithm have the same number of rotations and almost identical running time as the classic delete algorithm. While being extremely efficient, the proposed parity-seeking delete algorithm is easily understandable and suitable for pedagogical purposes.