binary tree red black

Red-Black Binary Trees: A Deep Dive into their Complexity and Applications

Red-Black Trees are a type of self-balancing binary search tree, first introduced by Rudolf Bayer in 1972. They are particularly useful in scenarios where a large number of insertions and deletions are performed on the tree, as their balance ensures a guaranteed worst-case time complexity of O(log n) for all operations. This paper explores the complexity of red-black trees, their properties and variations, and their applications in computer science. The structure of a red-black tree is based on the concept of a binary search tree, with the additional constraint that every node is either red or black.