dynamic efficiency: algorithms for maintaining binary search trees

A Binary Search Tree (BST) optimizes search operations by organizing data for fast lookups, insertions, and deletions. Various balancing algorithms, including single and double rotations, have been developed to maintain this efficiency. While double rotations are effective, they consume more computational resources, potentially impacting system performance in environments with frequent searches.Evaluations of different algorithms for dynamically maintaining BSTs focus on unpredictable search patterns, managing tasks like inserting new nodes and restructuring the tree to reduce path length and search time. Height-Balanced Trees, such as AVL Trees, keep minimal height differences between subtrees for efficient searches, while Bounded-Balance Trees, like Red-Black Trees, allow more relaxed balancing for specific operations.Hybrid algorithms blend features of both tree types for enhanced performance. The paper presents a novel method that improves upon double rotations, achieving similar balancing results with nearly half the computational steps. This advancement promises to significantly enhance BST maintenance efficiency and overall system performance in dynamic search environments.