An AVL tree, named after its inventors Adelson-Velsky and Landis, is a self-balancing binary search tree used in computer science. The key characteristic that distinguishes AVL trees from other binary search trees is their self-balancing nature. For any node in an AVL tree, the heights of the two child subtrees differ by at most one. If at any time the height difference exceeds one, rebalancing is performed to restore this property[7].
The AVL tree maintains its balance through rotations, which are operations that adjust the structure of the tree to ensure that the height difference condition is met. This self-balancing property ensures that the tree remains approximately balanced, preventing the tree from becoming skewed. A skewed tree would have poor performance for operations such as insertion, deletion, and lookup, potentially degrading to O(n) in the worst case, where n is the number of nodes in the tree. The AVL tree, by maintaining its balance, ensures that these operations can be performed in O(log n) time, where n is the number of nodes in the tree, making it efficient for various applications[7][8].
The balance of an AVL tree is maintained through four types of rotations: single left, single right, left-right, and right-left. These rotations are applied based on the imbalance detected during insertion or deletion operations. The balance factor of each node, which is the difference in heights between the left and right subtrees, is used to determine the type of rotation needed. The balance factor can be -1, 0, or +1, ensuring that the tree remains balanced[11].
AVL trees are particularly useful in applications that require frequent and fast lookup operations, such as databases and in-m...
