AVL trees are self-balancing binary search trees that maintain their balance through rotations, ensuring O(log n) time complexity for search, insertion, and deletion operations.

AVL trees are a specialized type of self-balancing binary search tree (BST) named after their inventors, Georgy Adelson-Velsky and Evgenii Landis. The key characteristic that distinguishes AVL trees from regular binary search trees is their self-balancing property, which ensures that the heights of the two child subtrees of any node differ by no more than one. This balance is maintained through a series of rotations during insertion and deletion operations.

The primary advantage of AVL trees is that they provide guaranteed O(log n) time complexity for search, insertion, and deletion operations, which is a significant improvement over unbalanced binary search trees that can degrade to O(n) time complexity in the worst case (when the tree resembles a linked list).

When a new node is inserted or deleted, the AVL tree checks the balance factor (the difference between the heights of the left and right subtrees) and performs rotations (single or double) as necessary to restore balance. For example, a single right rotation is performed when a left-heavy tree needs to be balanced after an insertion in the left subtree. Conversely, a double rotation is necessary when the left subtree is right-heavy.

AVL trees are particularly useful in applications where frequent insertions and deletions occur, and maintaining a balanced tree structure is critical for performance. Understanding AVL trees is essential for algorithm designers and software engineers looking to optimize search operations and improve the efficiency of their data structures.