AVL trees are a type of self-balancing binary search tree, named after their inventors Georgy Adelson-Velsky and Evgenii Landis. They are designed to maintain a balanced tree structure, ensuring that the heights of the left and right subtrees of any node differ by at most one. This balance property is crucial for guaranteeing efficient search, insertion, and deletion operations, which have a worst-case time complexity of O(log n) in an AVL tree.
The main advantage of AVL trees over regular binary search trees is their ability to prevent the tree from becoming skewed or unbalanced. In a standard binary search tree, if elements are inserted in a sorted or nearly sorted order, the tree can degenerate into a linked list, resulting in O(n) time complexity for operations. AVL trees, on the other hand, automatically rebalance themselves through tree rotations whenever an insertion or deletion causes a violation of the balance property. This ensures that the height of the tree remains logarithmic, maintaining the efficient logarithmic time complexity for all operations.
AVL trees find applications in various scenarios where fast search, insertion, and deletion are required, such as in databases, file systems, and computer graphics. They are particularly useful when the data is frequently modified and needs to be kept sorted. However, the overhead of maintaining the balance property makes AVL trees slightly slower than other self-balancing trees like Red-Black trees for insertions and deletions. Despite this, AVL trees remain a popular choice due to their strict balancing guarantee and relatively simple implementation compared to other self-balancing tree structures.