What is an AVL tree?

An AVL tree, named after its inventors Adelson-Velsky and Landis, is a self-balancing binary search tree. It is designed to maintain its balance by ensuring that the heights of its left and right subtrees differ by at most 1. This balance property helps in achieving efficient search, insertion, and deletion operations.

In an AVL tree, each node contains a key and pointers to its left and right child nodes. The keys in the left subtree are smaller than the key in the current node, while the keys in the right subtree are greater. This property allows for efficient searching within the tree.

To maintain balance, AVL trees use rotations to adjust the structure whenever an insertion or deletion causes the heights of subtrees to become imbalanced. There are four types of rotations: left rotation, right rotation, left-right rotation, and right-left rotation. These rotations help in preserving the balance of the tree and ensuring that the height difference between the left and right subtrees remains within the allowed limit.

The balance factor of a node in an AVL tree is defined as the difference between the heights of its left and right subtrees. It can have three possible values: -1, 0, or 1. If the balance factor of any node is outside this range, the tree is considered unbalanced, and rotations are performed to restore balance.

The main advantage of AVL trees is their efficient time complexity for search, insertion, and deletion operations, which is O(log n) in the worst case. This makes them suitable for applications that require frequent dynamic updates and fast retrieval of data.

However, the AVL tree's self-balancing mechanism comes with a cost. The rotations required to maintain balance can be computationally expensive, especially during frequent updates. Additionally, the extra space required to store balance factors for each node increases the memory overhead.

Overall, AVL trees provide a balance between efficient search operations and maintaining a balanced structure, making them a popular choice for various applications where both search and dynamic updates are crucial.