What is a self-balancing AVL tree and how is it different from a red-black tree?

A self-balancing AVL tree is a type of binary search tree that automatically maintains its balance during insertions and deletions. It was named after its inventors, Adelson-Velsky and Landis. The balance of an AVL tree is determined by the heights of its left and right subtrees, which should differ by at most 1.

To ensure balance, AVL trees use a technique called rotation. When a node is inserted or deleted, the tree is checked for balance, and if necessary, rotations are performed to restore balance. Rotations involve changing the structure of the tree by rotating nodes around their parent nodes.

On the other hand, a red-black tree is another type of self-balancing binary search tree. It was introduced by Rudolf Bayer in 1972 and later refined by Leonidas J. Guibas and Robert Sedgewick. Red-black trees also maintain balance by using a set of rules and performing rotations when necessary.

The main difference between AVL trees and red-black trees lies in their balancing strategies. AVL trees strictly maintain balance by ensuring that the heights of the left and right subtrees differ by at most 1. This makes AVL trees more rigidly balanced than red-black trees.

Red-black trees, on the other hand, are more relaxed in terms of balance. They allow the heights of the left and right subtrees to differ by at most a constant factor, which is typically 2. This flexibility allows red-black trees to have a slightly faster insertion and deletion performance compared to AVL trees.

Another difference is the number of rotations required to maintain balance. AVL trees may require more rotations compared to red-black trees, as they aim for stricter balance. Red-black trees, with their more relaxed balance requirements, tend to have fewer rotations during insertions and deletions.

In terms of implementation complexity, AVL trees are generally considered more complex than red-black trees. AVL trees require additional bookkeeping to maintain balance factors and perform rotations, while red-black trees only need to maintain color information for each node.

In summary, both AVL trees and red-black trees are self-balancing binary search trees, but they differ in their balancing strategies and the level of balance they aim to achieve. AVL trees provide stricter balance at the cost of increased complexity, while red-black trees offer a more relaxed balance with slightly better performance.