What is the concept of AVL trees and their operations?

AVL trees are self-balancing binary search trees that maintain their balance by ensuring that the heights of the left and right subtrees differ by at most 1. This balance is achieved through rotations, which are the main operations performed on AVL trees.

The operations on AVL trees include:
1. Insertion: When a new node is inserted into the AVL tree, the tree is rebalanced if necessary to maintain the AVL property. This is done by performing rotations to restore balance.
2. Deletion: When a node is deleted from the AVL tree, the tree is rebalanced if necessary to maintain the AVL property. Similar to insertion, rotations are performed to restore balance.
3. Searching: AVL trees support efficient searching for a given key. The tree is traversed by comparing the key with the current node and moving left or right accordingly until the key is found or the end of the tree is reached.
4. Traversals: AVL trees can be traversed in different orders, such as in-order, pre-order, and post-order. These traversals allow accessing the elements of the tree in a specific order.

The concept of AVL trees and their operations ensure that the tree remains balanced, which leads to efficient search, insertion, and deletion operations with a time complexity of O(log n), where n is the number of nodes in the tree.