AVL Trees

AVL trees are a type of self-balancing binary search tree. They were invented by Adelson-Velsky and Landis in 1962. AVL trees are used to store data in a way that allows for efficient searching, insertion, and deletion. AVL tress are used in a variety of applications, including databases, file systems, and network routing.

Searching in AVL Trees

Searching for a value in an AVL tree is similar to searching for a value in a binary search tree. The search process starts at the root of the tree and compares the value of the search key to the value of the root node. If the search key is less than the value of the root node, then the search continues in the left subtree of the root node. If the search key is greater than the value of the root node, then the search continues in the right subtree of the root node. This process continues until the search key is found or until the search reaches a leaf node.

Insertion in AVL Trees

Inserting a value into an AVL tree is more complex than searching for a value in an AVL tree. When a value is inserted into an AVL tree, the tree must be rebalanced to maintain its AVL tree property. The rebalancing process involves rotating the tree to maintain the height balance of the tree. There are four types of rotations that can be used to rebalance an AVL tree: left rotation, right rotation, left-right rotation, and right-left rotation.

Deletion in AVL Trees

Deleting a value from an AVL tree is also more complex than searching for a value in an AVL tree. When a value is deleted from an AVL tree, the tree must be rebalanced to maintain its AVL tree property. The rebalancing process involves rotating the tree to maintain the height balance of the tree. There are four types of rotations that can be used to rebalance an AVL tree: left rotation, right rotation, left-right rotation, and right-left rotation.

Applications of AVL Trees