What are AVL trees? How do they differ from Splay trees.

Question

27 Apr 2023

Answer :

Word Count : 1283

An AVL tree, named after its inventors Adelson-Velsky and Landis, is a self-balancing binary search tree (BST) in which the difference between the heights of the left and right subtrees of any node is at most one. This balancing condition ensures that the tree remains balanced after insertions and deletions, thereby providing efficient search, insertion, and deletion operations.

### AVL Tree Properties

An AVL tree is a type of binary search tree where, for every node in the tree, the difference between the heights of the left and right subtrees (called the balance factor) is constrained to be between -1 and 1. This is mathematically represented as:

\[
\text{Balance Factor} = \text{Height of Left Subtree} - \text{Height of Right Subtree}
\]

The balance factor can have one of the following values:
- 0: The heights of the left and right subtrees are equal.
- 1: The left subtree is one level taller than the right.
- -1: The right subtree is one level taller than the left.

If the balance factor of any node becomes less than -1 or greater than 1, the tree is unbalanced, and it requires rebalancing.

### Balancing in AVL Trees

To maintain the AVL property, the tree is balanced after every insertion or deletion. This balancing is achieved using rotations, which are classified as:

1. Single Right Rotation (Right-Right case): This occurs when a node becomes unbalanced due to an insertion in the right subtree of the right child. A right rotation fixes this imbalance.

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