What is tree rotation and when is it used?

Tree rotation is a process used in computer science to rebalance binary search trees, improving their efficiency.

In more detail, tree rotation is a fundamental operation in computer science that is used to maintain the balance of binary search trees. Binary search trees are a type of data structure that store items in memory. They allow for efficient searching, insertion, and deletion of items. However, when items are inserted or deleted, the tree can become unbalanced, leading to inefficient operations. This is where tree rotation comes in.

Tree rotation is a process that changes the structure of the tree without affecting the in-order traversal of the tree. It involves changing the parent-child relationships between nodes. There are two types of tree rotations: right rotation and left rotation. In a right rotation, the root node becomes the right child of its left child. In a left rotation, the root node becomes the left child of its right child.

Tree rotations are used in various types of self-balancing binary search trees, such as AVL trees and red-black trees. These trees use rotations to ensure that the tree remains approximately balanced, which guarantees that search, insert, and delete operations all run in logarithmic time.

For example, in an AVL tree, after every insertion or deletion, the tree checks the balance factor of each node (the difference in height between the left and right subtrees). If the balance factor of any node is not -1, 0, or 1, the tree performs a rotation to rebalance the tree.

In conclusion, tree rotation is a crucial operation in computer science that helps maintain the efficiency of binary search trees. It's a concept that's fundamental to understanding how data is stored and manipulated in computer systems.