Here is the detailed explanation of Self – Adjusting Tree:

- A self-adjusting tree, also known as a self-balancing tree or dynamic tree, is a type of data structure that automatically adjusts its shape to maintain balance, typically after insertions or deletions of elements.
- The purpose of self-adjusting trees is to ensure efficient operations such as searching, insertion, and deletion by keeping the tree balanced, which helps maintain optimal performance characteristics.

## Types of Self – Adjusting Tree:

There are various types of self-adjusting trees, each with its own balancing mechanism. Some popular self-adjusting trees include:

AVL Tree:

Named after its inventors, Adelson-Velsky and Landis, AVL trees are binary search trees that maintain a balance factor for each node, ensuring that the height difference between the left and right subtrees (the balance factor) is at most one for every node. When an insertion or deletion violates this property, rotations are performed to rebalance the tree.

Red-Black Tree:

Red-black trees are another type of self-adjusting binary search tree where each node is colored either red or black. They enforce several properties such as maintaining a balanced black height across the tree and ensuring that no two adjacent red nodes exist. Insertions and deletions in red-black trees are accompanied by color flips and rotations to maintain these properties.

Splay Tree:

Splay trees are a type of binary search tree that perform tree rotations, called “splays,” on nodes to bring frequently accessed elements closer to the root. The idea behind splay trees is to minimize the access time for frequently accessed elements by restructuring the tree based on access patterns.

Treap:

A treap is a combination of a binary search tree and a heap. In a treap, each node has both a key (like in a binary search tree) and a priority (like in a heap). The treap maintains both the binary search tree property and the heap property, and rotations are performed based on priorities to ensure balance.

AVL-Based Trees:

There are variations and extensions of AVL trees, such as AVL-B trees and AVL-B+ trees, which are used for implementing data structures like AVL-based priority queues and AVL-based balanced search trees.