AVL Rotations (LL, RR, LR, RL) šŸŽÆ

beginner
22 min

AVL Rotations (LL, RR, LR, RL) šŸŽÆ

Welcome to our deep dive into AVL Rotations! In this lesson, we'll learn about the four types of AVL rotations (LL, RR, LR, RL) and understand their importance in maintaining the balance of AVL trees.

What are AVL Rotations? šŸ“

AVL rotations are a part of AVL tree's balance factor adjustment. They are used to rearrange the tree structure when a rotating subtree violates the AVL tree's height balance condition.

Understanding AVL Tree Balance šŸ’”

An AVL tree ensures that the height difference between any of its child nodes is no more than 1. When a node is inserted or deleted, this balance might be compromised, leading to unbalanced subtrees.

LL, RR, LR, RL Rotations Explained šŸ’”

LL Rotation šŸ“

A left-left rotation (LL) is performed on a subtree with a left heavy node (a node whose left subtree is taller). In this rotation, the left subtree of the parent node is rotated to become the new root, and the parent node becomes a child of the new root.

python
A / \ B D / \ C E -> B / \ A D / \ C E

RR Rotation šŸ“

A right-right rotation (RR) is performed on a subtree with a right heavy node (a node whose right subtree is taller). In this rotation, the right subtree of the parent node is rotated to become the new root, and the parent node becomes a child of the new root.

python
A / \ B C / \ D E -> C / \ A B / \ D E

LR Rotation šŸ“

A left-right rotation (LR) is performed when a left heavy node has a left heavy left subtree. In this rotation, the left subtree of the left-heavy node is first rotated right, and then the left-heavy node is rotated right.

python
A / \ B D / \ C E / F -> D / \ B A / \ C E / F

RL Rotation šŸ“

An right-left rotation (RL) is performed when a right heavy node has a right heavy right subtree. In this rotation, the right subtree of the right-heavy node is first rotated left, and then the right-heavy node is rotated left.

python
A / \ B D / \ C E / F -> D / \ A B / \ C E / F

Quiz šŸ’”

Quick Quiz
Question 1 of 1

Which rotation is performed when a left-heavy node has a left heavy left subtree?

Practical Applications šŸ’”

AVL rotations ensure that the AVL tree remains balanced, allowing for efficient search, insertion, and deletion operations. They are particularly useful in data structures where fast search, insert, and delete operations are required, such as compilers, operating systems, and databases.

Stay tuned as we dive deeper into AVL tree operations in the following lessons! šŸš€