AVL Tree Data Structure: A Complete End-to-End Guide

Introduction

GM Adelson-Velsky and EM Landis invented the AVL tree data structure in 1962. This tree is named AVL in memory of its inventors. A height-balanced binary search tree is known as An AVL tree is. Each node is related to a balance factor, estimated by subtracting the height of its right subtree from that of its left subtree.

An AVL tree is considered balanced when the balance factor of each node falls within its range of -1 to 1; otherwise, this AVL tree data structure is deemed unbalanced and requires balancing.

What is the AVL Balance Factor?

A Balance element of a node in an AVL tree is the distinction between the height of the left subtree and that of the right subtree of that code. Balance Factor = (Height of the Subtree - Height of the Right Subtree) or (Height of Right Subtree - The height of Left subtree). Moreover, the balance factor maintains its self-balancing property, and its value should always be -1, 0 + 1.

What are the Operations of AVL Tree Data Structure?

Since AVL trees are a type of binary search tree, their operations, such as searching and traversing, follow the same principles as those in a binary search tree without compromising the AVL tree's properties. 

However, insertion and deletion operations can potentially disrupt these properties, necessitating special attention during these operations.

Why an AVL Tree?

An AVL tree manages the height of the binary search tree by not allowing it be skewed. Also, the time for all operations in a binary search tree of height h is noted as O (h). However, it can also be expanded to O(n) if the BST is skewed (i.e., worst case).

Lastly, by limiting this height to log n, an AVL tree data structure would impose an upper bound on each of its operations to be O(log n); n is the number of nodes.

AVL Rotations

If Balance Factor other than -1, 0, and 1, then we should perform rotation in an AVL tree data structure. Further, there are four types of rotations, which are as follows:

• LL Rotation: The inserted node would be in the left subtree of the left subtree of A.
• RR Rotation: An inserted node is in the right subtree of the right subtree of A.
• LR Rotation: The inserted node would be in the right subtree of the left subtree of A.
• RL Rotation: An inserted subtree node is in the left node of the right subtree of A.

For a tree to be unbalanced, at least one node must have a height difference of at least two levels between its left and right subtrees.

RR Rotations

When a binary search tree becomes unbalanced because a new node is inserted into the right subtree of the right subtree of a specific node A, we need to perform what is called an RR rotation. This rotation is like a counter-clockwise turn and is used when a node's balance factor becomes -2. In simpler terms, if a node becomes too heavy on its right side and then a new node is added to the right side of that right side, we perform an RR rotation to rebalance the tree. 

In the given scenario, node A has a balance factor of -2 because node C was inserted into the right subtree of A's right subtree. So, to fix the imbalance, we apply the RR rotation specifically on the edge below node A.

LL Rotations

When a BST becomes unbalanced due to one of the nodes inserted in the left subtree of the left subtree of C, when we perform an LL rotation, as it is a clockwise rotation, that is applied on the edges below any node having a balance factor 2.

LR Rotations

Double rotations are more complicated than single rotations. LR rotation involves two steps: first, we do an RR rotation on a subtree, and then an LL rotation on the entire tree. By "entire tree," we mean starting from the first node along the path of the inserted node whose balance factor is not -1, 0, or 1. So, LR rotation is like doing an RR rotation first on a more minor part of the tree and then doing an LL rotation on the more significant part to balance it out.

RL Rotations

Double rotations are more complex than single rotations. RL rotation involves two steps: first, we perform an LL rotation on a subtree, and then an RR rotation on the entire tree. By "entire tree," we mean starting from the first node along the path of the inserted node whose balance factor is not -1, 0, or 1. So, in simpler terms, RL rotation is like doing an LL rotation first on a more minor part of the tree and then doing an RR rotation on the more significant part to balance it out.

Practical Examples in AVL Tree Data Structure

Let us construct an AVL tree with the following elements:

Insert H, I, and J

The binary search tree can become unbalanced when we add new elements, like the one mentioned. For instance, the tree becomes unbalanced when adding H because H's balance factor is -2. This happens when the tree is leaning too much to the right. To fix this, we perform an RR Rotation specifically to node H to rebalance the tree.

Insert B, A

When we add the mentioned elements, particularly A, to the binary search tree, it becomes unbalanced because the balance factor of H and I is 2. We focus on the first node from the last one we inserted, H. Seeing that the tree leans too much to the left from H, we perform an LL Rotation specifically on node H to rebalance the tree.

Insert E

When we add E to the binary search tree, it becomes unbalanced because the balance factor of I is 2. This happens because E is inserted into the left and right subtrees of I. To fix this, we perform an LR Rotation on node I. This rotation involves doing an RR Rotation first, followed by an LL Rotation.

Advantages of an AVL Tree Data Structure

AVL trees offer several benefits; read through this section to understand a few benefits of AVL tree data structure.

• One of the main advantages of the AVL tree is that it can self-balance itself.
• Moreover, it is not skewed.
• Thirdly, it provides a faster lookup than a Red-Black tree
• It has a better searching time complexity than other trees, such as a binary tree.
• In this data structure, the height cannot exceed log(N) where N is the number of total nodes in the tree.

However, despite these advantages, AVL trees also have their drawbacks. Now, let us understand the disadvantages of an AVL tree algorithm.

Disadvantages of an AVL Tree Algorithm

Apart from the above-mentioned advantages, the AVL tree algorithm has a few drawbacks, some of which are mentioned in the section below.

• They are hard to put into practice.
• Some operations take a lot of effort.
• They are less popular than Red-Black trees.
• Because they need to stay perfectly balanced, adding or removing things from AVL trees can get tricky and require more steps.
• Balancing them out takes more computing power.
  

Few AVL Tree Applications

Let's understand the practical applications and contexts in which AVL trees play a crucial role in efficiently organizing and retrieving data.

• Organizing large databases makes it easier to find specific records.
• Managing collections of data in computer memory, like sets and dictionaries.
• In database programs, where adding or removing data does not happen often, but searching does.
• Software that needs to search through data quickly and efficiently.
• They are used in business settings and certain video games with complex storylines.
  

Wrapping Up

This blog gives a comprehensive guide to the AVL tree data structure, covering all aspects from its definition to its implementation. AVLs in systems and computer science are valuable tools for understanding and optimizing trees.

FAQs

1. What is the AVL tree condition?

The condition of an AVL tree is that it always stays balanced. This means that the difference in height between the left and right subtrees of any node can't be more than 1 level.

2. What is the difference between AVL and BST?

AVL trees are a class of binary search tree (BST), but they have an extra rule—they stay balanced. Regular BSTs do not necessarily stay balanced, which can sometimes make searching slower.

3. What are the AVL tree and B-tree in the data structure?

It is a binary search tree that keeps itself balanced. A B-tree is another type of tree structure that is often used in databases. They are excellent for storing and searching data, but they work differently.

4. Why is the AVL tree used?

AVL trees are used because they keep data organized and quickly found. They remain balanced automatically, which means searching for stuff in them is fast, even when there is a lot of data.

5. What are the properties of AVL?

The main property of AVL trees is that they stay balanced. This means that the height difference between the left and right subtrees of any node is always less than or equal to 

6. Why is AVL better than BST?

AVL trees are often considered better than regular BSTs because they are always balanced. This makes searching for stuff in them faster, especially when there is a lot of data.

7. Is AVL a binary tree?

Yes, AVL trees are a type of binary tree. They are like a special kind of binary tree that automatically stays balanced.