# AVL Tree | AVL Tree Example | AVL Tree Rotation

## AVL Tree-

• AVL trees are special kind of binary search trees.
• In AVL trees, height of left subtree and right subtree of every node differs by at most one.
• AVL trees are also called as self-balancing binary search trees.

## Example-

Following tree is an example of AVL tree- This tree is an AVL tree because-

• It is a binary search tree.
• The difference between height of left subtree and right subtree of every node is at most one.

Following tree is not an example of AVL Tree- This tree is not an AVL tree because-

• The difference between height of left subtree and right subtree of root node = 4 – 2 = 2.
• This difference is greater than one.

## Balance Factor-

In AVL tree,

• Balance factor is defined for every node.
• Balance factor of a node = Height of its left subtree – Height of its right subtree

 In AVL tree, Balance factor of every node is either 0 or 1 or -1.

## AVL Tree Operations-

Like BST Operations, commonly performed operations on AVL tree are-

1. Search Operation
2. Insertion Operation
3. Deletion Operation

Also Read- Insertion in AVL Tree

After performing any operation on AVL tree, the balance factor of each node is checked.

There are following two cases possible-

### Case-01:

• After the operation, the balance factor of each node is either 0 or 1 or -1.
• In this case, the AVL tree is considered to be balanced.
• The operation is concluded.

### Case-02:

• After the operation, the balance factor of at least one node is not 0 or 1 or -1.
• In this case, the AVL tree is considered to be imbalanced.
• Rotations are then performed to balance the tree.

## AVL Tree Rotations-

 Rotation is the process of moving the nodes to make tree balanced.

## Kinds of Rotations-

There are 4 kinds of rotations possible in AVL Trees- 1. Left Rotation (LL Rotation)
2. Right Rotation (RR Rotation)
3. Left-Right Rotation (LR Rotation)
4. Right-Left Rotation (RL Rotation)

### Case-01: ### Case-02: ### Case-03: ### Case-04: To gain better understanding about AVL Trees and Rotations,

Watch this Video Lecture Next Article- AVL Tree Properties

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Summary Article Name
AVL Tree | AVL Tree Example | AVL Tree Rotation
Description
AVL Tree in data structure is a self balancing binary search tree. AVL Tree Examples are given. AVL Tree Rotations refer to the process of moving nodes to make the tree balanced.
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Publisher Name
Gate Vidyalay
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