Explain any two rotations performed on an AVL tree with the he* of example.

 

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-

AVL Tree Operations-

Like BST Operation commonly performed operations on AVL tree are-

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

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-

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)

Cases Of Imbalance And Their Balancing Using Rotation Operations-

Case-01:

Case-02:

Case-03:

Case-04: