Introduction to AVL Tree and how to calculate tree height, insert and delete node hence how to rotate if the tree become unbalance.

1. AVL (Adelson-Velskii
& Landis) Tree
.
Presented By
Sana Rahim

2. AVL Tree
A balanced binary search tree where
the height of the two subtrees
(children) of a node differs by at most
one. Look-up, insertion, and deletion
are O( log n), where n is the number of
nodes in the tree

3. Definition of height
Height: the length of the longest
path from a node to a leaf.
 All leaves have a height of 0
 An empty tree has a height of –1

4. AVL Rotations
To balance itself, an AVL tree may perform the following four
kinds of rotations
• Left rotation
• Right rotation
• Left-Right rotation
• Right-Left rotation

5. Insertion
14
17
11
7 53
4
14,
17,
11,
7,
53,
4,
13
13

6. 14
17
7
4 53
11
13
Right Rotation
11
7
4

7. Insert: 12
14
17
7
4
53
11
13
12

8. First left Rotation then Right:
14
17
7
4
53
11
12
13

9. AVL tree is balanced.
14
17
7
4 53
12
13
11

10. Deletion of Node
14
17
7
4
53
11
12
8 13

11. Unbalanced
14
17
7
4
11
12
8 13

12. Balanced!
14
17
7
4
11
12
8
13

13. Questions