The document discusses inserting and removing nodes from an AVL tree through examples. It shows how inserting nodes 14, 17, 11, 7, 53, 4, 13 creates an initially unbalanced tree that is then balanced through subsequent insertions and rotations. It then demonstrates removing nodes 53 and 11, becoming unbalanced, before balancing again. Finally, it provides an exercise to build an AVL tree from values and remove nodes 24 and 20.

1.  Animation PPT
 Insertion with balanced binary tree
 Example with solution
 Exercise Problem
Mrs.R.Sabitha,
Assistant Professor,
Department of Computer Science(SF)
V.V.Vanniaperumal College for Women,
Virudhunagar

2. AVL Tree Example:
• Insert 14, 17, 11, 7, 53, 4, 13 into an empty AVL tree
14
17
11
7 53
4

3. AVL Tree Example:
• Insert 14, 17, 11, 7, 53, 4, 13 into an empty AVL tree
14
17
7
4 53
11
13

4. AVL Tree Example:
• Now insert 12
14
17
7
4 53
11
13
12

5. AVL Tree Example:
• Now insert 12
14
17
7
4 53
11
12
13

6. AVL Tree Example:
• Now the AVL tree is balanced.
14
17
7
4 53
12
13
11

7. AVL Tree Example:
• Now insert 8
14
17
7
4 53
12
13
11
8

8. AVL Tree Example:
• Now insert 8
14
17
7
4 53
11
12
8
13

9. AVL Tree Example:
• Now the AVL tree is balanced.
14
17
7
4
53
11
12
8 13

10. AVL Tree Example:
• Now remove 53
14
17
7
4
53
11
12
8 13

11. AVL Tree Example:
• Now remove 53, unbalanced
14
17
7
4
11
12
8 13

12. AVL Tree Example:
• Balanced! Remove 11
14
17
7
4
11
12
8
13

13. AVL Tree Example:
• Remove 11, replace it with the largest in its left branch
14
17
7
4
8
12
13

14. AVL Tree Example:
• Remove 8, unbalanced
14
17
4
7
12
13

15. AVL Tree Example:
• Remove 8, unbalanced
14
17
4
7
12
13

16. AVL Tree Example:
• Balanced!!
14
17
4
7
12
13

17. In Class Exercises
• Build an AVL tree with the following values:
15, 20, 24, 10, 13, 7, 30, 36, 25

18. 15
15, 20, 24, 10, 13, 7, 30, 36, 25
20
24
15
20
24
10
13
15
20
24
13
10
13
20
24
15
10

19. 13
20
24
15
10
15, 20, 24, 10, 13, 7, 30, 36, 25
7
13
20
24
15
10
7
30
36
13
20
30
15
10
7
36
24

20. 13
20
30
15
10
7
36
24
15, 20, 24, 10, 13, 7, 30, 36, 25
25
13
20
30
15
10
7
36
24
25
13
24
36
20
10
7
25
30
15

21. Remove 24 and 20 from the AVL tree.
13
24
36
20
10
7
25
30
15
13
20
36
15
10
7
25
30
13
15
36
10
7
25
30
13
30
36
10
7
25
15