1. Draft for an AVL tree insertion visualization with multiple levels of engagement
T Special Course in Software Techniques: Directions for Future Research in Algorithm Visualization
Lasse Hakulinen A V

2. AVL tree insertion
Mode 1: Animation

3. The AVL tree is now balaced Insert the next key (5) to the AVL tree
Input: 5 2 3 9 10 4 1
Balance factor =
height of left subtree – height of right subtree 5

4. Insert the next key (2) to the AVL tree The AVL tree is now balaced
Input: 5 2 3 9 10 4 1 5 1 2

5. Insert the next key (0) to the AVL tree
The tree is unbalanced: The balance factor of node with key ”5” is 2.
Do a single rotation right.
Insert the next key (0) to the AVL tree
Input: 5 2 3 9 10 4 1 5 2 1 2 1

6. The AVL tree is now balaced
The tree is unbalanced: The balance factor of the node with key ”5” is 2.
Do a single rotation right.
Input: 5 2 3 9 10 4 1 5 1 2

7. Mode 2: User defined input
AVL tree insertion
Mode 2: User defined input

8. The AVL tree is now balaced
Insert a key
Input key: 12
Insert
Insert random key 12

9. The AVL tree is now balaced
Insert a key
The AVL tree is now balaced
Input key:
100
Insert
Insert random key 12 -1
100

10. The tree is unbalanced: The balance factor of node with key ”12” is -2.
Do a right-left double rotation
Insert a key
Input key:
Insert
Insert random key 12 -1 -2
TODO:
Smooth animation of the rotation 1
100 13

11. The AVL tree is now balaced
Input key:
Insert
Insert random key 13 12
100

12. Mode 3: Challenge yourself
AVL tree insertion
Mode 3: Challenge yourself

13. Task 1: Insert a key so that the node ”21” will be the new root
The tree is unbalanced: The balance factor of node with key ”5” is -2.
Do a single left rotation
Input key: 30
Insert
Insert random key 5 -1 -2
TODO:
Smooth animation of the rotation 3 21 -1 -1 11 28 30

14. Task correct!
Input key:
Insert
Insert random key 21 5 28 -1 30 3 11

15. Task 2: Insert a key so that the node ”11” will be the new root
The tree is unbalanced: The balance factor of node with key ”5” is -2.
Do a double right-left rotation
Task 2: Insert a key so that the node ”11” will be the new root
Input key: 7
Insert
Insert random key 5 -1 -2
TODO:
Smooth animation of the rotation 3 21 1 1 11 28 7

16. Task correct!
Input key:
Insert
Insert random key 11 5 21 -1 28 3 7

17. Task 3: Insert maximum of 3 keys so that the right child of root's left child (highlighted) has a key ”16”.
The tree is unbalanced: The balance factor of node with key ”20” is 2.
Do a double left-right rotation
Input key: 16
Insert
Insert random key 20 1 2
TODO:
Smooth animation of the rotation -1 9 27 -1 3 14 16

18. Task 3: Insert maximum of 3 keys so that the right child of root's left child (highlighted) has a key ”16”.
Input key:
Insert
Insert random key 14 1 9 20 3 16 27

19. Let's try again...

20. Task 3: Insert maximum of 3 keys so that the right child of root's left child (highlighted) has a key ”16”.
Input key: 30
Insert
Insert random key 20 1 -1 9 27 3 14 30

21. Task 3: Insert maximum of 3 keys so that the right child of root's left child (highlighted) has a key ”16”.
Input key: 16
Insert
Insert random key 20 -1 9 27 3 14 30 16

22. Task 3: Insert maximum of 3 keys so that the right child of root's left child (highlighted) has a key ”16”.
Input key: 17
Insert
Insert random key 20 1 -1 -1 9 27 -1 3 14 30 16 17

23. Task 3: Insert maximum of 3 keys so that the right child of root's left child (highlighted) has a key ”16”.
The tree is unbalanced: The balance factor of node with key ”14” is -2.
Do a single left rotation
Input key: 17
Insert
Insert random key 20 2
TODO:
Smooth animation of the rotation -2 -1 9 27 -2 3 14 30 -1 16 17

24. Task 3: Insert maximum of 3 keys so that the right child of root's left child (highlighted) has a key ”16”.
Task correct!
Input key:
Insert
Insert random key 1 20 -1 -1 9 27 3 16 30 14 17