1. AVL Search Tree 1 -1 10 7 8 3 5 30 40 20 25 35 45 60
put(9)

2. put(9) No imbalance -1 -1 10 1 1 7 40 -1 1 45 3 8 30 -1 60 35 1 9 20 51 1 7 40 -1 -1 1 45 3 8 30
Some balance factors on insert path change. -1 60 35 1 9 20 5 25
No imbalance

3. RR imbalance - put(29) 10 -1 1 1 7 40 -1 1 45 3 8 30 -1 60 35 20 1 201 45 3 8 30 -1 60 35 20 1 20 5 25

4. RR imbalance - put(29) RR imbalance: new node is in right subtree10 1 -1 7 1 40 3 8 -1 1 45 30 1 5 -1 -2 60 35 20 20
RR imbalance: new
node is in right subtree
of right subtree of blue node
(node with bf = -2) -1 25 29
FIX: Single rotation

5. RR imbalance - put(29) AFTER ROTATION 10 1 -1 7 1 40 3 8 -1 1 45 30 13 8 -1 1 45 30 1 5 60 35 25 20 29
AFTER ROTATION

6. AVL Rotations RR LL RL LR

7. LL imbalance - put(1) -1 10 1 7 40 50 3 30 20 35 45 60 20

8. LL imbalance - put(1) -1 10 2 1 7 40 1 50 3 30 1 20 35 45 60 20
LL imbalance => new node is in left subtree of left subtree of blue node (node with bf = 2)
FIX: Single right rotation

9. LL imbalance - put(1) AFTER rotation -1 10 3 40 50 1 7 30 20 35 45 603 40 50 1 7 30 20 35 45 60 20
AFTER rotation

10. LR imbalance - put(8) 1 10 3 40 2 4

11. LR imbalance - put(8) 2 1 10 -1 3 40 -1 2 4 8
LR imbalance => new node is in right subtree of left subtree of blue node (node with bf = 2)
FIX: Double rotation

12. LR imbalance - put(8) 2 1 -1 10 3 40
LL ROTATION 2 4
RR ROTATION 8
LR rotation is an RR rotation followed by LL rotation

13. LR imbalance - put(8) AFTER FIRST ROTATION LL ROTATION 2 1 -1 10 4 404 40
LL ROTATION 3 8 2
AFTER FIRST ROTATION

14. LR imbalance - put(8) 4 1 10 3 8 2 40
AFTER SECOND ROTATION

15. RL imbalance - put(5) -1 2 8 1 9 7

16. RL imbalance - put(5) -2 -1 2 1 8 1 1 9 7 5
RL imbalance => new node is in left subtree of right subtree of blue node (node with bf = -2)
FIX: Double rotation

17. RL imbalance - put(5) RR ROTATION LL ROTATION-2 -1 2 1 8 1
RR ROTATION 1 9 7 5
LL ROTATION
RL rotation is an LL rotation followed by an RR rotation

18. RL imbalance - put(5) AFTER FIRST ROTATION RR ROTATION -2 -1 2 -1 7 17 1 -1
RR ROTATION 8 5 9
AFTER FIRST ROTATION

19. RL imbalance - put(5) 7 -1 8 2 9 1 5
AFTER SECOND ROTATION

20. delete(45) 1 2 10 -1 6 40 45 3 8
Some balance factors on insert path change. 1 5 7 9

21. delete(45) After R0 rotation -1 6 1 3 10 1 5 40 8 7 91 3 10 1 5 40 8
Some balance factors on insert path change. 7 9
After R0 rotation

22. delete(45) 1 2 10 1 -1 6 40 45 3 8
Some balance factors on insert path change. 1 5

23. delete(45) After R1 rotation 6 3 10 1 5 40 86 3 10 1 5 40 8
Some balance factors on insert path change.
After R1 rotation

24. delete(45) 1 2 10 -1 -1 6 40 45 3 8
Some balance factors on insert path change. 7 9

25. delete(45) After R-1 rotation 8 6 10 3 7 9 408 6 10 3 7 9 40
Some balance factors on insert path change.
After R-1 rotation