The document discusses B-trees, which are self-balancing search trees commonly used in databases. It provides an example of a B-tree of order 5, showing how keys are inserted and nodes split without violating the ordering and occupancy rules. Keys can be deleted from the B-tree by removing them from nodes and rebalancing the tree if needed.

1. B Trees

2. Sample B tree

3. Minimization Factor : No of allowable Children for each node every node must have at least t - 1 keys Every node may have at most 2t - 1

4. the height of an n -key b-tree With t greater than or equal to 2,

5. Sample B tree

7. B-tree of order 5 all internal nodes have at least ceil(5 / 2) = ceil(2.5) = 3 children maximum number of children that a node can have is 5

8. Insertion B-tree of order 5: C N G A H E K Q M F W L T Z D P R X Y S Order 5 means that a node can have a maximum of 5 children and 4 keys. All nodes other than the root must have a minimum of 2 keys.

9. C N G A Order this ACGN Inserting ACGN

10. Inserting H

11. Inserting E, K, and Q proceeds without requiring any splits:

12. Inserting M requires a split

13. The letters F, W, L, and T are then added without needing any split

14. Adding Z

15. Inserting D

16. Inserting s

17. DELETION (H)

18. Delete T

19. Delete R

20. Delete E