B Trees
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This document discusses B-trees, which are self-balancing search trees used to store data in databases. It provides an example of inserting and deleting keys from a B-tree of order 5. The main points are: - B-trees allow for efficient retrieval and insertion/deletion of data in databases by keeping the tree balanced. - In a B-tree of order 5, each node can have up to 5 children and must have at least 3 keys. - The example shows inserting and deleting keys from an empty B-tree, with some insertions requiring splits and some deletions leaving nodes with fewer than the minimum keys.
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B Trees
- 1. B Trees
- 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,
- 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