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# B Trees

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dbms btrees

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### B Trees

1. 1. B Trees
2. 2. Sample B tree
3. 3. <ul><li>Minimization Factor : No of allowable Children for each node </li></ul><ul><li>every node must have at least t - 1 keys </li></ul><ul><li>Every node may have at most 2t - 1 </li></ul>
4. 4. <ul><li>the height of an n -key b-tree </li></ul><ul><li>With t greater than or equal to 2, </li></ul>
5. 5. Sample B tree
6. 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
7. 8. Insertion <ul><li>B-tree of order 5: </li></ul><ul><li>C N G A H E K Q M F W L T Z D P R X Y S </li></ul><ul><li>Order 5 means that a node can have a maximum of 5 children and 4 keys. </li></ul><ul><li>All nodes other than the root must have a minimum of 2 keys. </li></ul>
8. 9. <ul><li>C N G A Order this ACGN </li></ul><ul><li>Inserting ACGN </li></ul>
9. 10. Inserting H
10. 11. Inserting E, K, and Q proceeds without requiring any splits:
11. 12. Inserting M requires a split
12. 13. The letters F, W, L, and T are then added without needing any split