The order of an internal node in a B+ tree index is the maximum number of…

2004

The order of an internal node in a B+ tree index is the maximum number of children it can have. Suppose that a child pointer takes 6 bytes, the search field value takes 14 bytes, and the block size is 512 bytes. What is the order of the internal node?

  1. A.

    24

  2. B.

    25

  3. C.

    26

  4. D.

    27

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Correct answer: C

Key formula: m * (pointer size) + (m - 1) * (key size) ≤ block size

  • Substitute pointer size = 6 bytes, key size = 14 bytes, block size = 512 bytes: 6m + 14(m - 1) ≤ 512

  • Simplify the inequality: 6m + 14m - 14 ≤ 512 → 20m ≤ 526 → m ≤ 526/20 = 26.3

  • m must be an integer, so the maximum feasible m is 26.

  • Verify: for m = 26 the used space is 26*6 + 25*14 = 156 + 350 = 506 bytes ≤ 512; for m = 27 used space = 27*6 + 26*14 = 162 + 364 = 526 bytes > 512 (not allowed).

Answer: The order of the internal node is 26.

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