What would the branching factor b need to be for a tree with n = 1,000,000,000 elements at the bottom to have a height (depth) d of 3?

  • A: 2
  • B: 10
  • C: 30
  • D: 100
  • E: 1000

    Answer: E

    Our formula for trees is n = b d.

    Thus, we have 1,000,000,000 = b3, which gives b = 1,000.

    A large branching factor, as found in B-trees, allows a desired record to be found in a large database with a small number of (slow) disk accesses. If the first 2 levels of this tree are kept in memory (1,000 + 1,000,000 items), any record in the billion-record database can be gotten with a single disk access.

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