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What is the best case height of a B-tree of order n and which has k keys?

(a) logn (k+1) – 1

(b) nk

(c) logk (n+1) – 1

(d) klogn

The origin of the question is B-Trees topic in portion B-Trees of Data Structures & Algorithms I

This question was addressed to me in my homework.

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Right choice is (a) logn (k+1) – 1

Easiest explanation - B-tree of order n and with height k has best case height h, where h = logn (k+1) – 1. The best case occurs when all the nodes are completely filled with keys.

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