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What is the time complexity for searching k+1 auxiliary trees?

(a) k+2 O (log (log n))

(b) k+1 O (log n)

(c) K+2 O (log n)

(d) k+1 O (log (log n))

I'd like to ask this question from Binary Trees topic in division Binary Trees of Data Structures & Algorithms I

I had been asked this question in an interview for internship.

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The correct option is (d) k+1 O (log (log n))

The best I can explain: Since each search operation in the auxiliary tree takes O (log (log n)) time as auxiliary tree size is bounded by the height of the reference tree that is log n. So for k+1 auxiliary trees, total search time is k+1 O (log (log n)).

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