GATE DA 2024 Q40: Recurrence for worst-case comparisons in binary search

Let $F(n)$ denote the maximum number of comparisons made while searching for an entry in a sorted array of size $n$ using binary search.

Which ONE of the following options is TRUE?

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

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Answer: A (official GATE 2024 final answer key)

Concept used: Binary search does one comparison and then recurses into one half.

First step: In the worst case, after comparing with the middle element the search continues in a half of size about $\lfloor n/2 \rfloor$ .

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key