GATE CSE 2024 Session 1 Q43: Possible positions of the maximum in a 105-element min-heap

Programming and Data Structures
2 marks
MCQ
−2/3 if wrong

Consider a binary min-heap containing 105 distinct elements. Let $k$ be the index (in the underlying array) of the maximum element stored in the heap. The number of possible values of $k$ is

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Answer: A (official GATE 2024 final answer key)

Concept used: In a min-heap the maximum must be a leaf, and any leaf can hold it.

First step: A heap with $n$ nodes has $\lceil n/2 \rceil$ leaves.

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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GATE CSE 2024 Session 1 Q43: Possible positions of the maximum in a 105-element min-heap

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