GATE CSE 2025 Session 1 Q35: Height of a min-heap with 32 keys

The height of any rooted tree is defined as the maximum number of edges in the path from the root node to any leaf node.

Suppose a Min-Heap $T$ stores 32 keys. The height of $T$ is _____________. (Answer in integer)

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 5 (official GATE 2025 final answer key)

Concept used: A heap is a complete binary tree, so its height is $\lfloor \log_2 n \rfloor$ .

First step: Levels 0 to 4 hold $1 + 2 + 4 + 8 + 16 = 31$ keys, so the 32nd key starts a new level.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key