GATE CSE 2026 Session 1 Q23: Non-leaf indices in a 1-indexed binary heap with n odd

Let $n$ be an odd number greater than 100. Consider a binary minheap with $n$ elements stored in an array $P$ whose index starts from 1.

Which of the following indices of $P$ do/does NOT correspond to any leaf node of the minheap?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: B, C (official GATE 2026 final answer key)

Concept used: In a 1-indexed heap, node $i$ has children $2i$ and $2i+1$ ; internal nodes are $1$ to $\lfloor n/2 \rfloor$ .

First step: For odd $n$ , $\lfloor n/2 \rfloor = (n-1)/2$ ; indices up to that are internal.

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key