GATE CS 2026 Set 1 Q.23: Binary Heaps and Priority Queues

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?

$\frac{n+1}{2}$

$\frac{n-1}{2}$

$\frac{n-3}{2}$

$n$

Official answer and solution

Official answer: B and C
From: Official GATE 2026 answer key

Solution

Use the 1-indexed binary heap property that internal (non-leaf) nodes occupy indices $1$ through $\lfloor n/2 \rfloor$ .

In a 1-indexed binary heap with $n$ elements, node $i$ has left child $2i$ and right child $2i + 1$ . Thus node $i$ is a non-leaf (internal) node if and only if $2i \le n$ , i.e., $1 \le i \le \lfloor n/2 \rfloor$ , while leaf nodes occupy indices $\lfloor n/2 \rfloor + 1$ through $n$ .

Since $n > 100$ is odd, $\lfloor n/2 \rfloor = \frac{n-1}{2}$ . Therefore:

$\frac{n-1}{2}$ and $\frac{n-3}{2}$ are $\le \frac{n-1}{2}$ , so they correspond to non-leaf nodes.
$\frac{n+1}{2}$ and $n$ are $> \frac{n-1}{2}$ , so they correspond to leaf nodes.

Final answer

Options (B), (C)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 23 of 65
Section: Computer Science and Information Technology

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