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?

In a 1-indexed complete binary tree (or binary heap) with $n$ elements:

• The internal (non-leaf) nodes are located at indices $1, 2, \dots, \lfloor n/2 \rfloor$.

• The leaf nodes are located at indices $\lfloor n/2 \rfloor + 1, \dots, n$.

Since $n$ is an odd number ($n > 100$):

Thus:

1. The internal nodes have indices from $1$ up to $\frac{n-1}{2}$.

2. The leaf nodes have indices from $\frac{n+1}{2}$ up to $n$.

Checking the given options:

• (A) $\frac{n+1}{2}$: This is the index of the very first leaf node.

• (B) $\frac{n-1}{2}$: This is the index of the last internal node, so it is not a leaf node.

• (C) $\frac{n-3}{2}$: Since $\frac{n-3}{2} \le \frac{n-1}{2}$, this is also an internal node and not a leaf node.

• (D) $n$: This is the index of the last leaf node.

Therefore, the indices that do NOT correspond to any leaf node are B and C.