Let $H$ be a binary min-heap consisting of $n$ elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in $H$?

In a binary min-heap:

1. The root element is always the minimum element in the heap.

2. By the min-heap property, every parent node has a value less than or equal to its children. Therefore, the maximum element cannot be an internal node with children; it must reside in one of the leaf nodes.

3. In a binary heap of $n$ elements implemented as an array, the leaves are stored from index $\lfloor n/2 \rfloor + 1$ to $n$, which accounts for $\lceil n/2 \rceil$ elements.

4. Since the leaf nodes are unordered relative to each other, finding the maximum element requires performing a linear scan over all $\lceil n/2 \rceil$ leaf elements.

Thus, the worst-case time complexity is $\Theta(n)$ [cite: 1]. Hence, (C) is the correct option.