GATE CS 2024 Set 1 — Question 43

In a min-heap, the property is that every parent node is smaller than or equal to its children. Consequently, the smallest element is at the root, and the largest element must be one of the leaf nodes. It cannot be an internal node because an internal node must be smaller than its children.In a binary heap with $n$ distinct elements, the structure is a complete binary tree. The number of leaf nodes in a complete binary tree with $n$ nodes is given by $\lceil n/2 \rceil$.Given $n = 105$:
Number of leaves = $\lceil 105/2 \rceil = \lceil 52.5 \rceil = 53$.The maximum element can be located at any of these leaf positions. Therefore, there are 53 possible values for the index $k$.