Question

In a max-heap containing n elements, what is the position of the element with the greatest value?

2∗n+2
The rightmost leaf node
The leftmost leaf node

n+1
Possibly in any leaf node

n−1
0
2∗n+1
n

Answer 1

In a max-heap, the element with the greatest value is always located at the root node, corresponding to the first position in the array representation of the heap (index 1 in one-based or index 0 in zero-based).

Step-by-step explanation:

In a max heap containing n elements, the element with the greatest value is always at the top of the heap, which is the root node of the heap structure. This is because a max-heap is a complete binary tree where every level, except possibly the last, is filled, and all nodes are as far left as possible. The heap property mandates that for any given node i, the value of i is greater than or equal to the values of its children.

This is what ensures the largest element resides at the root. Hence, the position of the element with the greatest value is always the first element in the heap, which corresponds to the array index of 1 assuming a one-based array index scheme (or 0 in a zero-based index scheme, which is common in many programming languages).