Question

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

n
0
2∗n+2
n+1

Possibly in any leaf node
2∗n+1
n−1

The rightmost leaf node
The leftmost leaf node

Answer 1

The minimal element in a max-heap is located at one of the leaf nodes, which can be any of the leaf nodes present in the heap.

Step-by-step explanation:

In a max-heap, the element with the highest value is always at the root of the heap, which is the first position in the array representation of the heap. The order of all other elements, especially the location of the minimum element, cannot be determined just based on the nature of the max-heap. However, we do know that in a max-heap, every parent node is greater than its children. Because of this property, the smallest element must be a leaf node, as leaf nodes do not have any children to be compared with.

Since a heap is a complete binary tree, the leaf nodes begin after the last parent node. This typically occurs at the element after the ½n'th position when the heap is represented as an array (because the first half would be comprised of all parent nodes, given a 0-indexed array).

The exact position of the minimally valued element within the leaf nodes isn't guaranteed without inspecting the values, but it is guaranteed to be one of the leaf nodes in the heap. Therefore, the answer is that the minimum element can be found in 'Possibly in any leaf node'.