Question

2 point) what is the height of a d-heap that contains n elements? the height should be a function of n and

Answer 1

Assuming a d-heap means the order of the tree representing the heap is d.
Most of the computer applications use binary trees, so they are 2-heaps.

A heap is a complete tree where each level is filled (complete) except the last one (leaves) which may or may not be filled.

The height of the heap is the number of levels.  Hence the height of a binary tree is Ceiling(log_2(n)), for example, for 48 elements, log_2(48)=5.58.
Ceiling(5.58)=6.  Thus a binary tree of 6 levels contains from 2^5+1=33 to 2^6=64 elements, and 48 is one of the possibilities.  So the height of a binary-heap with 48 elements is 6.

Similarly, for a d-heap, the height is ceiling(log_d(n)).