Show that there are at most dn/2 h+1e nodes of height h in any n-element heap.
(b) for a min heap with n elements, what are the possible array subscript locations for the third smallest value in the heap? assume the array index begins at 1, and that all values are distinct. justify your answer.
(c) a d-ary heap is similar to a binary heap, except that nodes have d children instead of two children. justify your answers to the questions below.
i. what is the height of the tree representing a d-ary heap with n elements?
ii. what is the time taken for an insert operation in a d-ary heap? how does it compare with that for a binary heap?
iii. what is the time taken for a delete-max operation in a d-ary heap?