An array $A$ of length $n$ with distinct elements is said to be bitonic if there is an index $1=i=n$ such that $A[1 . . i]$ is sorted in the non-decreasing order and $A[i+1 . . n]$ is sorted in the non-increasing order.

Which ONE of the following represents the best possible asymptotic bound for the worstcase number of comparisons by an algorithm that searches for an element in a bitonic array $A$?

An operator $$delete(i)$$ for a binary heap data structure is to be designed to delete the item in the $$i$$-th node. Assume that the heap is implemented in an array and i refers to the $$i$$-th index of the array. If the heap tree has depth $$d$$ (number of edges on the path from the root to the farthest leaf), then what is the time complexity to re-fix the heap efficiently after the removal of the element?

A complete binary min-heap is made by including each integer in $$[1,1023]$$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth $$0.$$ The maximum depth at which integer $$9$$ can appear is ___________.

Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4.

Array Index	1	2	3	4	5	6	7	8	9
Value	40	30	20	10	15	16	17	8	4

Now consider that a value 35 is inserted into this heap. After insertion, the new heap is