A) Here is an array with exactly 15 elements: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Suppose that we are doing a binary search for an element. Circle any elements that will be found by examining two or fewer numbers from the array.

4, 8 and 12

Explanation:

Given

Required

Elements that would be found by examining 2 or fewer numbers

To do this, we apply the following binary search algorithm

at 0-index

at 14-index

Calculate the mid-index

The mid-element (at 7th index) is:

The element at the mid-index is found by just 1 comparison

For 2 comparisons, we search in either directions

For the lower half, the new head and tail are:

---- at 0-index

at 6-index

Calculate the mid-index

The mid-element (at 3rd index) is:

For the upper half, the new head and tail are:

---- at 8-index

at 14-index

Calculate the mid-index

The mid-element (at 11th index) is:

The elements at the mid-index of both halves is found by 2 comparisons

Hence, the numbers are: