Question

Given the array below and a target value of 42, which of the following represents the value of the mid variable as the binary search algorithm progresses to locating the target?

{3, 7, 9, 15, 21, 24, 27, 29, 31, 35, 37, 41}
A. 5, 7, 10, 11
B. 5, 8, 10, 11
C. 5, 7, 9, 10, 11
D. None of the above.

Answer 1

The mid variable sequence in a binary search for the target value 42 in the given array is 5, 7, 10, 11. These represent indices in the array as the algorithm divides the search interval in half, progressively narrowing down the search area until the target is found or the search ends unsuccessfully.

Step-by-step explanation:

The student is asking about the progress of the mid variable during a binary search algorithm within an array when searching for a target value of 42. To execute a binary search, we start with the middle of the array and compare the target value to this middle element, and then depending on whether the target is higher or lower, we continue the search on the respective half of the array. We keep splitting halves until we find the target or conclude that it's not in the array.

For the given array {3, 7, 9, 15, 21, 24, 27, 29, 31, 35, 37, 41}, a binary search for the target value 42 proceeds as follows:

1. First, we calculate the middle index of the array, which is 5 (the middle of indices 0 to 11).
2. Since the target is greater than the element at index 5 (24), we search the right half.
3. Next, the middle index of the new subarray {27, 29, 31, 35, 37, 41} is 8 (the middle of indices 6 to 11).
4. Again, the target (42) is greater than the element at index 8 (31), so we continue with the right half.
5. The subsequent mid index is now 10 (the middle of indices 9 to 11).
6. Since the target is still greater, we narrow down to index 11, which is also not the target.
7. As 42 is not found in the array, the search ends unsuccesfully.

Therefore, the correct sequence of mid variable values as the binary search progresses to locate the target value of 42 is A. 5, 7, 10, 11.