The Problem:
We are given an array of 200 elements and we need to find the maximum and minimum elements in the array. The task is to determine the total number of comparisons needed to find the maximum and minimum elements.

Approach:
To find the maximum and minimum elements in an array, we can use the following algorithm:
1. Initialize the maximum and minimum elements as the first element of the array.
2. Iterate through the array, comparing each element with the current maximum and minimum elements.
3. Update the maximum and minimum elements if necessary.
4. Continue until all elements in the array have been checked.

Explanation:
To understand the total number of comparisons needed, let's analyze the algorithm step by step.

Step 1:
We initialize the maximum and minimum elements as the first element of the array. This requires no comparisons.

Step 2:
We iterate through the array, comparing each element with the current maximum and minimum elements. Since we have 200 elements in the array, we need to perform 199 comparisons in this step. This is because we compare each element with the current maximum and minimum, excluding the first element which was already considered in the initialization step.

Step 3:
In this step, we update the maximum and minimum elements if necessary. The number of comparisons required in this step depends on the values in the array. If the maximum or minimum elements are found in the first or last positions of the array, then no comparisons are needed. However, if the maximum or minimum elements are found in any other position, we would need to perform additional comparisons. In the worst case scenario, the maximum and minimum elements are at the opposite ends of the array, which would require 198 comparisons (99 for finding the maximum and 99 for finding the minimum).

Total Comparisons:
To calculate the total number of comparisons needed, we sum up the comparisons from all steps:
Total Comparisons = Comparisons in Step 2 + Comparisons in Step 3

Comparisons in Step 2 = 199
Comparisons in Step 3 = 198

Total Comparisons = 199 + 198 = 397

However, note that the question specifically asks for the total number of comparisons needed to find both the maximum and minimum elements. Since we have counted the comparisons for finding only the maximum or minimum elements, we need to divide the total by 2.

Total Comparisons for both maximum and minimum = Total Comparisons / 2 = 397 / 2 = 198.5

Since the number of comparisons cannot be a decimal value, we round it up to the nearest whole number.

Total Comparisons for both maximum and minimum = 199

Therefore, the correct answer is 199.