Question

Given N distinct elements in an array, determine the number of comparisons required to find the element which is not the largest:

• A. \( 2N - 1 \)
• B. \( N - 1 \)
• C. 0
• D. \( 1 \)

Hint:

When finding the non-largest element in an array, focus on first identifying the largest element and then selecting any element that is not the largest. This minimizes the number of comparisons.

Answer 1

The Correct Option is D

Step 1: Understanding the problem.

We are given \( N \) distinct elements in an array, and we need to determine how many comparisons are required to find the element which is not the largest.

To clarify, we are interested in finding an element that is not the largest. We are looking for any element except the largest element.

Step 2: Finding the largest element.

The natural way to find the largest element in an array is by performing comparisons. For each element in the array, we compare it with the current largest element.

In this process:
- Initially, we assume the first element as the largest.
- Then, we iterate through each remaining element in the array and compare it with the current largest element.
- If the current element is larger, we update the largest element.
- The number of comparisons required to find the largest element is \( N - 1 \), because each of the \( N-1 \) elements is compared with the largest element found so far.

Step 3: Finding the element that is not the largest.

Once we find the largest element, we are interested in the element that is not the largest. This can be easily done in a single comparison. We simply choose the first element that does not match the largest element.

Thus, after identifying the largest element, we only need 1 comparison to find the element that is not the largest.

Step 4: Conclusion.

Hence, the total number of comparisons required to find the element that is not the largest is:

\[ 1 \quad \text{(after finding the largest element)}. \]

Thus, the correct answer is \( \boxed{1} \).