Overview

Given the vote counts of \(N\) students, output the student number if there is exactly one student with the most votes, or \(-1\) if there are multiple such students.

Analysis

The processing required for this problem consists of the following two steps:

1. Find the maximum vote count: What is the largest value among all students’ vote counts?
2. Count how many people have that maximum vote count: If it’s 1 person, the class president is determined; if it’s 2 or more, the president cannot be decided.

For example, consider the case where \(N = 5\) and the vote counts are [3, 5, 2, 5, 1]. - The maximum vote count is \(5\) - There are 2 students who received \(5\) votes: student 2 and student 4 - Therefore, the class president cannot be determined, and the answer is \(-1\)

As another example, consider the case where the vote counts are [3, 7, 2, 5, 1]: - The maximum vote count is \(7\) - There is only 1 student who received \(7\) votes: student 2 - Therefore, the answer is \(2\)

This problem can be solved fast enough by simply scanning the list naively. Since \(N\) is at most \(2 \times 10^5\), an \(O(N)\) solution that scans the list a few times is perfectly fine.

Algorithm

1. Find the maximum value max_val from the vote count list \(A\) (max(A)).
2. Count how many elements in the list are equal to max_val (A.count(max_val)).
3. If the count is \(1\), find the index of the element with the maximum value (A.index(max_val)), convert it to 1-indexed, and output it.
4. If the count is \(2\) or more, output \(-1\).

Complexity

• Time complexity: \(O(N)\)
  • One scan of the list with max(A): \(O(N)\)
  • One scan of the list with A.count(max_val): \(O(N)\)
  • At most one scan of the list with A.index(max_val): \(O(N)\)
  • Total: \(O(N)\)
• Space complexity: \(O(N)\) (for storing the list of vote counts)

Implementation Notes

• Converting between 1-indexed and 0-indexed: Python lists start from 0 (0-indexed), but in the problem, student numbers start from 1 (1-indexed). Since A.index(max_val) returns a 0-indexed position, you need to add +1 when outputting.

• Using count and index: Python lists have convenient methods — count easily retrieves the number of occurrences of a specific value, and index retrieves the position of its first occurrence.

• When the maximum value is 0: Although \(A_i = 0\) is allowed, even if everyone has \(0\) votes, the program correctly outputs \(-1\) as “multiple students with the most votes” (when \(N \geq 2\)). When \(N = 1\), that single person always becomes the class president.

  Source Code

N = int(input())
A = list(map(int, input().split()))
max_val = max(A)
if A.count(max_val) == 1:
    print(A.index(max_val) + 1)
else:
    print(-1)

This editorial was generated by claude4.6opus-thinking.