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Leetcode 1688. Count of Matches in Tournament

Problem Statement

You are given an integer n, the number of teams in a tournament that follows a knockout format. In each match, two teams compete against each other, and the loser of each match is eliminated. This process is repeated until only one team remains as the winner of the tournament. Your task is to return the total number of matches played in the tournament.

Clarifying Questions

  1. Q: Is n always greater than or equal to 1? A: Yes, n is always a positive integer, and it is guaranteed to be at least 1.

  2. Q: What should be the output if n is 1? A: If n is 1, there are no matches to be played, so the output should be 0.

  3. Q: Should the solution handle only large inputs or both small and large inputs efficiently? A: The solution should handle all inputs efficiently since n can be quite large.

Strategy

  1. Tournament Observation: Each match reduces the number of teams by exactly 1 because one team gets eliminated. Hence, for n teams, to find a winner, n - 1 matches are required.

    • For example, if you start with 8 teams, you need to play 7 matches to determine the winner:
      • 8 teams, 4 matches -> 4 teams
      • 4 teams, 2 matches -> 2 teams
      • 2 teams, 1 match -> 1 winner

  2. Implementation Plan:

    • Given n teams, the total matches needed is n - 1.
    • Implement this in a straightforward manner, directly returning n - 1.

Code

public class Solution {
    public int numberOfMatches(int n) {
        return n - 1;
    }

    public static void main(String[] args) {
        Solution solution = new Solution();
        // Example Test Cases
        System.out.println(solution.numberOfMatches(7));  // Expected output: 6
        System.out.println(solution.numberOfMatches(1));  // Expected output: 0
    }
}

Time Complexity

The time complexity of this solution is (O(1)) because the number of operations does not depend on the size of the input n. The solution computes the result using a single mathematical operation.

Thus, the implementation is both efficient and simple, precisely aligning with the problem requirements.

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