Count of Matches in Tournament

How it works

Every match eliminates exactly one team. To go from n teams to 1 winner, we need to eliminate n - 1 teams. Therefore, exactly n - 1 matches are played regardless of the tournament bracket structure.

Steps

1. Return n - 1.

Complexity

• Time complexity: O(1)
• Space complexity: O(1)

Things to watch for

Overcomplicating with Simulation

Many beginners implement a full round-by-round simulation when the mathematical insight n - 1 gives the answer directly. Each match eliminates exactly one team, and to get from n teams to 1 winner requires eliminating n - 1 teams.

Off-by-One in Winner Calculation

When simulating, incorrectly calculating the number of teams advancing to the next round. The correct formula is (n + 1) / 2 (integer division), not n / 2, because the bye team also advances.

class Solution:
    def numberOfMatches(self, n: int) -> int:
        return n - 1

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