Count of Matches in Tournament

The direct answer is n - 1. A tournament starts with n teams and ends with one champion, so exactly n - 1 teams must be eliminated. Every match eliminates exactly one team, regardless of whether a round has a bye, therefore there must be n - 1 matches. You can also simulate: each round contributes floor(n/2) matches and leaves ceil(n/2) teams, but that merely verifies the invariant. Mention the base case n = 1, where zero matches are required. This is an example where proving the quantity is more valuable than writing loops. Time and extra space are O(1) for the formula; a simulation is O(log n) rounds but is not needed.