#1688

Easy

LeetCode Problem Workspace

Count of Matches in Tournament

Calculate the total matches in a tournament by simulating rounds and applying simple math rules for advancing teams.

Problem Statement

You are given an integer n representing the number of teams in a tournament. The tournament follows a unique elimination pattern where each round, teams are paired for matches: if the number of teams is even, all teams play matches and half advance; if odd, one team advances automatically while the rest play matches.

Your task is to calculate and return the total number of matches played until a single team is declared the winner. For example, given n = 7, the first round has 3 matches with 4 teams advancing, the next round has 2 matches with 2 teams advancing, and the final round has 1 match to determine the champion, totaling 6 matches.

Examples

Example 1

Input: n = 7

Output: 6

Details of the tournament:

1st Round: Teams = 7, Matches = 3, and 4 teams advance.
2nd Round: Teams = 4, Matches = 2, and 2 teams advance.
3rd Round: Teams = 2, Matches = 1, and 1 team is declared the winner. Total number of matches = 3 + 2 + 1 = 6.

Example 2

Input: n = 14

Output: 13

Details of the tournament:

1st Round: Teams = 14, Matches = 7, and 7 teams advance.
2nd Round: Teams = 7, Matches = 3, and 4 teams advance.
3rd Round: Teams = 4, Matches = 2, and 2 teams advance.
4th Round: Teams = 2, Matches = 1, and 1 team is declared the winner. Total number of matches = 7 + 3 + 2 + 1 = 13.

Constraints

1 <= n <= 200

Solution Approach

Iterative Simulation

Simulate the tournament round by round. At each round, calculate the number of matches as teams divided by 2, advance winners, and handle odd teams by allowing one to skip a match. Sum the matches until only one team remains.

Direct Mathematical Observation

Observe that each match eliminates exactly one team. Since the tournament ends when one team remains, the total number of matches equals n - 1. This is a constant-time O(1) solution without explicit simulation.

Hybrid Approach

Combine math and simulation: simulate rounds for clarity but verify with the formula n - 1. This ensures understanding of the elimination pattern while keeping computation simple.

Complexity Analysis

Metric	Value
Time	O(1)
Space	O(1)

Time complexity is O(1) because the total matches can be calculated directly using n - 1. Space complexity is O(1) as no additional structures are needed; only counters for matches and teams are used.

What Interviewers Usually Probe

Expect the candidate to identify the elimination pattern quickly.
Watch for correct handling of odd numbers of teams in rounds.
Check whether the candidate recognizes the O(1) formula versus full simulation.

Common Pitfalls or Variants

Common pitfalls

Forgetting that an odd team automatically advances, leading to off-by-one errors.
Simulating unnecessarily without realizing total matches equal n - 1.
Incorrectly summing matches when counting advancing teams in each round.

Follow-up variants

Count total matches for a double-elimination tournament with similar pairing rules.
Compute total matches if the tournament allows random byes instead of fixed odd-team advancement.
Determine total rounds instead of matches while applying the same elimination pattern.

FAQ

How do you calculate total matches in Count of Matches in Tournament without simulating each round?

You can use the direct formula: total matches = n - 1, since each match eliminates exactly one team until one remains.

Why is this problem categorized under Math plus Simulation?

It combines simple mathematical elimination logic with the need to simulate rounds to handle odd team counts correctly.

What should I watch out for with odd numbers of teams?

Ensure that one team automatically advances each round when the count is odd, otherwise match totals will be miscounted.

Can this solution scale for large n values?

Yes, using the n - 1 formula is O(1) and handles any valid n up to the problem constraints efficiently.

Is it necessary to track each round individually?

Not strictly; simulation is useful for understanding, but mathematically total matches can be derived directly without step-by-step tracking.

terminal

Solution

Solution 1: Quick Thinking

From the problem description, we know that there are $n$ teams in total. Each pairing will eliminate one team. Therefore, the number of pairings is equal to the number of teams eliminated, which is $n - 1$.

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

Continue Practicing

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