Count of Matches in Tournament - Problem

Math Simulation Easy

You are given an integer n, the number of teams in a tournament that has strange rules:

If the current number of teams is even, each team gets paired with another team. A total of n / 2 matches are played, and n / 2 teams advance to the next round.

If the current number of teams is odd, one team randomly advances in the tournament, and the rest gets paired. A total of (n - 1) / 2 matches are played, and (n - 1) / 2 + 1 teams advance to the next round.

Return the number of matches played in the tournament until a winner is decided.

Input & Output

Example 1 — Odd Number of Teams

$ Input: n = 7

› Output: 6

💡 Note: Round 1: 7 teams (odd) → 3 matches, 4 teams advance. Round 2: 4 teams (even) → 2 matches, 2 teams advance. Round 3: 2 teams (even) → 1 match, 1 winner. Total: 3 + 2 + 1 = 6 matches.

Example 2 — Even Number of Teams

$ Input: n = 14

› Output: 13

💡 Note: Mathematical insight: each match eliminates exactly 1 team. To go from 14 teams to 1 winner, we eliminate 13 teams, requiring 13 matches.

Example 3 — Minimum Case

$ Input: n = 2

› Output: 1

💡 Note: Only 2 teams need just 1 match to determine the winner. Using formula: n - 1 = 2 - 1 = 1.

Constraints

1 ≤ n ≤ 200

Visualization

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Asked in

G Google 15 a Amazon 12

The key insight is that each match eliminates exactly one team. To go from n teams to 1 winner, we need n-1 eliminations, so the answer is always n-1. Best approach uses mathematical reasoning for O(1) solution. Time: O(1), Space: O(1)

Common Approaches

✓ Mathematical Insight

⏱️ Time: O(1) Space: O(1)

The key insight is that every match eliminates exactly one team. To go from n teams to 1 winner, we must eliminate n-1 teams, requiring exactly n-1 matches.

Simulation Approach

⏱️ Time: O(log n) Space: O(1)

Follow the tournament rules exactly: simulate each round, count matches played, and calculate teams advancing until only one team remains.

Mathematical Insight — Algorithm Steps

Observe that each match eliminates exactly 1 team
To get from n teams to 1 winner, eliminate n-1 teams
Therefore, total matches needed = n - 1

Visualization

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Step-by-Step Walkthrough

Start

7 teams need to become 1 winner

Elimination

Each match eliminates exactly 1 team

Result

Need 6 eliminations = 6 matches

Code -

solution.c — C

#include <stdio.h>

int solution(int n) {
    // Key insight: each match eliminates exactly 1 team
    // To go from n teams to 1 winner, we need to eliminate n-1 teams
    // Therefore, total matches = n - 1
    return n - 1;
}

int main() {
    int n;
    scanf("%d", &n);
    int result = solution(n);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Simple arithmetic calculation, no loops needed

⚡ Linearithmic

Space Complexity

O(1)

Only storing the input and result

✓ Linear Space

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Medium Frequency

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Count of Matches in Tournament - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Mathematical Insight — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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