1688. Count of Matches in Tournament #

Problem #

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.

Example 1:

Input: n = 7
Output: 6
Explanation: 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
Explanation: 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

Problem Summary #

You are given an integer n, representing the number of teams in the tournament. The tournament follows a unique format:

• If the current number of teams is even, then each team is 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, then one team randomly gets a bye and advances, while the remaining teams are 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 pairings played in the tournament until the winning team is decided.

Solution Approach #

• Easy problem; simulate according to the rules in the problem.
• There is an even more concise solution for this problem; see Solution 1. With n teams and one champion, n-1 teams need to be eliminated. Each match eliminates one team, so n-1 matches are played. Therefore, there are n-1 pairings in total.

Code #

package leetcode

// Solution 1
func numberOfMatches(n int) int {
	return n - 1
}

// Solution 2 Simulation
func numberOfMatches1(n int) int {
	sum := 0
	for n != 1 {
		if n&1 == 0 {
			sum += n / 2
			n = n / 2
		} else {
			sum += (n - 1) / 2
			n = (n-1)/2 + 1
		}
	}
	return sum
}