algoadvance

You are given an integer n, the number of teams in a tournament that operates as follows:

• If the number of teams is even, each team pairs with another team, resulting in n / 2 matches with n / 2 winners advancing to the next round.
• If the number of teams is odd, one team automatically advances to the next round, and the other n - 1 teams are paired to play ((n - 1) / 2) matches, with ((n - 1) / 2) + 1 winners advancing to the next round.

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

Clarifying Questions

1. Input Constraints:
   • Can the number of teams n be zero or one? (Typically, it’s at least 1 from the problem’s context).
2. Output Details:
   • Do we expect the function to handle only positive integers?

Assuming that n is at least 1 as per the problem’s context.

Strategy

We can simulate the process round by round until we are left with one team. In each round:

• If the number of teams is even, halve the number of teams, and the number of matches is half the current number of teams.
• If the number of teams is odd, reduce the number of teams by one, halve the resulting even number, and add one team that advances automatically to the next round. The number of matches is (n - 1) / 2.

Repeat these steps and keep a count of the total matches until there’s only one team left.

Time Complexity

The time complexity of this approach is O(log n). Each iteration reduces the number of teams approximately by half, leading to a logarithmic number of iterations.

Code

def numberOfMatches(n: int) -> int:
    # Initialize the number of matches to 0
    total_matches = 0
    
    # Continue until one team is left
    while n > 1:
        if n % 2 == 0:
            matches = n // 2
            n = n // 2
        else:
            matches = (n - 1) // 2
            n = (n - 1) // 2 + 1
        total_matches += matches

    return total_matches

# Example usage
print(numberOfMatches(7))  # Output: 6
print(numberOfMatches(14)) # Output: 13

In this implementation, we initialize the total number of matches to zero and simulate each round of the tournament until there is only one team remaining. We check if the current number of teams is even or odd, update the number of matches and teams accordingly, and accumulate the count of matches played.

Try our interview co-pilot at AlgoAdvance.com

• Got blindsided by a question you didn’t expect?

• Spend too much time studying?

• Or simply don’t have the time to go over all 3000 questions?