Last Updated: 11 Mar, 2021
Count of Matches in Tournament
Easy
Asked in company
You are given a positive integer 'N' representing the number of teams playing in a tournament. Your task is to find the total number of matches played in the tournament if the condition for the tournament is as follows:
1. If the current number of teams(N) playing in the tournament is even then, a total of N / 2 matches will be played. The winning N / 2 teams will advance to the next round, and the losing N / 2 teams will be eliminated.
2. If the current number of teams(N) playing in the tournament is odd then, 1 team will be advanced to the next round directly, and a total of (N - 1) / 2 matches will be played. The winning (N - 1) / 2 teams will advance to the next round, and the losing (N - 1) / 2 teams will be eliminated.
Input Format:
The first line contains an integer, ‘T,’ which denotes the number of test cases or queries to be run. Then, the T test cases follow.
The first and the only line of each test case contains one integer 'N', as described in the problem statement.
Output Format:
For each test case, print a single line containing a single integer denoting the total number of matches played in the tournament.
The output of each test case will be printed in a separate line.
Note:
You do not need to print anything. It has already been taken care of. Just implement the given function.
Constraints:
1 <= T <= 100
1 <= N <= 10 ^ 8
Time Limit: 1 second
Approaches
In this approach, we will be calculating the answer by recursion. We know that if the current number of teams(N) is even, then they will be playing N / 2 matches in this round, and the remaining N / 2 teams will play till there is a final winner. If the current number of teams is odd, then they will play (N - 1) / 2 matches, and the remaining (N - 1) / 2 + 1 teams will advance to the next round and play till there is a final winner. So we can simply write a recursive relation for the number of matches.
The recursive relation is as follows:
- totalMatches(N) = Matches played in this round + totalMatches(remaining teams).
Steps:
- Create a function named totalMatches(N) that will calculate the total number of matches played in the tournament.
- totalMatches(N):
- If N == 1:
- return 0.
- Create a variable to store the answer (say, ans) and initialize it to 0, i.e., ans = 0.
- If N is odd:
- ans = (N - 1) / 2 + totalMatches((N - 1) / 2 + 1).
- else:
- ans = N / 2 + totalMatches(N / 2).
- Finally, return the ans variable.
- If N == 1:
We can see that in this tournament, once a team loses, it will be eliminated from the tournament. So we need to eliminate N - 1 team to get one winner And to eliminate N - 1 team, we must have N - 1 matches. Therefore there will always be N - 1 matches played in the tournament.