Count of Matches in Tournament

Posted: 11 Mar, 2021
Difficulty: Easy

PROBLEM STATEMENT

Try Problem

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
Approach 1

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.
Try Problem