Count of Matches in Tournament

Easy

0/40

Average time to solve is 20m

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8 upvotes

Asked in company

Problem statement

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.

Detailed explanation ( Input/output format, Notes, Images )

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

Sample Input 1:

1
9

Sample Output 1:

Explanation for sample input 1:

In the first round, 8 teams will play 4 matches, and 1 team will be directly advanced to the next round. So including the winners of the first round, a total of 5 teams will advance to the next round.

In the second round, 5 teams will play 2 matches, and 1 team will directly advance to the next round. So including the winners of the second round, a total of 3 teams will advance to the next round.   

In the third round, 3 teams will play 1 match, and 1 team will directly advance to the next round. So including the winners of the third round, a total of 2 teams will advance to the next round.

In the final round, the 2 teams will play 1 match, and then there will be a winner of the tournament.

Therefore the total number of matches played is 4 + 2 + 1 + 1 = 8.

Sample Input 2:

2
32
78

Sample Output 2:

31
77

Console