Count Matches Played in Tournament using Python

Suppose we have a number n. So there are n number of teams in a tournament that has some rules −

• If the number of teams is even currently, then each team gets merged with another team. And a total of (n/2) matches are played, from them (n/2) winner teams will move to the next round.

• If the number of teams is odd, then one team randomly moved in the tournament, and the rest gets merged. So a total of (n-1)/2 matches are played, and (n-1)/2+1 teams are moved to the next round as winner.

We have to find total number of matches are played so that we get the final winner.

So, if the input is like n = 10, then the output will be 9 because

• Initially there will be 5-5 division, among them 5 will be qualified

• Now pass one team to the game and divide 2-2 teams, so 3 will be qualified

• Now pass one team to the game and divide 1-1 teams, so 2 will be qualified

• Divide 1-1 and one will be qualified as winner.

To solve this, we will follow these steps −

• ans := 0

• while n is not same as 1, do

  • f := floor of (n/2)

  • remainder := n mod 2

  • ans := ans + f

  • n := f + remainder

• return ans

Example (Python)

Let us see the following implementation to get better understanding −

 Live Demo

def solve(n):
   ans = 0
   while n != 1:
      f = n//2
      remainder = n % 2
      ans += f
      n = f + remainder

   return ans

n = 10
print(solve(n))

Input

10

Output

9