Problem
You are given an integer n
, the number of teams in a tournament that has strange rules:
If the current number of teams is even, each team gets paired with another team. A total of
n / 2
matches are played, andn / 2
teams advance to the next round.If the current number of teams is odd, one team randomly advances in the tournament, and the rest gets paired. A total of
(n - 1) / 2
matches are played, and(n - 1) / 2 + 1
teams advance to the next round.
Return the number of matches played in the tournament until a winner is decided.
Example 1:
Input: n = 7
Output: 6
Explanation: Details of the tournament:
- 1st Round: Teams = 7, Matches = 3, and 4 teams advance.
- 2nd Round: Teams = 4, Matches = 2, and 2 teams advance.
- 3rd Round: Teams = 2, Matches = 1, and 1 team is declared the winner.
Total number of matches = 3 + 2 + 1 = 6.
Example 2:
Input: n = 14
Output: 13
Explanation: Details of the tournament:
- 1st Round: Teams = 14, Matches = 7, and 7 teams advance.
- 2nd Round: Teams = 7, Matches = 3, and 4 teams advance.
- 3rd Round: Teams = 4, Matches = 2, and 2 teams advance.
- 4th Round: Teams = 2, Matches = 1, and 1 team is declared the winner.
Total number of matches = 7 + 3 + 2 + 1 = 13.
Constraints:
1 <= n <= 200
Solution
/**
* @param {number} n
* @return {number}
*/
var numberOfMatches = function(n) {
if (n === 1) return 0;
if (n % 2) {
return Math.floor(n / 2) + numberOfMatches((n + 1) / 2);
} else {
return (n / 2) + numberOfMatches(n / 2);
}
};
Explain:
nope.
Complexity:
- Time complexity : O(log(n)).
- Space complexity : O(1).