# 544. Output Contest Matches 输出比赛匹配对

@TOC

## # 题目描述

During the NBA playoffs, we always arrange the rather strong team to play with the rather weak team, like make the rank 1 team play with the rank nth team, which is a good strategy to make the contest more interesting. Now, you're given n teams, you need to output their final contest matches in the form of a string.

The n teams are given in the form of positive integers from 1 to n, which represents their initial rank. (Rank 1 is the strongest team and Rank n is the weakest team.) We'll use parentheses('(', ')') and commas(',') to represent the contest team pairing - parentheses('(' , ')') for pairing and commas(',') for partition. During the pairing process in each round, you always need to follow the strategy of making the rather strong one pair with the rather weak one.

Example 1:

``````Input: 2
Output: (1,2)
Explanation:
Initially, we have the team 1 and the team 2, placed like: 1,2.
Then we pair the team (1,2) together with '(', ')' and ',', which is the final answer.
``````

Example 2:

``````Input: 4
Output: ((1,4),(2,3))
Explanation:
In the first round, we pair the team 1 and 4, the team 2 and 3 together, as we need to make the strong team and weak team together.
And we got (1,4),(2,3).
In the second round, the winners of (1,4) and (2,3) need to play again to generate the final winner, so you need to add the paratheses outside them.
And we got the final answer ((1,4),(2,3)).
``````

Example 3:

``````Input: 8
Output: (((1,8),(4,5)),((2,7),(3,6)))
Explanation:
First round: (1,8),(2,7),(3,6),(4,5)
Second round: ((1,8),(4,5)),((2,7),(3,6))
Third round: (((1,8),(4,5)),((2,7),(3,6)))
Since the third round will generate the final winner, you need to output the answer (((1,8),(4,5)),((2,7),(3,6))).
``````

Note:

• The n is in range [2, 212].
• We ensure that the input n can be converted into the form 2k, where k is a positive integer.

## # 题目大意

n 支队伍按从 1 到 n 的正整数格式给出，分别代表它们的初始排名（排名 1 最强，排名 n 最弱）。我们用括号（'(', ')'）和逗号（','）来表示匹配对——括号（'(', ')'）表示匹配，逗号（','）来用于分割。 在每一轮的匹配过程中，你都需要遵循将强队与弱队配对的原则。

## # 解题方法

### # 遍历

``````First round: (1,8),(2,7),(3,6),(4,5)
``````

``````Second round: ((1,8),(4,5)),((2,7),(3,6))
``````

(1,8)是第一轮的第一个，(4,5)是第一轮的最后一个，这两个构成了一个新的组，说明也是同样的最前和最后的组合。

``````Third round: (((1,8),(4,5)),((2,7),(3,6)))
``````

C++代码如下：

``````class Solution {
public:
string findContestMatch(int n) {
vector<string> nums(n, "");
for (int i = 1; i <= n; ++i) {
nums[i - 1] = to_string(i);
}
while (n) {
for (int i = 0; i < n / 2; ++i) {
nums[i] = "(" + nums[i] + "," + nums.back() + ")";
nums.pop_back();
}
n /= 2;
}
return nums[0];
}
};
``````

## # 日期

2019 年 9 月 24 日 —— 梦见回到了小学，小学已经芳草萋萋破败不堪