LeetCode 544----Output Contest Matches

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 n_th 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:

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

算法分析

要实现最强的队伍跟最弱的队伍匹配，就是要将1~n顺序排列，然后第一队跟倒数第一队匹配，构成一个"(1,n)",将这个字符串放入另一个链表里，然后将第二队跟倒数第二队匹配，构成"(2,n-1)"，并加入链表里。第一个链表处理完后，递归处理新生成的链表，直到新的链表里字符串的数量为1.

Java算法实现：

public class Solution {
    public String findContestMatch(int n) {
        List<String>list=new ArrayList<>();
        for(int i=1;i<=n;i++){
        	list.add(String.valueOf(i));
        }
        List<String>ans=doAdd(list, n);
        return ans.get(0);
    }
    
    public List<String> doAdd(List<String>list,int n){
    	if(n<=1){
    		return list;
    	}
    	else{
    		List<String>ans=new ArrayList<>();
    		int mid=n>>1;
    		int end=n-1;
    		for(int i=0;i<mid;i++){
    			ans.add("("+list.get(i)+","+list.get(end-i)+")");
    		}
    		return doAdd(ans, mid);
    	}
    }
}