hdu 5831 Rikka with Parenthesis II 括号匹配+交换

Rikka with Parenthesis II

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 136    Accepted Submission(s): 97

Problem Description

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

Correct parentheses sequences can be defined recursively as follows:
1.The empty string "" is a correct sequence.
2.If "X" and "Y" are correct sequences, then "XY" (the concatenation of X and Y) is a correct sequence.
3.If "X" is a correct sequence, then "(X)" is a correct sequence.
Each correct parentheses sequence can be derived using the above rules.
Examples of correct parentheses sequences include "", "()", "()()()", "(()())", and "(((())))".

Now Yuta has a parentheses sequence S, and he wants Rikka to choose two different position i,j and swap Si,Sj. 

Rikka likes correct parentheses sequence. So she wants to know if she can change S to a correct parentheses sequence after this operation.

It is too difficult for Rikka. Can you help her?

 

Input

The first line contains a number t(1<=t<=1000), the number of the testcases. And there are no more then 10 testcases with n>100

For each testcase, the first line contains an integers n(1<=n<=100000), the length of S. And the second line contains a string of length S which only contains ‘(’ and ‘)’.

 

Output

For each testcase, print "Yes" or "No" in a line.

 

Sample Input

3 4 ())( 4 ()() 6 )))(((

 

Sample Output

Yes Yes No

Hint

For the second sample input, Rikka can choose (1,3) or (2,4) to swap. But do nothing is not allowed.

 

Author

学军中学

 

Source

2016 Multi-University Training Contest 8

 

Recommend

wange2014   |   We have carefully selected several similar problems for you:  5830 5829 5828 5827 5826 

 题意：给你一个由'('和')'组成的字符串，首先你必须交换其中两个不同位置的字符，然后判断是否有一种方案使得最后形成的字符串 合法；

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <algorithm>
#include <set>
using namespace std;
typedef long long ll;
typedef unsigned long long Ull;
#define MM(a,b) memset(a,b,sizeof(a));
const double eps = 1e-10;
const int  inf =0x7f7f7f7f;
const double pi=acos(-1);
const int N=100005;

char s[N];
int main()
{
    int cas,n;
    scanf("%d",&cas);
    while(cas--)
    {
        scanf("%d",&n);
        scanf("%s",s);
        int l=0,r=0,len=n;
        if(len%2==1) {printf("No
");continue;}
        for(int i=0;s[i]!='';i++)
        {
            if(s[i]=='(') r++;
            else if(s[i]==')')
            {
                if(r>=1) r--;
                else l++;
            }
        }
        if(len==2)
          {
            if(l==1&&r==1) printf("Yes
");
            else printf("No
");
            continue;
          }

         if(l==0&&r==0) printf("Yes
");
         else if(l+r==2)
         {
             if(l==1&&r==1) printf("Yes
");
             else printf("No
");
         }
         else if(l+r==4)
         {
             if(l==2&&r==2) printf("Yes
");
             else printf("No
");
         }
         else printf("No
");
    }
    return 0;
}

　　分析：比赛时只看到这道题是以前做过的题目的简化版，，结果还是太大意了，，，

本来分析出来了  ))((  这种特殊情况也是可以的，但是草稿纸没打好，一不留神以为是右移成了())(,,,,其实是()()。。悲剧