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D - Scope Editorial / 

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Time Limit: 2 sec / Memory Limit: 1024 MB

Score : 400400 points

Problem Statement

A string consisting of lowercase English letters, (, and ) is said to be a good string if you can make it an empty string by the following procedure:

• First, remove all lowercase English letters.
• Then, repeatedly remove consecutive () while possible.

For example, ((a)ba) is a good string, because removing all lowercase English letters yields (()), from which we can remove consecutive () at the 22-nd and 33-rd characters to obtain (), which in turn ends up in an empty string.

You are given a good string SS. We denote by S_iSi​ the ii-th character of SS.

For each lowercase English letter a, b, \ldots…, and z, we have a ball with the letter written on it. Additionally, we have an empty box.

For each i = 1,2,i=1,2, \ldots… ,|S|,∣S∣ in this order, Takahashi performs the following operation unless he faints.

• If S_iSi​ is a lowercase English letter, put the ball with the letter written on it into the box. If the ball is already in the box, he faints.
• If S_iSi​ is (, do nothing.
• If S_iSi​ is ), take the maximum integer jj less than ii such that the jj-th through ii-th characters of SS form a good string. (We can prove that such an integer jj always exists.) Take out from the box all the balls that he has put in the jj-th through ii-th operations.

Determine if Takahashi can complete the sequence of operations without fainting.

Constraints

• 1 \leq |S| \leq 3 \times 10^51≤∣S∣≤3×105
• SS is a good string.

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Input

The input is given from Standard Input in the following format:

SS

Output

Print Yes if he can complete the sequence of operations without fainting; print No otherwise.

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Sample Input 1 Copy

Copy

((a)ba)

Sample Output 1 Copy

Copy

Yes

For i = 1i=1, he does nothing.
For i = 2i=2, he does nothing.
For i = 3i=3, he puts the ball with a written on it into the box.
For i = 4i=4, j=2j=2 is the maximum integer less than 44 such that the jj-th through 44-th characters of SS form a good string, so he takes out the ball with a written on it from the box.
For i = 5i=5, he puts the ball with b written on it into the box.
For i = 6i=6, he puts the ball with a written on it into the box.
For i = 7i=7, j=1j=1 is the maximum integer less than 77 such that the jj-th through 77-th characters of SS form a good string, so he takes out the ball with a written on it, and another with b, from the box.

Therefore, the answer to this case is Yes.

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Sample Input 2 Copy

Copy

(a(ba))

Sample Output 2 Copy

Copy

No

For i = 1i=1, he does nothing.
For i = 2i=2, he puts the ball with a written on it into the box.
For i = 3i=3, he does nothing.
For i = 4i=4, he puts the ball with b written on it into the box.
For i = 5i=5, the ball with a written on it is already in the box, so he faints, aborting the sequence of operations.

Therefore, the answer to this case is No.

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Sample Input 3 Copy

Copy

(((())))

Sample Output 3 Copy

Copy

Yes

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Sample Input 4 Copy

Copy

abca

Sample Output 4 Copy

Copy

No

分析

这题就算用栈模拟一下，然后如果在消除前不能让所有的字母的个数都小于等于1，就yes了。

代码

#include <iostream>
#include <algorithm>
#define ll long long
#include <cmath>
#include <stack>
#include <cstring>
using namespace std;
const int N=300010;
int a[N];
stack<char>stk;
int main(){
	string s;
	cin>>s;
	int cnt[30];
	memset(cnt,0,sizeof cnt);
	for(int i=0;i<s.size();i++){
		if(s[i]=='('){
			stk.push(s[i]);
		}
		else if(s[i]>='a' && s[i]<='z'){
			int now=s[i]-'a';
			//cout<<cnt[now]<<endl;
			if(cnt[now]==1){
				puts("No");
				return 0;
			}
			cnt[now]++;
			stk.push(s[i]);
		}
		else{
			while(stk.top()!='(' && !stk.empty()){
				cnt[stk.top()-'a']--;
				stk.pop();
			}
			if(!stk.empty())
			    stk.pop();
		}
		//cout<<"****************************************8"<<endl;
	} 
	puts("Yes");
}