LS 24 Bracket sequence(DP)

Bracket sequence

Given string s made up with (, ), ?, count the way to substitude ? with ( or ) to form regular bracket sequence.

Input

A string s.

(1≤|s|≤1000)

Ouptut

An integer denotes the number of ways modulo (109+7).

Sample input

????

Sample output

2

思路：dp[x][y]字符串长为x时，左括号还有y个未匹配。

#include<iostream>
#include<cstring>
using namespace std;
const int mm=1009;
const int mod=1e9+7;
char s[mm];
int dp[2][mm];
int main()
{while(cin>>s){int len=strlen(s);memset(dp,0,sizeof(dp));dp[0][0]=1;int z=0;for(int i=1;i<=len;i++){if(s[i-1]=='('){for(int j=1;j<=i;j++)dp[z^1][j]=dp[z][j-1];dp[z^1][0]=0;}else if(s[i-1]==')'){for(int j=0;j<i;j++)dp[z^1][j]=dp[z][j+1];}else{for(int j=1;j<=i;j++)dp[z^1][j]=dp[z][j-1];dp[z^1][0]=0;for(int j=0;j<i;j++)dp[z^1][j]=(dp[z][j+1]+dp[z^1][j])%mod;}z^=1;}cout<<dp[z][0]<<"\n";}
}