思路：没用完全背包优化的动态规划只能O(n^3)只能过 40%

#include<bits/stdc++.h>
using namespace std;
const int N = 5e3+7;
const int mod = 1e9+7;
string s;
int len;
int num[N],dp[N][N];

int solve(int need,int flag){
    memset(num, 0, sizeof(num));
    memset(dp, 0, sizeof(dp));
    if(!flag){
        reverse(s.begin(),s.end());
        for(int i=0;i<len;i++){
            if(s[i]=='(')s[i]=')';
            else s[i]='(';
        }
    }
    
    int left = 0,cnt = 0;
    for(int i=0;i<len;i++){
        if(s[i]=='(')left++;
        if(s[i]==')') num[++cnt] = left;
    }
    if(num[1]>0)dp[1][0]=1;
    for(int i=1;i<=cnt;i++){
        dp[1][i] = 1;
    }
    for(int i=2;i<=cnt;i++){
        for(int j = ((0ll>i-num[i])?0ll:i-num[i]) ; j<=need ; j++){
            for(int k = 0;k<=j;k++){
                dp[i][j] += dp[i-1][k];
                dp[i][j] %= mod;
            }
        }
    }
    return dp[cnt][need];
}

int main( ){
    ios::sync_with_stdio(0);
    cin.tie(0),cout.tie(0);
    cin>>s;
    len = s.size();
    int need1=0,need2=0;
    int left = 0,right = 0;
    for(int i=0;i<len;i++){
        if(s[i]=='(')left++;
        else left--;
        if(left<0)need1++,left=0;
    }
    for(int j=len-1;j>=0;j--){
        if(s[j]==')')right++;
        else right--;
        if(right<0)need2++,right=0;
    }
    cout<<solve(need1,1)*solve(need2,0)%mod<<endl;
    return 0;
}