The problem is about bracket matching . link

I have solved it. Didn't thought it would pass the time limit . I used segment tree. My update function seems too slow to me, but couldn't think of other way Please Help to optimise

struct dta {
        vector<char> V; // Using vector , stack may be the best
        dta(){}
        dta(char n){V.push_back(n);}
        
}T[3 * MX];


void init( int node , int b , int e)
{
        if(b == e ){
                T[node] = dta(str[b]);
                return;
        }
        int mid = ( b + e ) / 2;
        init(node * 2, b, mid);
        init(node *2 +1 , mid + 1, e);
        T[node].V = T[node *2].V;
        int top = T[node].V.size() - 1;

        // merging the two segments 

        for(int i = 0 ; i< T[node *2+ 1].V.size(); i ++ ){
                if(top>=0 && T[node *2+ 1].V[i] == ')' && T[node].V[top] == '('){
                        T[node].V.pop_back();
                        top -- ;
                }
                else {
                        T[node].V.push_back(T[node *2+ 1].V[i]);
                        top ++;
                }
        }
        
}

void upd ( int node, int b , int e , int pos )
{
        if(b == e ){
                T[node] = dta(str[b]);
                return;
        }
        int mid = ( b + e ) / 2;
        if(pos <= mid ){
                upd(node * 2, b, mid, pos);
        }
        else upd(node *2 +1, mid +1 ,e, pos);
        T[node].V = T[node *2].V;
        int top = (int)T[node].V.size() - 1;
        
        // Update & merge The left & right segment

        for(int i = 0 ; i< T[node *2+ 1].V.size(); i ++ ){
                if(top>=0 && T[node *2+ 1].V[i] == ')' && T[node].V[top] == '('){
                        T[node].V.pop_back();
                        top -- ;
                }
                else {
                        T[node].V.push_back(T[node *2+ 1].V[i]);
                        top ++;
                }
        }
        
        
}

But storing the whole segments and update is too heavy, Don't know the complexity of update operation ( may be n lg n )