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Sereja and Brackets

                                Sereja and Brackets

                                  segment tree

#include <iostream>
#include <cmath>
#include <cstring>

using namespace std;

string s;

struct node
{

    long int len; //max length of matched brackets
    int tn, tp; // tp = total number of '(' brackets

                //tn = total number of ')' brackets
};

node func(node a, node b)
{
    node temp;

    int len = min(a.tp, b.tn);

    temp.len = a.len + b.len + 2 * len;
    temp.tp = a.tp + b.tp - len;
    temp.tn = a.tn + b.tn - len;

    return temp;
}

void buildTree(node seg[], int l, int r, int index)
{
    if(l == r)
    {
        seg[index].len = seg[index].tp = seg[index].tn = 0;
        if(s[l] == ')')
        {
            seg[index].tn = 1;
        }
        else
        {
            seg[index].tp = 1;
        }
     }
     else
     {
         int mid = (l + r) / 2;
         buildTree(seg, l, mid, 2 * index + 1);
         buildTree(seg, mid + 1, r, 2 * index + 2);

         seg[index] = func(seg[2 * index + 1], seg[2 * index + 2]);
     }
}

node query(node seg[], int l, int r, int qs, int qe, int index)
{
    if((qs > r || qe < l))
    {
        node temp;
        temp.len = temp.tp = temp.tn = 0;

        return temp;
    }

    else if(qs <= l && qe >= r)
        return seg[index];

    else
    {
        int mid = (l + r ) / 2;

        node p1 = query(seg, l, mid, qs, qe, 2 * index + 1);
        node p2 = query(seg, mid + 1, r, qs, qe, 2 * index + 2);

        node temp = func(p1, p2);
        return temp;
    }

}

int main()
{
    int m, l, r;

    cin >> s;

    long int size = 4 * s.size();

    node seg[size];

    buildTree(seg, 0, s.size() - 1, 0);

    cin >> m;

    while(m--)
    {
        cin >> l >> r;

        node temp = query(seg, 0, s.size() - 1, l - 1, r - 1, 0);
        cout << temp.len << endl;
    }
    return 0;
}

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