TLE on Segment Tree for QSET

Hello,

I’m wondering if someone can help me optimize my code for QSET on the last challenge. I was upset that I had a correct algorithm but it simply was just a bit too slow to run in under 1 second for the large input. Here is my code:

#include <iostream>
#include <vector>
#include <string>

using namespace std;

typedef long long LL;
typedef vector<LL> vn;

vn add(vn one, vn two)
{
    for (size_t i = 0; i < 3; ++i)
        one[i] += two[i];

    return one;
}

vn shift(vn &arr, LL amount)
{
    vn result(3, 0);

    for (size_t i = 0; i < 3; ++i)
        result[(i+amount)%3] = arr[i];

    return result;
}

struct SegmentNode
{
    vn leftEnd, rightEnd;
    LL whole;
    LL numD3;
    size_t L, R;

    SegmentNode() {}

    SegmentNode(vn leftEnd, vn rightEnd, LL whole, LL numD3, size_t L, size_t R)
        : leftEnd(leftEnd), rightEnd(rightEnd), whole(whole), numD3(numD3), L(L), R(R) {}
};

struct SegmentTree
{
    vector<SegmentNode> st;

    size_t left(size_t cur) { return cur << 1; }
    size_t right(size_t cur) { return (cur << 1) + 1; }

    SegmentNode merge(SegmentNode &left, SegmentNode &right)
    {
        vn leftEnd = add(left.leftEnd, shift(right.leftEnd, left.whole));
        ++leftEnd[left.whole];

        vn rightEnd = add(right.rightEnd, shift(left.rightEnd, right.whole)); 
        ++rightEnd[right.whole];

        LL whole = (left.whole + right.whole) % 3;

        LL numD3 = left.numD3 + right.numD3;
        for (size_t i = 0; i < 3; ++i)
            numD3 += left.rightEnd[i] * right.leftEnd[(3-i)%3];

        numD3 += left.rightEnd[(3-right.whole)%3];
        numD3 += right.leftEnd[(3-left.whole)%3];
        
        if (whole == 0)
            ++numD3;

        return SegmentNode(leftEnd, rightEnd, whole, numD3, left.L, right.R);
    }
    
    void build(size_t cur, size_t L, size_t R, vn &A)
    {
        if (L == R)
        {
            LL numD3 = (A[L])%3 == 0 ? 1 : 0;
            st[cur] = SegmentNode(vn(3, 0), vn(3, 0), A[L]%3, numD3, L, R);
        }
        else
        {
            build(left(cur), L, (L+R)/2, A);
            build(right(cur), (L+R)/2+1, R, A);

            st[cur] = merge(st[left(cur)], st[right(cur)]);
        }
    }

    SegmentTree(vn &A)
    {
        st = vector<SegmentNode>(A.size()*4);
        build(1, 0, A.size()-1, A);
    }

    SegmentNode query(size_t cur, size_t LQ, size_t RQ)
    {
        if (st[cur].L >= LQ && st[cur].R <= RQ)
            return st[cur];

        if (st[left(cur)].R < LQ)
            return query(right(cur), LQ, RQ);

        if (st[right(cur)].L > RQ)
            return query(left(cur), LQ, RQ);

        SegmentNode leftResult = query(left(cur), LQ, RQ);
        SegmentNode rightResult = query(right(cur), LQ, RQ);

        SegmentNode result = merge(leftResult, rightResult);
        
        return result;
    }

    void update(size_t cur, size_t idx, LL val)
    {
        if (st[cur].L == idx && st[cur].R == idx)
        {
            st[cur].whole = val%3;
            st[cur].numD3 = val%3 == 0 ? 1 : 0;
        }
        else if (st[cur].L <= idx && st[cur].R >= idx)
        {
            update(left(cur), idx, val);
            update(right(cur), idx, val);
            
            st[cur] = merge(st[left(cur)], st[right(cur)]);
        }
    }
};

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    LL N, M;
    cin >> N >> M;

    string line;
    cin >> line;

    vn A(N);
    for (size_t i = 0; i < N; ++i)
    {
        A[i] = line[i] - '0';
    }

    SegmentTree tree(A);

    for (size_t i = 0; i < M; ++i)
    {
        LL type;
        cin >> type;

        if (type == 1)
        {
            size_t X;
            LL Y;
            cin >> X >> Y;
            tree.update(1, X-1, Y);
        }
        else
        {
            size_t C, D;
            cin >> C >> D;
            SegmentNode result = tree.query(1, C-1, D-1);
            cout << result.numD3 << endl;
        }
    }
}
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