## [$GSS3$ - $Can$ $you$ $answer$ $these$ $queries$ $III$](https://www.luogu.com.cn/problem/SP1716)
[SPOJ](https://www.spoj.com/problems/GSS3/en/)


与$GSS1$对比，只是增加了一个单点修改。

```cpp {.line-numbers}
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>

using namespace std;
const int N = 500010;

int n, m;
int a[N];

struct Node {
    int l, r;
    int sum, lmax, rmax, tmax;
} tr[N << 2];

void calc(Node &u, Node &l, Node &r) {
    u.sum = l.sum + r.sum;
    u.lmax = max(l.lmax, l.sum + r.lmax);
    u.rmax = max(r.rmax, r.sum + l.rmax);
    u.tmax = max({l.tmax, r.tmax, l.rmax + r.lmax});
}

void pushup(int u) {
    calc(tr[u], tr[u << 1], tr[u << 1 | 1]);
}

void build(int u, int l, int r) {
    tr[u] = {l, r, 0, 0, 0, 0}; // 无初始值
    if (l == r) {
        tr[u].sum = tr[u].lmax = tr[u].rmax = tr[u].tmax = a[l];
        return;
    }
    int mid = (l + r) >> 1;
    build(u << 1, l, mid), build(u << 1 | 1, mid + 1, r);
    pushup(u);
}

void modify(int u, int x, int v) {
    if (tr[u].l == tr[u].r) {
        tr[u] = {x, x, v, v, v, v};
        return;
    }

    int mid = tr[u].l + tr[u].r >> 1;
    if (x <= mid)
        modify(u << 1, x, v);
    else
        modify(u << 1 | 1, x, v);
    pushup(u);
}

Node query(int u, int l, int r) {
    if (tr[u].l >= l && tr[u].r <= r) return tr[u];

    int mid = tr[u].l + tr[u].r >> 1;
    if (r <= mid) return query(u << 1, l, r);
    if (l > mid) return query(u << 1 | 1, l, r);

    Node a = query(u << 1, l, r), b = query(u << 1 | 1, l, r), res;
    calc(res, a, b);
    return res;
}

int main() {
    ios::sync_with_stdio(false), cin.tie(0);
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];

    build(1, 1, n);

    int op, x, y;
    cin >> m;
    while (m--) {
        cin >> op >> x >> y;
        if (op == 1) {
            if (x > y) swap(x, y);
            printf("%d\n", query(1, x, y).tmax);
        } else
            modify(1, x, y);
    }
    return 0;
}
```