CH4301 区间最大子段和

给定长度为N的数组A，以及M条指令，每条指令可能是以下两种之一：

• 1 x y，查询区间[x,y]中的最大连续子段和。
• 2 x y，把A[x]改成y。

对于每个询问，输出一个整数表示答案。
数据限制：N<=5e5, M<=1e5, |A[i]|<=1000。

提示：线段树，每个区间需要维护答案、前缀、后缀以及区间和。

#include <bits/stdc++.h>

template<class Info>
struct SegmentTree {
    int n;
    std::vector<Info> info;
    SegmentTree():n(0) {}
    SegmentTree(int _n, Info v = Info()) {
        init(_n, v);
    }
    void init(int _n, Info v = Info()) {
        init(std::vector<Info>(_n, v));
    }
    template<class T>
    SegmentTree(std::vector<T> v) {
        init(v);
    }
    template<class T>
    void init(std::vector<T> v) {
        n = v.size();
        info.assign(4 << std::__lg(n), Info());
        std::function<void(int,int,int)> build = [&](int x, int l, int r) {
            if (l + 1 == r) {
                info[x] = v[l]; //fixme
                return;
            }
            int m = (l + r) / 2;
            build(2*x+1, l, m);
            build(2*x+2, m, r);
            pushup(x);
        };
        build(0, 0, n);
    }
    void pushup(int x) {
        info[x] = info[2*x+1] + info[2*x+2];
    }
    void modify(int x, int l, int r, int p, const Info &v) {
        if (l + 1 == r) {
            info[x] = v; //fixme
            return;
        }
        int m = (l + r) / 2;
        if (p < m) {
            modify(2*x+1, l, m, p, v);
        } else {
            modify(2*x+2, m, r, p, v);
        }
        pushup(x);
    }
    void modify(int p, const Info &v) {
        modify(0, 0, n, p, v);
    }
    Info rangeQuery(int x, int l, int r, int L, int R) {
        if (R <= l || r <= L) {
            return Info();
        }
        if (L <= l && r <= R) {
            return info[x];
        }
        int m = (l + r) / 2;
        return rangeQuery(2*x+1, l, m, L, R) + rangeQuery(2*x+2, m, r, L, R);
    }
    Info rangeQuery(int L, int R) {
        return rangeQuery(0, 0, n, L, R);
    }
    template<class F>
    int findFirst(int x, int l, int r, int L, int R, F pred) {
        if (R <= l || r <= L || !pred(info[x])) {
            return -1;
        }
        if (l + 1 == r) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findFirst(2*x+1, l, m, L, R, pred);
        if (res == -1) {
            res = findFirst(2*x+2, m, r, L, R, pred);
        }
        return res;
    }
    template<class F>
    int findFirst(int L, int R, F pred) {
        return findFirst(0, 0, n, L, R, pred);
    }
    template<class F>
    int findLast(int x, int l, int r, int L, int R, F pred) {
        if (R <= l || r <= L || !pred(info[x])) {
            return -1;
        }
        if (l + 1 == r) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findLast(2*x+2, m, r, L, R, pred);
        if (res == -1) {
            res = findLast(2*x+1, l, m, L, R, pred);
        }
        return res;
    }
    template<class F>
    int findLast(int L, int R, F pred) {
        return findLast(0, 0, n, L, R, pred);
    }
};

struct Info {
    int val, pre, suf, sum;
    static const int inf = 1e8;
    Info(int v=inf):val(v),pre(v),suf(v),sum(v) {}
    friend Info operator+(const Info &a, const Info &b) {
        if (a.val == inf) {
            return b;
        }
        if (b.val == inf) {
            return a;
        }
        Info ans;
        ans.val = std::max(a.suf + b.pre, std::max(a.val, b.val));
        ans.pre = std::max(a.pre, a.sum+b.pre);
        ans.suf = std::max(a.suf+b.sum, b.suf);
        ans.sum = a.sum + b.sum;
        return ans;
    }
};

void solve() {
    int N, M;
    std::cin >> N >> M;
    std::vector<int> A(N);
    for (int i = 0; i < N; i++) {
        std::cin >> A[i];
    }
    SegmentTree<Info> seg(A);
    for (int i = 0; i < M; i++) {
        int k, x, y;
        std::cin >> k >> x >> y;
        if (k == 1) {
            x--, y--;
            if (x > y) {
                std::swap(x, y);
            }
            std::cout << seg.rangeQuery(x, y+1).val << "\n";
        } else {
            x--;
            seg.modify(x, Info(y));
        }
    }
}

int main() {
    std::cin.tie(0)->sync_with_stdio(0);
    int t = 1;
    while (t--) solve();
    return 0;
}