BZOJ 1135 P3488 LYZ-Ice Skates 线段树+Hall

https://www.luogu.org/problem/P3488

根据Hall定理 左边任意一个区间L-R a[i]的和sum[l~r] 都要<= (R-L+1+d)*K

把(R-L+1)*K 挪到左边 即为 对任意L-R区间 有 $\sum_{i=L}^R{(a[i]-k)} \le K*D$

然后用线段树最大字段和去维护它即可

 

#include<bits/stdc++.h>
#define RG register
using namespace std;
typedef long long ll;
const int MAXN = 500005;
struct segment_tree {
        ll lmax, rmax, ans, sum;
} sgt[MAXN << 2];
int n, m;
ll k, d;
inline void pushup(int x) {
        sgt[x].sum = sgt[x << 1].sum + sgt[x << 1 | 1].sum;
        sgt[x].lmax = max(sgt[x << 1].lmax, sgt[x << 1].sum + sgt[x << 1 | 1].lmax);
        sgt[x].rmax = max(sgt[x << 1 | 1].rmax, sgt[x << 1].rmax + sgt[x << 1 | 1].sum);
        sgt[x].ans = max(sgt[x << 1].ans, max(sgt[x << 1 | 1].ans, sgt[x << 1].rmax + sgt[x << 1 | 1].lmax));
}
void build(int x, int l, int r) {
        if (l == r) {
                sgt[x].lmax = sgt[x].rmax = 0;
                sgt[x].sum = sgt[x].ans = -k;
                return ;
        }
        int mid = (l + r) >> 1;
        build(x << 1, l, mid);
        build(x << 1 | 1, mid + 1, r);
        pushup(x);
}
void update(int x, int l, int r, int aim, ll add) {
        if (l == r) {
                sgt[x].sum += add, sgt[x].ans += add;
                sgt[x].lmax = sgt[x].rmax = max(sgt[x].sum, 0LL);
                return ;
        }
        int mid = (l + r) >> 1;
        if (aim <= mid) {
                update(x << 1, l, mid, aim, add);
        } else {
                update(x << 1 | 1, mid + 1, r, aim, add);
        }
        pushup(x);
}
int main() {
        ll x, y;
        scanf("%d %d %lld %lld", &n, &m, &k, &d);
        build(1, 1, n);
        for (int i = 1; i <= m; i++) {
                scanf("%lld %lld", &x, &y);
                update(1, 1, n, x, y);
                if (sgt[1].ans <= 1LL * k * d) {
                        printf("TAK\n");
                } else {
                        printf("NIE\n");
                }
        }
        return 0;
}