CF780G Andryusha and Nervous Barriers

CF780G Andryusha and Nervous Barriers

考虑树套树。

一维维护区间列，另一维维护列上的球的高度，保证点数正确。

维护单点加，区间查。

扫描线高度从大到小维护到每一个板时的情况。

优化：区间查是判区间球高度最小都只能穿过挡板就结束掉。

时间复杂度 $\mathcal{O}(n{\log }^{2}n)$。

#include<bits/stdc++.h>

using namespace std;

#define int long long
typedef long long ll;

#define ha putchar(' ')
#define he putchar('\n')

inline int read() {
    
	int x = 0, f = 1;
	char c = getchar();
	while (c < '0' || c > '9') {
    
		if (c == '-')
			f = -1;
		c = getchar();
	}
	while (c >= '0' && c <= '9')
		x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
	return x * f;
}

inline void write(int x) {
    
	if (x < 0) {
    
		putchar('-');
		x = -x;
	}
	if (x > 9)
		write(x / 10);
	putchar(x % 10 + 48);
}

const int _ = 1e5 + 10, mod = 1e9 + 7;

int h, w, n, N;

ll ans[_ << 2];

priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> q[_];

struct abc {
    
	int u, l, r, s;
	bool operator < (const abc &t) const {
    
		return u > t.u;
	}
} k[_];

void build(int o, int l, int r) {
    
	if (l == r) {
    
		q[l].push({
    h + 1, 1});
		ans[o] = h + 1;
		return;
	}
	int mid = (l + r) >> 1;
	build(o << 1, l, mid), build(o << 1 | 1, mid + 1, r);
	ans[o] = min(ans[o << 1], ans[o << 1 | 1]);
}

void upd(int o, int l, int r, int pos, int p, int h) {
    
	if (l == r) {
    
		q[l].push({
    h, p});
		ans[o] = min(ans[o], (ll)h);
		return;
	}
	int mid = (l + r) >> 1;
	if (pos <= mid) upd(o << 1, l, mid, pos, p, h);
	else upd(o << 1 | 1, mid + 1, r, pos, p, h);
	ans[o] = min(ans[o << 1], ans[o << 1 | 1]);
}

int qry(int o, int l, int r, int L, int R, int h, int s) {
    
	if (ans[o] > h + s) return 0;
	if (l == r) {
    
		int res = 0;
		while (!q[l].empty() && q[l].top().first <= h + s) {
    
			res = (res + q[l].top().second) % mod;
			q[l].pop();
		}
		ans[o] = q[l].empty() ? 1e10 + 7 : q[l].top().first;
		return res;
	}
	int mid = (l + r) >> 1, res = 0;
	if (L <= mid) res = qry(o << 1, l, mid, L, R, h, s);
	if (R > mid) res = (res + qry(o << 1 | 1, mid + 1, r, L, R, h, s)) % mod;
	ans[o] = min(ans[o << 1], ans[o << 1 | 1]);
	return res;
}

signed main() {
    
	h = read(), w = read(), n = read();
	for (int i = 1; i <= n; ++i) k[i].u = read(), k[i].l = read(), k[i].r = read(), k[i].s = read();
	N = w;
	build(1, 1, w);
	sort(k + 1, k + n + 1);
	for (int i = 1; i <= n; ++i) {
    
		int t = qry(1, 1, w, k[i].l, k[i].r, k[i].u, k[i].s);
		N = (N + t) % mod;
		if (k[i].l == 1) upd(1, 1, w, k[i].r + 1, (t << 1) % mod, k[i].u);
		else if (k[i].r == w) upd(1, 1, w, k[i].l - 1, (t << 1) % mod, k[i].u);
		else {
    
			upd(1, 1, w, k[i].l - 1, t, k[i].u);
			upd(1, 1, w, k[i].r + 1, t, k[i].u);
		}
	}
	write(N), he;
	return 0;
}