Submission #829674

#	Time	Username	Problem	Language	Result	Execution time	Memory
829674		Thanhs	Building Bridges (CEOI17_building)	C++14	100 / 100	76 ms	11316 KiB

building

#include <bits/stdc++.h>
typedef long long ll;
using namespace std;

struct Line {
	bool type;
	double x;
	ll m, c;
};

bool operator<(Line l1, Line l2) {
	if (l1.type || l2.type) return l1.x < l2.x;
	return l1.m > l2.m;
}

set<Line> cht;
ll h[100001], w[100001], tot = 0, dp[100001];

bool has_prev(set<Line>::iterator it) { return it != cht.begin(); }
bool has_next(set<Line>::iterator it) {
	return it != cht.end() && next(it) != cht.end();
}

double intersect(set<Line>::iterator l1, set<Line>::iterator l2) {
	return (double)(l1->c - l2->c) / (l2->m - l1->m);
}

void calc_x(set<Line>::iterator it) {
	if (has_prev(it)) {
		Line l = *it;
		l.x = intersect(prev(it), it);
		cht.insert(cht.erase(it), l);
	}
}

bool bad(set<Line>::iterator it) {
	if (has_next(it) && next(it)->c <= it->c) return true;
	return (has_prev(it) && has_next(it) &&
	        intersect(prev(it), next(it)) <= intersect(prev(it), it));
}

void add_line(ll m, ll c) {
	set<Line>::iterator it;

	it = cht.lower_bound({0, 0, m, c});
	if (it != cht.end() && it->m == m) {
		if (it->c <= c) return;
		cht.erase(it);
	}

	it = cht.insert({0, 0, m, c}).first;
	if (bad(it)) cht.erase(it);
	else {
		while (has_prev(it) && bad(prev(it))) cht.erase(prev(it));
		while (has_next(it) && bad(next(it))) cht.erase(next(it));

		if (has_next(it)) calc_x(next(it));
		calc_x(it);
	}
}

ll query(ll h) {
	Line l = *prev(cht.upper_bound({1, (double)h, 0, 0}));
	return l.m * h + l.c;
}

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin >> n;
	for (int i = 1; i <= n; i++) cin >> h[i];
	for (int i = 1; i <= n; i++) {
		cin >> w[i];
		tot += w[i];
	}

	dp[1] = -w[1];
	for (int i = 2; i <= n; i++) {
		add_line(-2 * h[i - 1], dp[i - 1] + h[i - 1] * h[i - 1]);
		dp[i] = query(h[i]) - w[i] + h[i] * h[i];
	}

	cout << tot + dp[n];
	return 0;
}

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40