oj.uz

Submission #895981

# Submission time Handle Problem Language Result Execution time Memory
895981 2023-12-31T10:02:28 Z xxx_xxx Building Bridges (CEOI17_building) C++11
100 / 100
 66 ms 11344 KB 
#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) {
	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
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2392 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 55 ms 3920 KB Output is correct
2 Correct 56 ms 3904 KB Output is correct
3 Correct 56 ms 3920 KB Output is correct
4 Correct 52 ms 3740 KB Output is correct
5 Correct 49 ms 5176 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2392 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 55 ms 3920 KB Output is correct
7 Correct 56 ms 3904 KB Output is correct
8 Correct 56 ms 3920 KB Output is correct
9 Correct 52 ms 3740 KB Output is correct
10 Correct 49 ms 5176 KB Output is correct
11 Correct 49 ms 3932 KB Output is correct
12 Correct 56 ms 3676 KB Output is correct
13 Correct 37 ms 3672 KB Output is correct
14 Correct 57 ms 4264 KB Output is correct
15 Correct 66 ms 11344 KB Output is correct
16 Correct 50 ms 5180 KB Output is correct
17 Correct 13 ms 3676 KB Output is correct
18 Correct 13 ms 3676 KB Output is correct