oj.uz

Submission #829676

# Submission time Handle Problem Language Result Execution time Memory
829676 2023-08-18T14:03:02 Z Thanhs Building Bridges (CEOI17_building) C++14
100 / 100
 68 ms 10416 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 0 ms 212 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 56 ms 2732 KB Output is correct
2 Correct 55 ms 2744 KB Output is correct
3 Correct 58 ms 2704 KB Output is correct
4 Correct 53 ms 2668 KB Output is correct
5 Correct 50 ms 4164 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 56 ms 2732 KB Output is correct
7 Correct 55 ms 2744 KB Output is correct
8 Correct 58 ms 2704 KB Output is correct
9 Correct 53 ms 2668 KB Output is correct
10 Correct 50 ms 4164 KB Output is correct
11 Correct 50 ms 2576 KB Output is correct
12 Correct 56 ms 2636 KB Output is correct
13 Correct 38 ms 2596 KB Output is correct
14 Correct 58 ms 2664 KB Output is correct
15 Correct 68 ms 10416 KB Output is correct
16 Correct 49 ms 4172 KB Output is correct
17 Correct 13 ms 2648 KB Output is correct
18 Correct 13 ms 2644 KB Output is correct