oj.uz

Submission #829674

# Submission time Handle Problem Language Result Execution time Memory
829674 2023-08-18T14:02:46 Z Thanhs Building Bridges (CEOI17_building) C++14
100 / 100
 76 ms 11316 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) {
	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
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 324 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 336 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 58 ms 3712 KB Output is correct
2 Correct 64 ms 3796 KB Output is correct
3 Correct 58 ms 3768 KB Output is correct
4 Correct 64 ms 3564 KB Output is correct
5 Correct 49 ms 5076 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 1 ms 340 KB Output is correct
3 Correct 1 ms 324 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 336 KB Output is correct
6 Correct 58 ms 3712 KB Output is correct
7 Correct 64 ms 3796 KB Output is correct
8 Correct 58 ms 3768 KB Output is correct
9 Correct 64 ms 3564 KB Output is correct
10 Correct 49 ms 5076 KB Output is correct
11 Correct 52 ms 3836 KB Output is correct
12 Correct 60 ms 3708 KB Output is correct
13 Correct 40 ms 3716 KB Output is correct
14 Correct 67 ms 3824 KB Output is correct
15 Correct 76 ms 11316 KB Output is correct
16 Correct 49 ms 5068 KB Output is correct
17 Correct 18 ms 3672 KB Output is correct
18 Correct 15 ms 3704 KB Output is correct