oj.uz

Submission #878933

# Submission time Handle Problem Language Result Execution time Memory
878933 2023-11-25T15:30:13 Z LarryMiller Building Bridges (CEOI17_building) C++11
100 / 100
 71 ms 11472 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 1 ms 2392 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2520 KB Output is correct
5 Correct 1 ms 2516 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 57 ms 4084 KB Output is correct
2 Correct 59 ms 3924 KB Output is correct
3 Correct 57 ms 3920 KB Output is correct
4 Correct 55 ms 3688 KB Output is correct
5 Correct 49 ms 5272 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 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2520 KB Output is correct
5 Correct 1 ms 2516 KB Output is correct
6 Correct 57 ms 4084 KB Output is correct
7 Correct 59 ms 3924 KB Output is correct
8 Correct 57 ms 3920 KB Output is correct
9 Correct 55 ms 3688 KB Output is correct
10 Correct 49 ms 5272 KB Output is correct
11 Correct 51 ms 4016 KB Output is correct
12 Correct 60 ms 4144 KB Output is correct
13 Correct 37 ms 3676 KB Output is correct
14 Correct 56 ms 3848 KB Output is correct
15 Correct 71 ms 11472 KB Output is correct
16 Correct 49 ms 5200 KB Output is correct
17 Correct 18 ms 4188 KB Output is correct
18 Correct 15 ms 3676 KB Output is correct