oj.uz

Submission #1109294

# Submission time Handle Problem Language Result Execution time Memory
1109294 2024-11-06T11:11:14 Z available3124 Building Bridges (CEOI17_building) C++14
100 / 100
 81 ms 11408 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 2384 KB Output is correct
2 Correct 1 ms 2384 KB Output is correct
3 Correct 1 ms 2384 KB Output is correct
4 Correct 2 ms 2396 KB Output is correct
5 Correct 1 ms 2384 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 53 ms 2892 KB Output is correct
2 Correct 54 ms 2896 KB Output is correct
3 Correct 53 ms 2880 KB Output is correct
4 Correct 58 ms 2844 KB Output is correct
5 Correct 47 ms 4188 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2384 KB Output is correct
2 Correct 1 ms 2384 KB Output is correct
3 Correct 1 ms 2384 KB Output is correct
4 Correct 2 ms 2396 KB Output is correct
5 Correct 1 ms 2384 KB Output is correct
6 Correct 53 ms 2892 KB Output is correct
7 Correct 54 ms 2896 KB Output is correct
8 Correct 53 ms 2880 KB Output is correct
9 Correct 58 ms 2844 KB Output is correct
10 Correct 47 ms 4188 KB Output is correct
11 Correct 50 ms 3824 KB Output is correct
12 Correct 69 ms 3664 KB Output is correct
13 Correct 35 ms 4088 KB Output is correct
14 Correct 54 ms 4040 KB Output is correct
15 Correct 81 ms 11408 KB Output is correct
16 Correct 50 ms 5212 KB Output is correct
17 Correct 17 ms 3888 KB Output is correct
18 Correct 13 ms 3772 KB Output is correct