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Submission #967346

# Submission time Handle Problem Language Result Execution time Memory
967346 2024-04-22T02:35:44 Z tminh_hk20 Building Bridges (CEOI17_building) C++14
100 / 100
 73 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.erase(it);
		cht.insert(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 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 60 ms 3900 KB Output is correct
2 Correct 71 ms 3676 KB Output is correct
3 Correct 60 ms 3672 KB Output is correct
4 Correct 57 ms 3664 KB Output is correct
5 Correct 64 ms 5268 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 60 ms 3900 KB Output is correct
7 Correct 71 ms 3676 KB Output is correct
8 Correct 60 ms 3672 KB Output is correct
9 Correct 57 ms 3664 KB Output is correct
10 Correct 64 ms 5268 KB Output is correct
11 Correct 53 ms 3932 KB Output is correct
12 Correct 61 ms 3676 KB Output is correct
13 Correct 39 ms 3672 KB Output is correct
14 Correct 59 ms 4040 KB Output is correct
15 Correct 73 ms 11344 KB Output is correct
16 Correct 57 ms 5260 KB Output is correct
17 Correct 12 ms 3676 KB Output is correct
18 Correct 15 ms 3736 KB Output is correct