oj.uz

Submission #166630

# Submission time Handle Problem Language Result Execution time Memory
166630 2019-12-03T10:16:16 Z thiago4532 Building Bridges (CEOI17_building) C++17
100 / 100
 228 ms 10560 KB 
#include <bits/stdc++.h>
#define int int64_t
using namespace std;
const int maxn = 1e5 + 10;
int h[maxn], pref[maxn], w[maxn];
int n, dp[maxn];

bool flag = 0;
struct line {
	int a, b;
	double x;

	bool operator<(line const& l) const {
		if(flag == 0) return a > l.a;
		else return x < l.x;
	}
};

typedef set<line>::iterator sit;

set<line> lines;

bool hasPrev(sit it)
{
	return (it != lines.begin());
}

bool hasNext(sit it)
{
	return (next(it) != lines.end() && ++it != lines.end());
}

template<typename Arg>
bool bad(Arg&& l1, Arg&& l2, Arg&& l3) {
	return (l2.a - l1.a)*(l3.b - l1.b) >= (l3.a -  l1.a)*(l2.b - l1.b);
}

double intersect(line const& l1, line const& l2) {
	return (double)(l2.b-l1.b)/(l1.a-l2.a);
}

void get_x(sit it) {
	if (hasPrev(it))
	{
		line l = *it;

		l.x = intersect(*prev(it), *it);

		lines.erase(it); lines.insert(l);
	}
}

void add(line const& l) {
	auto it = lines.lower_bound(l);
	if(it != lines.end() && it->a == l.a){
		if(it->b <= l.b) return;
		lines.erase(it);
	}

	lines.insert(l);
	it = lines.find(l);

	if (hasPrev(it) && hasNext(it) && bad(*prev(it), *it, *next(it))) {
		lines.erase(it);
		return;
	}

	while(hasNext(it) && hasNext(next(it)) && bad(*it, *next(it), *next(next(it)))) 
		lines.erase(next(it));

	while(hasPrev(it) && hasPrev(prev(it)) && bad(*prev(prev(it)), *prev(it), *it))
		lines.erase(prev(it));

	get_x(it);
	if (hasNext(it)) get_x(next(it));
}

inline int f(line const& l, int x) {
	return l.a*x + l.b;
}

int query(int x) {
	flag = true;
	auto it = lines.upper_bound({0, 0, (double)x});
	flag = false;
	it--;
	return f(*it, x);
}


int32_t main() {
	cin >> n;
	for(int i=1;i<=n;i++)
		cin >> h[i];

	for(int i=1;i<=n;i++)
		cin >> w[i], pref[i] = pref[i-1] + w[i];

	dp[1] = 0;
	add({-2*h[1], h[1]*h[1] + dp[1] - pref[1]});

	for(int i=2;i<=n;i++) {
		// dp[i] = 0x3f3f3f3f3f3f3f3f;

		// for(int j=1;j<i;j++) {
		// 	dp[i] = min(dp[i], dp[j] - pref[j] + h[j]*h[j] - 2*h[j] * h[i]);
		// }

		dp[i] = query(h[i]);

		dp[i] += h[i]*h[i] + pref[i-1];
		add({-2*h[i], h[i]*h[i] + dp[i] - pref[i]});
	}
	cout << dp[n] << "\n";
	return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 4 ms 376 KB Output is correct
5 Correct 4 ms 376 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 189 ms 4700 KB Output is correct
2 Correct 193 ms 4804 KB Output is correct
3 Correct 194 ms 4700 KB Output is correct
4 Correct 185 ms 4460 KB Output is correct
5 Correct 164 ms 5720 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 4 ms 376 KB Output is correct
5 Correct 4 ms 376 KB Output is correct
6 Correct 189 ms 4700 KB Output is correct
7 Correct 193 ms 4804 KB Output is correct
8 Correct 194 ms 4700 KB Output is correct
9 Correct 185 ms 4460 KB Output is correct
10 Correct 164 ms 5720 KB Output is correct
11 Correct 219 ms 4732 KB Output is correct
12 Correct 194 ms 4600 KB Output is correct
13 Correct 148 ms 4644 KB Output is correct
14 Correct 195 ms 4728 KB Output is correct
15 Correct 228 ms 10560 KB Output is correct
16 Correct 225 ms 5624 KB Output is correct
17 Correct 99 ms 4472 KB Output is correct
18 Correct 101 ms 4516 KB Output is correct