oj.uz

Submission #166665

# Submission time Handle Problem Language Result Execution time Memory
166665 2019-12-03T12:38:01 Z thiago4532 Building Bridges (CEOI17_building) C++17
100 / 100
 235 ms 12120 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];
 
struct frac {
    int a, b;

    bool operator<(frac const& c) const {
        return a*c.b < c.a*b;
    }
};

bool flag = 0;
struct line {
	int a, b;
	frac 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);
}
 
frac intersect(line const& l1, line const& l2) {
	return {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, {x, 1}});
	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 6 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 0 ms 376 KB Output is correct
5 Correct 3 ms 376 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 190 ms 4600 KB Output is correct
2 Correct 191 ms 3960 KB Output is correct
3 Correct 189 ms 3704 KB Output is correct
4 Correct 182 ms 4088 KB Output is correct
5 Correct 169 ms 5416 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 6 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 0 ms 376 KB Output is correct
5 Correct 3 ms 376 KB Output is correct
6 Correct 190 ms 4600 KB Output is correct
7 Correct 191 ms 3960 KB Output is correct
8 Correct 189 ms 3704 KB Output is correct
9 Correct 182 ms 4088 KB Output is correct
10 Correct 169 ms 5416 KB Output is correct
11 Correct 191 ms 4524 KB Output is correct
12 Correct 193 ms 4576 KB Output is correct
13 Correct 158 ms 4316 KB Output is correct
14 Correct 228 ms 4728 KB Output is correct
15 Correct 235 ms 12120 KB Output is correct
16 Correct 172 ms 5952 KB Output is correct
17 Correct 100 ms 4472 KB Output is correct
18 Correct 100 ms 4516 KB Output is correct