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Submission #860140

# Submission time Handle Problem Language Result Execution time Memory
860140 2023-10-11T18:44:16 Z Hacv16 Building Bridges (CEOI17_building) C++17
100 / 100
 47 ms 67236 KB 
#include <bits/stdc++.h>
using namespace std;
 
#define int long long int
 
const int MAX = 1e5 + 15;
const int MAXC = 1e6 + 10;
const int INF = 1e18 + 10;

int n, h[MAX], sw[MAX], dp[MAX];
 
struct Line
{
	int a, b;
	Line(int x = 0, int y = INF) : a(x), b(y) { }

	int operator ()(int x){ return a * x + b; }
 
} seg[4 * MAXC];
 
void update(int p, int l, int r, Line f)
{
	int m = (l + r) >> 1, e = 2 * p, d = e + 1;
 
	bool lessMid = f(m) < seg[p](m);
	bool lessLeft = f(l) < seg[p](l);
 
	if(lessMid) swap(seg[p], f);
 
	if(l == r) return;
 
	if(lessMid != lessLeft) update(e, l , m , f);
	else update(d, m + 1 , r , f);
}
 
int query(int x, int p, int l, int r)
{
	if(l == r) return seg[p](x);
	int m = (l + r) >> 1, e = 2 * p, d = e + 1;
 
	if(x <= m) return min(seg[p](x), query(x, e, l, m));
	else return min(seg[p](x), query(x, d, m + 1, r));
}
 
int32_t main(void)
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
 
	cin >> n;
 
	for(int i = 1; i <= n; i++) cin >> h[i];
	for(int i = 1; i <= n; i++) cin >> sw[i], sw[i] += sw[i - 1];
 
	auto getA = [&](int i){ return - 2 * h[i]; };
	auto getB = [&](int i){ return h[i] * h[i] - sw[i] + dp[i]; };
 
	dp[1] = 0;
	update(1, 1, MAXC, Line(getA(1), getB(1)));
 
	for(int i = 2; i <= n; i++)
	{
		dp[i] = h[i] * h[i] + sw[i - 1] + query(h[i], 1, 1, MAXC);
		update(1, 1, MAXC, Line(getA(i), getB(i)));
	}
 
	cout << dp[n] << '\n';
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 64088 KB Output is correct
2 Correct 9 ms 64264 KB Output is correct
3 Correct 9 ms 64092 KB Output is correct
4 Correct 9 ms 64208 KB Output is correct
5 Correct 10 ms 64196 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 42 ms 66396 KB Output is correct
2 Correct 41 ms 66388 KB Output is correct
3 Correct 41 ms 66396 KB Output is correct
4 Correct 39 ms 66176 KB Output is correct
5 Correct 37 ms 66136 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 64088 KB Output is correct
2 Correct 9 ms 64264 KB Output is correct
3 Correct 9 ms 64092 KB Output is correct
4 Correct 9 ms 64208 KB Output is correct
5 Correct 10 ms 64196 KB Output is correct
6 Correct 42 ms 66396 KB Output is correct
7 Correct 41 ms 66388 KB Output is correct
8 Correct 41 ms 66396 KB Output is correct
9 Correct 39 ms 66176 KB Output is correct
10 Correct 37 ms 66136 KB Output is correct
11 Correct 47 ms 67236 KB Output is correct
12 Correct 46 ms 66392 KB Output is correct
13 Correct 38 ms 66388 KB Output is correct
14 Correct 45 ms 66396 KB Output is correct
15 Correct 36 ms 66136 KB Output is correct
16 Correct 37 ms 66128 KB Output is correct
17 Correct 35 ms 66644 KB Output is correct
18 Correct 30 ms 66396 KB Output is correct