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Submission #637402

# Submission time Handle Problem Language Result Execution time Memory
637402 2022-09-01T16:03:35 Z gromperen Building Bridges (CEOI17_building) C++14
100 / 100
 52 ms 8908 KB 
#include <bits/stdc++.h>
using namespace std;

#define ll long long

const ll INF = 1e18;

struct Line {
	ll m, b;
};

ll f(Line l, ll x) {
	return l.m * x + l.b;
}

struct Node {
	Line line;
	Node* lchild = nullptr;
	Node* rchild = nullptr;
};

ll query(Node* &node, ll x, int l = 0, int r = 1e6+5) {
	if (node == nullptr) return INF;
	int m = (l+r)/2;
	if (x <= m) 	return min(f(node->line, x), query(node->lchild, x, l, m));
	else 		return min(f(node->line, x), query(node->rchild, x, m+1, r));
}

void insert(Node* &node, Line nw, int l = 0, int r = 1e6+5) {
	if (node == nullptr) {
		node = new Node();
		node->line = nw;
		return;
	}
	int m = (l+r)/2;
	if (f(nw, m) < f(node->line, m)) swap(nw, node->line);
	if (f(nw, l) < f(node->line, l))
		insert(node->lchild, nw, l, m);
	if (f(nw, r) < f(node->line, r))
		insert(node->rchild,nw,m+1,r);
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);

	int n; cin >> n;
	vector<ll> h(n+1), w(n+1);
	vector<ll> pre(n+1);
	for (int i = 1; i <= n; ++i) {
		cin>>h[i];
	}
	for (int i = 1; i <= n; ++i) {
		cin>>w[i];
		pre[i] = pre[i-1] + w[i];
	}
	vector<ll>dp(n+1);
	dp[1] = 0;
	w[1] = INF;
	Node* tree = nullptr;
	for (int i = 1; i <= n; ++i) {
		if (i > 1) dp[i] = query(tree, h[i]) + h[i] * h[i] + pre[i-1];
		Line ln;
		ln.m = -2*h[i];
		ln.b = dp[i] + h[i] * h[i] - pre[i];
		insert(tree, ln);
		//cout << dp[i] << " ";
	}
	cout << dp[n]<<"\n";

	return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 320 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 41 ms 4704 KB Output is correct
2 Correct 41 ms 4696 KB Output is correct
3 Correct 38 ms 4732 KB Output is correct
4 Correct 37 ms 4480 KB Output is correct
5 Correct 28 ms 5952 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 320 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 41 ms 4704 KB Output is correct
7 Correct 41 ms 4696 KB Output is correct
8 Correct 38 ms 4732 KB Output is correct
9 Correct 37 ms 4480 KB Output is correct
10 Correct 28 ms 5952 KB Output is correct
11 Correct 37 ms 4844 KB Output is correct
12 Correct 37 ms 4716 KB Output is correct
13 Correct 30 ms 4580 KB Output is correct
14 Correct 52 ms 4836 KB Output is correct
15 Correct 32 ms 8908 KB Output is correct
16 Correct 28 ms 5992 KB Output is correct
17 Correct 16 ms 4436 KB Output is correct
18 Correct 24 ms 4416 KB Output is correct