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Submission #939112

# Submission time Handle Problem Language Result Execution time Memory
939112 2024-03-06T05:48:58 Z vjudge1 Building Bridges (CEOI17_building) C++17
100 / 100
 102 ms 51948 KB 
#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define all(a) a.begin(), a.end()
#define int long long
const int inf = 1e9;
const int N = 1e5 + 5;
const int mod = 1e9 + 7;
struct line{
	int m, b;
	
	int operator * (int x){
		return m * x + b;
	}
	
	int operator ^ (line x){
		return ceil((b - x.b) / (x.m - m));
	};
};
 
struct LiChao{
	line tree[N * 30];
	int last, L[N * 30], R[N * 30];
	LiChao(){
		last = 0;
		for(int i=0;i<(N*30);i++) tree[i] = {inf, inf * inf};
	}
	
	void add(line v, int lx = 0, int rx = mod, int x = 0){
		if(lx == rx){
			if(tree[x] * lx > v * lx) swap(tree[x], v);
			return;
		}
		if(v.m == tree[x].m){
			tree[x].b = min(tree[x].b, v.b);
			return;
		}
		
		int m = (lx + rx) >> 1;
		int ix = tree[x] ^ v;
		if(ix <= m){
			if(tree[x] * (m + 1) > v * (m + 1)) swap(tree[x], v);
			add(v, lx, m, (L[x] ? L[x] : L[x] = ++last));
		} else {
			if(tree[x] * m > v * m) swap(tree[x], v);
			add(v, m + 1, rx, (R[x] ? R[x] : R[x] = ++last));
		}
	}
	
	int get(int i, int lx = 0, int rx = mod, int x = 0){
		if(lx == rx) return tree[x] * i;
		int m = (lx + rx) >> 1;
		if(i <= m && L[x]) return min(tree[x] * i, get(i, lx, m, L[x]));
		if(m < i && R[x]) return min(tree[x] * i, get(i, m + 1, rx, R[x]));
		return tree[x] * i;
	}
}tree;
/*
6
3 8 7 1 6 6
0 -1 9 1 2 0
*/
signed main(){
	int n; cin >> n;
	vector<int> h(n+1);
	for(int i = 1;i <= n; i++) cin >> h[i];
	vector<int> w(n+1, 0);
	for(int i = 1;i <= n; i++){
		cin >> w[i];
		w[i]+= w[i-1];
	}
	
	vector<int> dp(n+1);
	dp[1] = 0;
	tree.add({-2 * h[1], dp[1] - w[1] + h[1] * h[1]});
	for(int i = 2;i <= n; i++){
			
		// kx + b
		/*
		
			new_dp[i] = (h[i] - h[j])^2 + dp[j]
			(h[i] - h[j]) * (h[i] - h[j]) = kx
			h[i] * h[i] - h[i] * h[j] - h[j] * h[i] + h[j] * h[j]
			dp[i] = min(dp[i], -2 * h[i] * h[j] + dp[j] - w[j] + h[j] * h[j] + w[i-1] + h[i] * h[i]);
		
		*/
		/*int ans = MAX;
		for(int j = 1; j < i; j++){
			ans = min(ans, -2 * h[i] * h[j] + dp[j] - w[j] + h[j] * h[j] + w[i-1] + h[i] * h[i]);
			//dp[i] = min(dp[i], -2 * h[i] * h[j] + dp[j] - w[j] + h[j] * h[j] + w[i-1] + h[i] * h[i]);
		}
		*/
		int mn = tree.get(h[i]);
		
		//cout << i << " = " << ans << " , " << mn + h[i] * h[i] + w[i-1] << '\n';
		dp[i] = mn + h[i]*h[i] + w[i-1];
		tree.add({-2 * h[i], dp[i] - w[i] + h[i] * h[i]});
	}
	cout << dp[n];
	return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 47708 KB Output is correct
2 Correct 9 ms 47960 KB Output is correct
3 Correct 9 ms 47708 KB Output is correct
4 Correct 11 ms 47704 KB Output is correct
5 Correct 9 ms 47724 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 88 ms 50296 KB Output is correct
2 Correct 87 ms 50148 KB Output is correct
3 Correct 91 ms 50256 KB Output is correct
4 Correct 80 ms 50000 KB Output is correct
5 Correct 70 ms 51284 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 47708 KB Output is correct
2 Correct 9 ms 47960 KB Output is correct
3 Correct 9 ms 47708 KB Output is correct
4 Correct 11 ms 47704 KB Output is correct
5 Correct 9 ms 47724 KB Output is correct
6 Correct 88 ms 50296 KB Output is correct
7 Correct 87 ms 50148 KB Output is correct
8 Correct 91 ms 50256 KB Output is correct
9 Correct 80 ms 50000 KB Output is correct
10 Correct 70 ms 51284 KB Output is correct
11 Correct 99 ms 51424 KB Output is correct
12 Correct 97 ms 51424 KB Output is correct
13 Correct 86 ms 50260 KB Output is correct
14 Correct 102 ms 51536 KB Output is correct
15 Correct 69 ms 51948 KB Output is correct
16 Correct 70 ms 51212 KB Output is correct
17 Correct 58 ms 50160 KB Output is correct
18 Correct 47 ms 50160 KB Output is correct