oj.uz

Submission #939120

# Submission time Handle Problem Language Result Execution time Memory
939120 2024-03-06T05:54:59 Z vjudge1 Building Bridges (CEOI17_building) C++17
100 / 100
 99 ms 51928 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 k, b;
	int operator * (int x){
		return k * x + b;
	}
	int operator ^ (Line x){
		return ceil((b - x.b) / (x.k - k));
	};
};

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.k == tree[x].k){
			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]);
		
		*/
		/*
		for(int j = 1; j < i; 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 mn = tree.get(h[i]);
		
		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 9 ms 47708 KB Output is correct
2 Correct 8 ms 47708 KB Output is correct
3 Correct 8 ms 47744 KB Output is correct
4 Correct 8 ms 47708 KB Output is correct
5 Correct 8 ms 47708 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 87 ms 50288 KB Output is correct
2 Correct 85 ms 50268 KB Output is correct
3 Correct 87 ms 50296 KB Output is correct
4 Correct 82 ms 50000 KB Output is correct
5 Correct 71 ms 51796 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 47708 KB Output is correct
2 Correct 8 ms 47708 KB Output is correct
3 Correct 8 ms 47744 KB Output is correct
4 Correct 8 ms 47708 KB Output is correct
5 Correct 8 ms 47708 KB Output is correct
6 Correct 87 ms 50288 KB Output is correct
7 Correct 85 ms 50268 KB Output is correct
8 Correct 87 ms 50296 KB Output is correct
9 Correct 82 ms 50000 KB Output is correct
10 Correct 71 ms 51796 KB Output is correct
11 Correct 99 ms 51280 KB Output is correct
12 Correct 96 ms 51460 KB Output is correct
13 Correct 83 ms 50300 KB Output is correct
14 Correct 99 ms 51540 KB Output is correct
15 Correct 70 ms 51928 KB Output is correct
16 Correct 75 ms 51284 KB Output is correct
17 Correct 49 ms 50000 KB Output is correct
18 Correct 47 ms 50132 KB Output is correct