oj.uz

Submission #390166

# Submission time Handle Problem Language Result Execution time Memory
390166 2021-04-15T13:33:58 Z ronnith Building Bridges (CEOI17_building) C++14
100 / 100
 61 ms 8212 KB 
#include <bits/stdc++.h>

using namespace std;

struct line {
	long long m, c;
	line() : m(0), c(0) {}
	line(long long mm, long long cc) : m(mm), c(cc) {}
	inline long long get_y(long long x) { return m*x+c; }
};

void swap(line& x, line& y) {
	swap(x.m, y.m);
	swap(x.c, y.c);
}

struct node {
	int l, r;
	line crr;
	node* left;
	node* right;
	node(int ll, int rr) : l(ll), r(rr), left(nullptr), right(nullptr) {}
	node(int ll, int rr, line L) : l(ll), r(rr), crr(L), left(nullptr), right(nullptr) {}
};

struct li_chao_tree {
	int MX;
	node* root;

	li_chao_tree(int _) : MX(_) {
		root = nullptr;
	}

	inline bool is_mid_range(int l, int r, node* v, line L) {
		return (v->crr.get_y(l) > L.get_y(l)) != (v->crr.get_y(r) > L.get_y(r));
	}

	void insert(node* v, int lx, int rx, line L) {
		if(lx == rx) {
			if(L.get_y(lx) < v->crr.get_y(lx)) {
				v->crr = L;
			}
		} else {
			int mid = (lx+rx)/2;
			if(is_mid_range(lx, mid, v, L)) {
				if(v->crr.get_y(rx) > L.get_y(rx)) {
					swap(v->crr, L);
				}
				if(v->left == nullptr) {
					v->left = new node(lx, mid, L);
					return;
				}
				insert(v->left, lx, mid, L);
			} else {
				if(v->crr.get_y(lx) > L.get_y(lx)) {
					swap(v->crr, L);
				}
				if(v->right == nullptr) {
					v->right = new node(mid + 1, rx, L);
					return;
				}
				insert(v->right, mid + 1, rx, L);
			}
		}
	}

	void insert(line L) {
		if(root == nullptr) {
			root = new node(0, MX, L);
			return;
		}
		insert(root, 0, MX, L);
	}

	long long query(node* v, int x) {
		if(v == nullptr) return LONG_LONG_MAX;
		int mid = (v->l+v->r)/2;
		if(x <= mid) {
			return min(query(v->left, x), v->crr.get_y(x));
		} else {
			return min(query(v->right, x), v->crr.get_y(x));
		}
	}
	
	long long query(int x) {
		return query(root, x);
	}
};

const int N = (int)1e5;
const int MX = (int)1e6;
int n;
long long H[N], W[N], dp[N];

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	cin >> n;
	for(int i = 0;i < n;i ++) {
		cin >> H[i];
	}
	for(int i = 0;i < n;i ++) {
		cin >> W[i];
		if(i != 0) W[i] += W[i - 1];
	}
	dp[0] = 0;
	li_chao_tree lct(MX);
	lct.insert(line(-2*H[0], H[0]*H[0]-W[0]+dp[0]));
	for(int i = 1;i < n;i ++) {
		dp[i] = H[i]*H[i]+W[i-1] + lct.query(H[i]);
		lct.insert(line(-2*H[i], H[i]*H[i]-W[i]+dp[i]));
	}
	cout << dp[n - 1] << '\n';
	return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 320 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 336 KB Output is correct
5 Correct 1 ms 332 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 61 ms 4076 KB Output is correct
2 Correct 56 ms 4180 KB Output is correct
3 Correct 55 ms 4164 KB Output is correct
4 Correct 51 ms 3628 KB Output is correct
5 Correct 37 ms 6664 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 320 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 336 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 61 ms 4076 KB Output is correct
7 Correct 56 ms 4180 KB Output is correct
8 Correct 55 ms 4164 KB Output is correct
9 Correct 51 ms 3628 KB Output is correct
10 Correct 37 ms 6664 KB Output is correct
11 Correct 56 ms 4572 KB Output is correct
12 Correct 59 ms 4880 KB Output is correct
13 Correct 41 ms 3784 KB Output is correct
14 Correct 58 ms 4984 KB Output is correct
15 Correct 38 ms 8212 KB Output is correct
16 Correct 37 ms 6572 KB Output is correct
17 Correct 27 ms 3700 KB Output is correct
18 Correct 27 ms 3700 KB Output is correct