Submission #1099242

#	Time	Username	Problem	Language	Result	Execution time	Memory
1099242		tht2005	Building Bridges (CEOI17_building)	C++17	100 / 100	43 ms	9476 KiB

building

#include <bits/stdc++.h>
using namespace std;

/**
 * Author: Simon Lindholm
 * Date: 2017-04-20
 * License: CC0
 * Source: own work
 * Description: Container where you can add lines of the form kx+m, and query maximum values at points x.
 *  Useful for dynamic programming (``convex hull trick'').
 * Time: O(\log N)
 * Status: stress-tested
 */

typedef long long ll;

struct Line {
	mutable ll k, m, p;
	bool operator<(const Line& o) const { return k < o.k; }
	bool operator<(ll x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) return x->p = inf, 0;
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	void add(ll k, ll m) {
		auto z = insert({k, m, 0}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p)
			isect(x, erase(y));
	}
	ll query(ll x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};

const int N = (int)1e5 + 10;

int h[N];
ll s[N], f[N];

LineContainer L;

void add(int i) {
	L.add(2LL * h[i], -f[i] - (ll)h[i] * h[i] + s[i]);
}

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

	int n;
	cin >> n;
	for(int i = 1; i <= n; ++i)
		cin >> h[i];
	for(int i = 1; i <= n; ++i) {
		cin >> s[i];
		s[i] += s[i - 1];
	}

	f[1] = 0;
	add(1);
	for(int i = 2; i <= n; ++i) {
		f[i] = -L.query(h[i]) + (ll)h[i] * h[i] + s[i - 1];
		add(i);
	}

	cout << f[n];

	return 0;
}

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40