Submission #1066562

#	Time	Username	Problem	Language	Result	Execution time	Memory
1066562		ShadowShark	Building Bridges (CEOI17_building)	C++17	100 / 100	42 ms	10576 KiB

building

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

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<>> {

	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) {
		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;
	}
} LC;

const int maxN = 1e5 + 5;
long long h[maxN], w[maxN], dp[maxN], sum_w[maxN];

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

    int n;
    cin >> n;

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

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

    /// dp[i] = dp[j] + (sum_w[i] - sum_w[j] - w[i]) + (h[i] - h[j])^2
    ///       = dp[j] + h[i]^2 - 2 * h[i] * h[j] + h[j]^2 + sum_w[i] - sum_W[j] - w[i]
    ///       = (sum_w[i] + h[i]^2 - w[i]) - 2 * h[i] * h[j] + h[j]^2 - sum_W[j] + dp[j]
    LC.add(2 * h[1], -1LL * h[1] * h[1] + sum_w[1]);

    for (int i = 2; i <= n; i++) {
        dp[i] = LC.query(h[i]);
        dp[i] = -1LL * dp[i] + sum_w[i - 1] + 1LL * h[i] * h[i];

        LC.add(2 * h[i], -1LL * h[i] * h[i] + sum_w[i] - dp[i]);
    }

    cout << dp[n];
    return 0;
}

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