oj.uz

Submission #1066562

# Submission time Handle Problem Language Result Execution time Memory
1066562 2024-08-20T02:00:53 Z ShadowShark Building Bridges (CEOI17_building) C++17
100 / 100
 42 ms 10576 KB 
#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
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 508 KB Output is correct
5 Correct 0 ms 348 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 32 ms 4612 KB Output is correct
2 Correct 27 ms 4512 KB Output is correct
3 Correct 30 ms 4436 KB Output is correct
4 Correct 25 ms 4600 KB Output is correct
5 Correct 23 ms 5460 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 508 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 32 ms 4612 KB Output is correct
7 Correct 27 ms 4512 KB Output is correct
8 Correct 30 ms 4436 KB Output is correct
9 Correct 25 ms 4600 KB Output is correct
10 Correct 23 ms 5460 KB Output is correct
11 Correct 26 ms 4700 KB Output is correct
12 Correct 29 ms 4688 KB Output is correct
13 Correct 21 ms 4700 KB Output is correct
14 Correct 29 ms 4672 KB Output is correct
15 Correct 42 ms 10576 KB Output is correct
16 Correct 23 ms 5592 KB Output is correct
17 Correct 14 ms 4444 KB Output is correct
18 Correct 14 ms 4440 KB Output is correct