oj.uz

Submission #669589

# Submission time Handle Problem Language Result Execution time Memory
669589 2022-12-06T19:42:18 Z four_specks Building Bridges (CEOI17_building) C++17
100 / 100
 50 ms 8808 KB 
#include <bits/stdc++.h>

using namespace std;

inline namespace
{
    template <typename T>
    T fl_div(T a, T b) { return a / b - ((a ^ b) < 0 && a % b); }

    template <typename T>
    struct LineContainerObject
    {
        T m, c;
        mutable T p;

        bool operator<(const LineContainerObject &lc_obj) const { return pair(m, c) < pair(lc_obj.m, lc_obj.c); }
        bool operator<(T x) const { return p < x; }
    };

    template <typename T>
    struct LineContainer : set<LineContainerObject<T>, less<>>
    {
        void add(T m, T c)
        {
            auto it = this->insert({m, c, 0}).first;
            while (isect(it))
                this->erase(next(it));
            if (it != this->begin() && isect(--it))
            {
                this->erase(next(it));
                isect(it);
            }
            while (it != this->begin() && isect(--it))
            {
                this->erase(next(it));
                isect(it);
            }
        }

        T query(T x)
        {
            auto it = this->lower_bound(x);
            return it->m * x + it->c;
        }

    private:
        inline static const T INF = numeric_limits<T>::max();

        bool isect(typename set<LineContainerObject<T>, less<>>::iterator it)
        {
            if (next(it) == this->end())
            {
                it->p = INF;
                return 0;
            }

            if (it->m == next(it)->m)
                it->p = it->c > next(it)->c ? INF : -INF;
            else
                it->p = fl_div(next(it)->c - it->c, it->m - next(it)->m);

            return it->p >= next(it)->p;
        }
    };

} // namespace

void solve()
{
    int n;
    cin >> n;

    vector<long> h(n), w(n);
    for (long &x : h)
        cin >> x;
    for (long &x : w)
        cin >> x;

    long add = 0;
    for (long x : w)
        add += x;

    vector<long> dp(n);
    LineContainer<long> cht;
    dp[0] = w[0];
    cht.add(2 * h[0], dp[0] - h[0] * h[0]);
    for (int i = 1; i < n; i++)
    {
        dp[i] = cht.query(h[i]) - h[i] * h[i] + w[i];
        cht.add(2 * h[i], dp[i] - h[i] * h[i]);
    }

    cout << -dp[n - 1] + add << '\n';
}

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

    solve();

    return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 47 ms 2980 KB Output is correct
2 Correct 47 ms 2884 KB Output is correct
3 Correct 49 ms 2900 KB Output is correct
4 Correct 44 ms 2700 KB Output is correct
5 Correct 43 ms 4056 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 47 ms 2980 KB Output is correct
7 Correct 47 ms 2884 KB Output is correct
8 Correct 49 ms 2900 KB Output is correct
9 Correct 44 ms 2700 KB Output is correct
10 Correct 43 ms 4056 KB Output is correct
11 Correct 44 ms 2828 KB Output is correct
12 Correct 48 ms 2884 KB Output is correct
13 Correct 35 ms 2680 KB Output is correct
14 Correct 46 ms 2668 KB Output is correct
15 Correct 50 ms 8808 KB Output is correct
16 Correct 43 ms 4228 KB Output is correct
17 Correct 17 ms 2844 KB Output is correct
18 Correct 21 ms 2880 KB Output is correct