oj.uz

Submission #669568

# Submission time Handle Problem Language Result Execution time Memory
669568 2022-12-06T18:43:03 Z four_specks Building Bridges (CEOI17_building) C++17
100 / 100
 52 ms 8908 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 Line
    {
        T m, c;
        T operator()(T x) const { return m * x + c; }
    };

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

        bool operator<(const LineContainerObject &i_line) const { return m < i_line.m; }
        bool operator<(T x) const { return p < x; }
    };

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

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

    private:
        using Base = multiset<LineContainerObject<T>, less<>>;
        using Iterator = typename Base::iterator;

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

        bool isect(Iterator it)
        {
            if (next(it) == Base::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(Line<long>{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(Line<long>{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 45 ms 2736 KB Output is correct
2 Correct 44 ms 2744 KB Output is correct
3 Correct 45 ms 2744 KB Output is correct
4 Correct 40 ms 2672 KB Output is correct
5 Correct 43 ms 3780 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 45 ms 2736 KB Output is correct
7 Correct 44 ms 2744 KB Output is correct
8 Correct 45 ms 2744 KB Output is correct
9 Correct 40 ms 2672 KB Output is correct
10 Correct 43 ms 3780 KB Output is correct
11 Correct 43 ms 2688 KB Output is correct
12 Correct 42 ms 2748 KB Output is correct
13 Correct 33 ms 2668 KB Output is correct
14 Correct 47 ms 2644 KB Output is correct
15 Correct 52 ms 8908 KB Output is correct
16 Correct 43 ms 3796 KB Output is correct
17 Correct 23 ms 2644 KB Output is correct
18 Correct 21 ms 2644 KB Output is correct