oj.uz

Submission #669565

# Submission time Handle Problem Language Result Execution time Memory
669565 2022-12-06T18:40:18 Z four_specks Building Bridges (CEOI17_building) C++17
100 / 100
 52 ms 8900 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(prev(it)))
            {
                it = Base::erase(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 2672 KB Output is correct
2 Correct 43 ms 2740 KB Output is correct
3 Correct 44 ms 2716 KB Output is correct
4 Correct 39 ms 2672 KB Output is correct
5 Correct 44 ms 3776 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 2672 KB Output is correct
7 Correct 43 ms 2740 KB Output is correct
8 Correct 44 ms 2716 KB Output is correct
9 Correct 39 ms 2672 KB Output is correct
10 Correct 44 ms 3776 KB Output is correct
11 Correct 41 ms 2668 KB Output is correct
12 Correct 45 ms 2848 KB Output is correct
13 Correct 35 ms 2672 KB Output is correct
14 Correct 43 ms 2704 KB Output is correct
15 Correct 52 ms 8900 KB Output is correct
16 Correct 42 ms 3824 KB Output is correct
17 Correct 22 ms 2676 KB Output is correct
18 Correct 21 ms 2672 KB Output is correct