oj.uz

Submission #669144

# Submission time Handle Problem Language Result Execution time Memory
669144 2022-12-05T20:17:39 Z four_specks Building Bridges (CEOI17_building) C++17
100 / 100
 49 ms 9760 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 it1 = Base::insert({line.m, line.c, 0}), it2 = next(it1), it = it1;
            while (isect(it1, it2))
                it2 = Base::erase(it2);
            if (it != Base::begin() && isect(--it, it1))
                isect(it, it1 = Base::erase(it1));
            while (it != Base::begin() && prev(it)->p >= it->p)
            {
                --it;
                isect(it, Base::erase(next(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, Iterator it1)
        {
            if (it1 == Base::end())
            {
                it->p = INF;
                return 0;
            }

            if (it->m == it1->m)
                it->p = it->c > it1->c ? INF : -INF;
            else
                it->p = fl_div(it1->c - it->c, it->m - it1->m);

            return it->p >= it1->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 316 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 38 ms 3772 KB Output is correct
2 Correct 36 ms 3664 KB Output is correct
3 Correct 36 ms 3668 KB Output is correct
4 Correct 35 ms 3596 KB Output is correct
5 Correct 33 ms 4776 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 316 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 KB Output is correct
6 Correct 38 ms 3772 KB Output is correct
7 Correct 36 ms 3664 KB Output is correct
8 Correct 36 ms 3668 KB Output is correct
9 Correct 35 ms 3596 KB Output is correct
10 Correct 33 ms 4776 KB Output is correct
11 Correct 35 ms 3932 KB Output is correct
12 Correct 36 ms 3732 KB Output is correct
13 Correct 28 ms 3788 KB Output is correct
14 Correct 37 ms 3808 KB Output is correct
15 Correct 49 ms 9760 KB Output is correct
16 Correct 33 ms 4744 KB Output is correct
17 Correct 20 ms 3684 KB Output is correct
18 Correct 19 ms 3676 KB Output is correct