oj.uz

Submission #669150

# Submission time Handle Problem Language Result Execution time Memory
669150 2022-12-05T20:31:48 Z four_specks Building Bridges (CEOI17_building) C++17
100 / 100
 48 ms 9632 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 1 ms 212 KB Output is correct
2 Correct 1 ms 212 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 340 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 35 ms 2752 KB Output is correct
2 Correct 36 ms 3460 KB Output is correct
3 Correct 38 ms 3404 KB Output is correct
4 Correct 33 ms 3352 KB Output is correct
5 Correct 32 ms 4552 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 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 340 KB Output is correct
6 Correct 35 ms 2752 KB Output is correct
7 Correct 36 ms 3460 KB Output is correct
8 Correct 38 ms 3404 KB Output is correct
9 Correct 33 ms 3352 KB Output is correct
10 Correct 32 ms 4552 KB Output is correct
11 Correct 41 ms 3404 KB Output is correct
12 Correct 38 ms 3484 KB Output is correct
13 Correct 28 ms 3428 KB Output is correct
14 Correct 36 ms 3420 KB Output is correct
15 Correct 48 ms 9632 KB Output is correct
16 Correct 33 ms 4556 KB Output is correct
17 Correct 22 ms 3324 KB Output is correct
18 Correct 23 ms 3344 KB Output is correct