oj.uz

Submission #669581

# Submission time Handle Problem Language Result Execution time Memory
669581 2022-12-06T19:13:07 Z four_specks Building Bridges (CEOI17_building) C++17
100 / 100
 51 ms 8884 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 pair(m, c) < pair(i_line.m, i_line.c); }
        bool operator<(T x) const { return p < x; }
    };

    template <typename T>
    struct LineContainer : set<LineContainerObject<T>, less<>>
    {
        void add(const Line<T> &line)
        {
            auto it = this->insert({line.m, line.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(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 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 47 ms 2740 KB Output is correct
2 Correct 47 ms 2668 KB Output is correct
3 Correct 47 ms 2764 KB Output is correct
4 Correct 42 ms 2644 KB Output is correct
5 Correct 41 ms 3796 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 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 47 ms 2740 KB Output is correct
7 Correct 47 ms 2668 KB Output is correct
8 Correct 47 ms 2764 KB Output is correct
9 Correct 42 ms 2644 KB Output is correct
10 Correct 41 ms 3796 KB Output is correct
11 Correct 45 ms 2800 KB Output is correct
12 Correct 49 ms 2740 KB Output is correct
13 Correct 35 ms 2644 KB Output is correct
14 Correct 47 ms 2732 KB Output is correct
15 Correct 51 ms 8884 KB Output is correct
16 Correct 39 ms 3828 KB Output is correct
17 Correct 16 ms 2680 KB Output is correct
18 Correct 21 ms 2644 KB Output is correct