oj.uz

Submission #753488

# Submission time Handle Problem Language Result Execution time Memory
753488 2023-06-05T10:06:44 Z finn__ Building Bridges (CEOI17_building) C++17
100 / 100
 80 ms 7216 KB 
#include <bits/stdc++.h>
using namespace std;

struct linear_fn
{
    int64_t m, t;
    linear_fn(int64_t m, int64_t t) { this->m = m, this->t = t; }
    int64_t operator()(int64_t x) const { return m * x + t; }
    bool intersects_earlier(linear_fn const &g, linear_fn const &h)
    {
        return (__int128_t)(h.t - t) * (m - g.m) <= (__int128_t)(g.t - t) * (m - h.m);
    }
};

constexpr size_t N = 100000;

int64_t h[N], w[N], f[N];

void add_function(vector<linear_fn> &hull, linear_fn const &f)
{
    while (hull.size() >= 2 && hull[hull.size() - 2].intersects_earlier(hull.back(), f))
        hull.pop_back();
    hull.push_back(f);
}

vector<linear_fn> cdq(size_t a, size_t b)
{
    if (a == b)
        return {linear_fn(-2 * h[a], f[a] + h[a] * h[a] - w[a])};
    vector<linear_fn> r = cdq(a, (a + b) / 2);
    if (!r.empty())
        for (size_t i = (a + b) / 2 + 1; i <= b; ++i)
        {
            size_t x = 0, y = r.size() - 1;
            while (x < y)
            {
                size_t const mid = (x + y) / 2;
                if (r[mid](h[i]) <= r[mid + 1](h[i]))
                    y = mid;
                else
                    x = mid + 1;
            }
            f[i] = min(f[i], r[x](h[i]) + h[i] * h[i] + w[i - 1]);
        }
    vector<linear_fn> s = cdq((a + b) / 2 + 1, b), t;
    auto it = r.begin(), jt = s.begin();
    while (it != r.end() && jt != s.end())
        if (it->m > jt->m || (it->m == jt->m && it->t < jt->t))
            add_function(t, *it++);
        else
            add_function(t, *jt++);
    while (it != r.end())
        add_function(t, *it++);
    while (jt != s.end())
        add_function(t, *jt++);
    return t;
}

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    size_t n;
    cin >> n;
    for (size_t i = 0; i < n; ++i)
        cin >> h[i];
    for (size_t i = 0; i < n; ++i)
        cin >> w[i];
    for (size_t i = 1; i < n; ++i)
        w[i] += w[i - 1];
    for (size_t i = 1; i < n; ++i)
        f[i] = (h[i] - h[0]) * (h[i] - h[0]) + w[i - 1] - w[0];
    cdq(1, n - 1);
    cout << f[n - 1] << '\n';
}

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 340 KB Output is correct
3 Correct 1 ms 340 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 72 ms 2792 KB Output is correct
2 Correct 74 ms 2796 KB Output is correct
3 Correct 71 ms 3896 KB Output is correct
4 Correct 63 ms 3648 KB Output is correct
5 Correct 56 ms 4580 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 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 72 ms 2792 KB Output is correct
7 Correct 74 ms 2796 KB Output is correct
8 Correct 71 ms 3896 KB Output is correct
9 Correct 63 ms 3648 KB Output is correct
10 Correct 56 ms 4580 KB Output is correct
11 Correct 72 ms 3900 KB Output is correct
12 Correct 80 ms 3944 KB Output is correct
13 Correct 43 ms 3788 KB Output is correct
14 Correct 69 ms 3988 KB Output is correct
15 Correct 68 ms 7216 KB Output is correct
16 Correct 63 ms 4568 KB Output is correct
17 Correct 28 ms 3744 KB Output is correct
18 Correct 30 ms 3716 KB Output is correct