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Submission #705169

# Submission time Handle Problem Language Result Execution time Memory
705169 2023-03-03T13:24:20 Z finn__ Harbingers (CEOI09_harbingers) C++17
70 / 100
 1000 ms 29716 KB 
#include <bits/stdc++.h>
using namespace std;

struct LinearFn
{
    int64_t m, t;

    LinearFn(int64_t m_, int64_t t_) { m = m_, t = t_; }

    int64_t operator()(int64_t x) { return m * x + t; }
};

bool intersects_earlier(LinearFn f, LinearFn g, LinearFn h)
{
    return (double)(h.t - f.t) / (double)(f.m - h.m) <
           (double)(g.t - f.t) / (double)(f.m - g.m);
}

#define N 100000

int64_t s[N], v[N], d[N], ans[N];
vector<pair<size_t, int64_t>> g[N];

void find_shortest_route(size_t u, size_t p, deque<LinearFn> &q)
{
    vector<LinearFn> removed;
    if (!q.empty())
    {
        size_t a = 0, b = q.size() - 1;
        while (a < b)
        {
            size_t mid = (a + b) / 2;
            if (mid < q.size() - 1)
            {
                if (q[mid](v[u]) <= q[mid + 1](v[u]))
                    b = mid;
                else
                    a = mid + 1;
            }
            else
            {
                if (mid && q[mid - 1](v[u]) <= q[mid](v[u]))
                    b = mid - 1;
                else
                    a = mid;
            }
        }
        ans[u] = q[a](v[u]) + d[u] * v[u] + s[u];
        LinearFn f(-d[u], ans[u]);
        while (q.size() >= 2 && intersects_earlier(*(q.rbegin() + 1), *q.rbegin(), f))
        {
            removed.push_back(q.back());
            q.pop_back();
        }
        q.emplace_back(-d[u], ans[u]);
    }
    else
    {
        q.emplace_back(0, 0);
    }

    for (auto [x, w] : g[u])
    {
        if (x != p)
        {
            d[x] = d[u] + w;
            find_shortest_route(x, u, q);
        }
    }

    q.pop_back();
    for (auto it = removed.rbegin(); it != removed.rend(); it++)
        q.push_back(*it);
}

int main()
{
    size_t n;
    cin >> n;

    for (size_t i = 0; i + 1 < n; i++)
    {
        size_t u, v, w;
        cin >> u >> v >> w;
        g[u - 1].emplace_back(v - 1, w);
        g[v - 1].emplace_back(u - 1, w);
    }

    for (size_t i = 1; i < n; i++)
        cin >> s[i] >> v[i];

    deque<LinearFn> q;
    find_shortest_route(0, SIZE_MAX, q);

    for (size_t i = 1; i < n; i++)
        cout << ans[i] << ' ';
    cout << '\n';
}

Subtask #1
70.0 / 100.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 5 ms 3284 KB Output is correct
3 Correct 84 ms 13772 KB Output is correct
4 Correct 128 ms 19116 KB Output is correct
5 Correct 170 ms 24460 KB Output is correct
6 Correct 176 ms 29716 KB Output is correct
7 Correct 137 ms 13780 KB Output is correct
8 Execution timed out 1090 ms 19880 KB Time limit exceeded
9 Execution timed out 1072 ms 15348 KB Time limit exceeded
10 Execution timed out 1083 ms 21164 KB Time limit exceeded