Submission #963857

#	Time	Username	Problem	Language	Result	Execution time	Memory
963857		sheldon	Harbingers (CEOI09_harbingers)	C++14	70 / 100	1101 ms	25612 KiB

harbingers

#include <bits/stdc++.h>

using namespace std;


const int nax = 1e5 + 5;

struct line {
    long long m, b;

    long long eval (long long x) {
        return x * m + b;
    }

    pair<long long, long long> intersect (line ln) {
        // m1 * x + b1 = m2 * x = b2
        return {ln.b - b, m - ln.m};
    }
};

bool check (line x, line y, line z) {
    pair<long long, long long> p1 = x.intersect (y), p2 = y.intersect (z);

    return (__int128) p1.first * p2.second >= (__int128) p2.first * p1.second;
}

struct convex_hull {
    vector<line> st;

    void insert (line ln) {
        if (st.empty ()) {
            st.push_back (ln);
            return;
        }
        while (st.size () >= 2 && check (st[st.size () - 2], st.back (), ln)) {
            st.pop_back ();
        }
        st.push_back (ln);
    }

    long long query (long long x) {
        int l = 0, r = (int) st.size () - 2;
        long long ans = 2e18;
        while (l <= r) {
            int mid = (l + r) / 2;
            pair<long long, long long> p1 = st[mid].intersect (st[mid + 1]);

            if (p1.first < x * p1.second) {
                l = mid + 1;
            } else {
                r = mid - 1;
            }
        }
        return st[r + 1].eval (x);
    }
};

long long start[nax], per_km[nax];

long long ans[nax];

vector<pair<int, int>> edges[nax];

convex_hull hull;

void dfs (int u, int p, long long path) {
    if (u != 1) ans[u] = start[u] + path * per_km[u] + hull.query (per_km[u]);
    vector<line> deleted;
    line z {-path, ans[u]};
    while (hull.st.size () >= 2 && check (hull.st[hull.st.size () - 2], hull.st.back (), z)) {
        deleted.push_back (hull.st.back ());
        hull.st.pop_back ();
    }
    hull.st.push_back (z);
    for (auto &it: edges[u]) {
        int v = it.first, x = it.second;
        if (v != p) {
            dfs (v, u, path + x);

        }
    }
    hull.st.pop_back ();
    reverse (deleted.begin (), deleted.end ());
    for (auto &it : deleted)  {
        hull.st.push_back (it);
    }

}

void solve() {
    int n;
    cin >> n;
    for (int i = 0; i < n - 1; ++i) {
        int u, v, x;
        cin >> u >> v >> x;
        edges[u].push_back ({v, x});
        edges[v].push_back ({u, x});
    }
    for (int i = 2; i <= n; ++i) {
        cin >> start[i] >> per_km[i];
    }
    dfs (1, 0, 0);
    for (int i = 2; i <= n; ++i) {
        cout << ans[i] << ' ';
    }

}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    solve();
}

Compilation message (stderr)

harbingers.cpp: In member function 'long long int convex_hull::query(long long int)':
harbingers.cpp:43:19: warning: unused variable 'ans' [-Wunused-variable]
   43 |         long long ans = 2e18;
      |                   ^~~

• Subtask 1: 70 / 100