Submission #880687

#	Time	Username	Problem	Language	Result	Execution time	Memory
880687		DylanSmith	Harbingers (CEOI09_harbingers)	C++17	100 / 100	106 ms	27524 KiB

harbingers

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

#define pb push_back
#define sz(x) (int)x.size()
#define all(x) begin(x),end(x)
#define lb(x,y) lower_bound(all(x),y)-begin(x)

mt19937 rng;

struct Line {
    mutable ll k, m, p;
    bool operator<(const Line& o) const { return k < o.k; }
    bool operator<(ll x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
    // (for doubles, use inf = 1/.0, div(a,b) = a/b)
    static const ll inf = LLONG_MAX;
    ll div(ll a, ll b) { // floored division
        return a / b - ((a ^ b) < 0 && a % b); }
    bool isect(iterator x, iterator y) {
        if (y == end()) return x->p = inf, 0;
        if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
        else x->p = div(y->m - x->m, x->k - y->k);
        return x->p >= y->p;
    }
    void add(ll k, ll m) {
        auto z = insert({k, m, 0}), y = z++, x = y;
        while (isect(y, z)) z = erase(z);
        if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
        while ((y = x) != begin() && (--x)->p >= y->p)
            isect(x, erase(y));
    }
    ll query(ll x) {
        assert(!empty());
        auto l = *lower_bound(x);
        return l.k * x + l.m;
    }
};

void solve() {
    int N; cin >> N;
    vector<vector<pair<int, int>>> adj(N);
    for (int i = 0; i < N - 1; i++) {
        int u, v, k; cin >> u >> v >> k; u--; v--;
        adj[u].pb({v, k});
        adj[v].pb({u, k});
    }
    vector<int> S(N), V(N);
    for (int i = 1; i < sz(S); i++) cin >> S[i] >> V[i];
    queue<int> q; q.push(0);
    vector<int> p(N, 0);
    vector<LineContainer> lc(N);
    for (int i = 0; i < N; i++) lc[i].add(0, 0);
    vector<int> srt;
    while (!q.empty()) {
        int u = q.front(); q.pop();
        srt.pb(u);
        for (auto &edge : adj[u]) {
            int v = edge.first, k = edge.second;
            for (int i = 0; i < sz(adj[v]); i++) if (adj[v][i].first == u) adj[v].erase(adj[v].begin() + i);
            p[v] = p[u] + k;
            q.push(v);
        }
    }
    reverse(all(srt));
    vector<int> cnt(N, 1);
    for (int u : srt) {
        for (auto &edge : adj[u]) {
            int v = edge.first;
            cnt[u] += cnt[v];
        }
    }
    reverse(all(srt));
    vector<ll> res(N, LLONG_MAX);
    for (int u : srt) {
        res[u] = min(res[u], -lc[u].query(V[u]) + S[u] + (ll)V[u] * p[u]);
        lc[u].add(p[u], -res[u]);
        for (auto &edge : adj[u]) {
            int v = edge.first;
            if (cnt[v] * 2 < cnt[u]) {
                q.push(v);
                while (!q.empty()) {
                    int u2 = q.front(); q.pop();
                    res[u2] = min(res[u2], -lc[u].query(V[u2]) + S[u2] + (ll)V[u2] * p[u2]);
                    for (auto &edge : adj[u2]) {
                        int v2 = edge.first;
                        q.push(v2);
                    }
                }
            }
        }
        for (auto &edge : adj[u]) {
            int v = edge.first;
            if (cnt[v] * 2 >= cnt[u]) swap(lc[u], lc[v]);
        }
    }
    for (int i = 1; i < sz(res); i++) {
        cout << res[i] << (i == sz(res) - 1 ? "\n" : " ");
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    rng = mt19937(chrono::steady_clock::now().time_since_epoch().count());

    solve();

    return 0;
}

• Subtask 1: 100 / 100