Submission #473735

#	Time	Username	Problem	Language	Result	Execution time	Memory
473735		jalsol	Harbingers (CEOI09_harbingers)	C++17	50 / 100	149 ms	18420 KiB

harbingers

// looking to shine brighter in this world...

#define TASK "harbingers"

#ifdef LOCAL
#include "local.h"
#else
#include <bits/stdc++.h>
#define debug(...)
#define DB(...)
#endif

using namespace std;

using ll = long long;
using ld = long double;

#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define fi first
#define se second

#define For(i, l, r) for (int i = (l); i <= (r); ++i)
#define Ford(i, r, l) for (int i = (r); i >= (l); --i)
#define Rep(i, n) For (i, 0, (n) - 1)
#define Repd(i, n) Ford (i, (n) - 1, 0)
#define Fe(...) for (auto __VA_ARGS__)

template <class C> inline int isz(const C& c) { return static_cast<int>(c.size()); }
template <class T> inline bool chmin(T& a, const T& b) { return (a > b) ? a = b, true : false; }
template <class T> inline bool chmax(T& a, const T& b) { return (a < b) ? a = b, true : false; }

const bool __initialization = []() {
    cin.tie(nullptr)->sync_with_stdio(false);
    if (fopen(TASK".inp", "r")) {
        (void)(!freopen(TASK".inp", "r", stdin));
        (void)(!freopen(TASK".out", "w", stdout)); }
    cout << setprecision(12) << fixed;
    return true;
}();

constexpr ld eps = 1e-9;
constexpr int inf = 1e9;
constexpr ll linf = 1e18;

// =============================================================================

constexpr int maxn = 1e5 + 5;

struct Data {
    int v; ll c;

    Data() : v(0), c(0) {}
    Data(int _v, ll _c) : v(_v), c(_c) {}
};

struct Town {
    ll init, speed;

    Town() : init(0), speed(0) {}
    Town(ll _i, ll _s) : init(_i), speed(_s) {}
};

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 CHT {
    struct Line {
        mutable ll a, b, p;

        bool operator<(const Line& o) const {
            return a < o.a;
        }
        bool operator<(ll x) const {
            return p < x;
        }
    };

    using itr = multiset<Line>::iterator;

    static constexpr ll inf = LLONG_MAX;
    multiset<Line, less<>> mts;

    ll div(ll a, ll b) {
        return a / b - ((a ^ b) < 0 && a % b);
    }

    bool isect(itr x, itr y) {
        if (y == mts.end()) {
            x->p = inf;
            return 0;
        }

        if (x->a == y->a) {
            x->p = (x->b > y->b) ? inf : -inf;
        }
        else {
            x->p = div(y->b - x->b, x->a - y->a);
        }

        return x->p >= y->p;
    }

    void insert(ll a, ll b) {
        auto z = mts.insert({ a, b, 0 });
        auto y = z++;
        auto x = y;

        while (isect(y, z)) z = mts.erase(z);

        if (x != mts.begin() && isect(--x, y)) {
            y = mts.erase(y);
            isect(x, y);
        }

        y = x;
        while (y != mts.begin() && (--x)->p >= y->p) {
            isect(x, mts.erase(y));
            y = x;
        }
    }

    ll query(ll x) {
        auto l = *mts.lower_bound(x);
        return l.a * x + l.b;
    }
};

int n;
vector<Data> g[maxn];
Town a[maxn];

CHT hull;
ll dp[maxn];
ll dist[maxn];

void Dfs(int u, int p) {
    dp[u] = a[u].init + a[u].speed * dist[u]
            - hull.query(a[u].speed);

    hull.insert(dist[u], -dp[u]);

    Fe (&[v, c] : g[u]) {
        if (v == p) continue;
        dist[v] = dist[u] + c;
        Dfs(v, u);
    }
}

signed main() {
    cin >> n;

    Rep (_, n - 1) {
        int u, v; ll c; cin >> u >> v >> c;
        g[u].emplace_back(v, c);
        g[v].emplace_back(u, c);
    }

    For (i, 2, n) cin >> a[i].init >> a[i].speed;

    hull.insert(0, 0);
    Dfs(1, -1);

    // dp[u] + a[v].init + a[v].speed * (dist[v] - dist[u])
    // dp[u] + s[v] + v[v] * (d[v] - d[u])
    // dp[u] + s[v] + v[v] * d[v] - v[v] * d[u]
    // s[v] + v[v] * d[v] - v[v] * d[u] + dp[u]
    // s[v] + v[v] * d[v] + f(v[v])

    For (i, 2, n) {
        cout << dp[i] << " \n"[i == n];
    }

    return 0;
}

• Subtask 1: 50 / 100