Submission #473728

#	Time	Username	Problem	Language	Result	Execution time	Memory
473728		jalsol	Harbingers (CEOI09_harbingers)	C++17	10 / 100	1093 ms	17664 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 CHT {
    struct Line {
        ll a, b;
 
        Line(ll _a, ll _b) : a(_a), b(_b) {}
 
        ll f(ll x) {
            return a * x + b;
        }
 
        ld isect(const Line& o) const {
            return ld(b - o.b) / (o.a - a);
        }
    };
 
    deque<Line> q;
 
    void insert(ll a, ll b) {
        Line l(a, b);
        int sz = isz(q);
 
        while (sz >= 2 && l.isect(q[0]) <= q[0].isect(q[1])) {
            q.pop_front();
            --sz;
        }
 
        q.push_front(l);
    }
 
    ll query(ll x) {
        int sz = isz(q);
 
        while (sz >= 2 && q[sz - 1].f(x) >= q[sz - 2].f(x)) {
            q.pop_back();
            --sz;
        }
 
        return q[sz - 1].f(x);
    }
};
 
int n;
vector<Data> g[maxn];
Town a[maxn];
 
int order[maxn];
int cnt;
ll dist[maxn];
 
CHT hull;
ll dp[maxn];
 
void Dfs(int u, int p = -1) {
    order[++cnt] = u;
 
    Fe (&[v, c] : g[u]) {
        if (v != p) {
            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;
 
    Dfs(1, -1);
 
    hull.insert(0, 0);
 
    For (i, 2, n) {
        int u = order[i];
 
        dp[u] = hull.query(a[u].speed) + a[u].init + a[u].speed * dist[u];
        hull.insert(-dist[u], dp[u]);
    }
 
    memset(dp + 2, 0x3f, 8 * n);
 
    For (i, 2, n) {
    	For (j, 1, i - 1) {
           int v = order[i];
           int u = order[j];
 
           chmin(dp[v], dp[u] + a[v].init + a[v].speed * (dist[v] - dist[u]));
       }
    }
 
    For (i, 2, n) {
        cout << dp[i] << " \n"[i == n];
    }
 
    return 0;
}

• Subtask 1: 10 / 100