Submission #495656

#	Time	Username	Problem	Language	Result	Execution time	Memory
495656		blue	Harbingers (CEOI09_harbingers)	C++17	100 / 100	204 ms	30904 KiB

harbingers

#include <iostream>
#include <vector>
#include <cassert>
using namespace std;

using vi = vector<int>;
using ll = long long;
using vl = vector<ll>;
using pl = pair<ll, ll>;

const int maxN = 100'000;
const int logN = 17;

ll INF = 1'000'000'000'000'000'000LL;

vector<pl> edge[1+maxN];

vl S(1+maxN), V(1+maxN), P(1+maxN), D(1+maxN, 0);
vl ord;

void dfs(int u, int p)
{
    ord.push_back(u);
    P[u] = p;
    for(auto x: edge[u])
    {
        ll v = x.first;
        ll d = x.second;
        if(v == p) continue;
        D[v] = D[u] + d;
        dfs(v, u);
    }
}

struct line
{
    ll a;
    ll b;

    ll eval(ll x)
    {
        return ll(a)*x + ll(b);
    }
};

double intersect(line A, line B)
{
    return double(B.b - A.b)/double(A.a - B.a);
}

bool intersect_comp(line A, line B, line C, line D)
{
    return intersect(A, B) < intersect(C, D);
    // ll mul = 1;
    // if(A.a - B.a < 0) mul *= -1;
    // if(C.a - D.a < 0) mul *= -1;
    // return mul * (B.b - A.b) * (C.a - D.a) < mul * (D.b - C.b) * (A.a - B.a);
}

vector<line> cht(1+maxN);
int cht_anc[1+maxN][1+logN];

void insert_line(int u, line l)
{
    cht[u] = l;
    int a = P[u];

    for(int e = logN; e >= -1; e--)
    {
        int v = (e == -1 ? a : cht_anc[a][e]);
        if(v == 1) continue;
        int w = cht_anc[v][0];

        if(!intersect_comp(cht[w], cht[v], cht[v], l))
            a = w;
    }

    cht_anc[u][0] = a;
    for(int e = 1; e <= logN; e++)
        cht_anc[u][e] = cht_anc[ cht_anc[u][e-1] ][e-1];
}

ll query(int u, ll x)
{
    for(int e = logN; e >= -1; e--)
    {
        int v = (e == -1 ? u : cht_anc[u][e]);
        if(v == 1) continue;
        int w = cht_anc[v][0];

        ll mul = 1;
        if(cht[w].a - cht[v].a < 0) mul *= -1;

        if(x * (cht[w].a - cht[v].a) * mul < (cht[v].b - cht[w].b) * mul)
            u = w;
    }

    return min(cht[u].eval(x), cht[cht_anc[u][0]].eval(x));
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int N;
    cin >> N;

    for(int i = 1; i <= N-1; i++)
    {
        int u, v;
        ll d;
        cin >> u >> v >> d;

        edge[u].push_back({v, d});
        edge[v].push_back({u, d});
    }

    for(int i = 2; i <= N; i++) cin >> S[i] >> V[i];


    dfs(1, 1);


    for(int i = 1; i <= N; i++)
        for(int e = 0; e <= logN; e++)
            cht_anc[i][e] = i;

    insert_line(1, {0, 0});

    vl dp(1+N, INF);
    dp[1] = 0;
    for(int u: ord)
    {
        if(u == 1) continue;

        dp[u] = ll(S[u]) + ll(V[u])*ll(D[u]) + query(P[u], V[u]);
        insert_line(u, {-D[u], dp[u]});
    }

    // cerr << cht_anc[1][0] << ' ' << cht_anc[2][0] << ' ' << cht_anc[3][0] << '\n';

    for(int i = 2; i <= N; i++) cout << dp[i] << ' ';
    cout << '\n';
}

• Subtask 1: 100 / 100