Submission #1211047

#	Time	Username	Problem	Language	Result	Execution time	Memory
1211047		dosts	Harbingers (CEOI09_harbingers)	C++20	In queue	0 ms	0 KiB

harbingers

#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
//#define int long long
#define pii pair<int,int>
#define vi vector<int>
#define ff first
#define ss second
#define sp << " " <<
#define all(x) x.begin(),x.end()
#define big(x) ((int)(x.size()))
using namespace std;
const int MOD = 1e9+7, LIM = 1e9, inf = 2e9,MAXN = 1e6+1;

const int N = 1e5+1;


int s[N],v[N],d[N];
long long dp[N];
vector<pii> edges[N];

struct Line {
    int m;
    long long b;
    long long eval(int x) {
        return 1LL*m*x+b;
    }
};


Line lines[4*N+1];
stack<pair<int,Line>> upds;
int ids = 0;

vi vals;

int idx(int x) {
    return upper_bound(all(vals),x)-vals.begin();
}


void update(int node, int l,int r,Line& line) {
    if (line.m == inf && line.b == inf) return;
    int m = (l+r) >> 1;
    bool good = lines[node].eval(vals[l-1]) > line.eval(vals[l-1]);
    bool goodmid = lines[node].eval(vals[m-1]) > line.eval(vals[m-1]);
    if (goodmid) {
        upds.push({node,lines[node]});
        swap(lines[node],line);
    }
    if (l == r) return;
    if (goodmid != good) update(2*node,l,m,line);
    else update(2*node+1,m+1,r,line);
};

long long query(int node,int l,int r,const int x) {
    if (l == r) return lines[node].eval(vals[x-1]);
    int m = (l+r) >> 1;
    if (x <= m) return min(lines[node].eval(vals[x-1]),query(2*node,l,m,x));
    return min(lines[node].eval(vals[x-1]),query(2*node+1,m+1,r,x));
}

void rollback(int k) {
    while (k--) {
        lines[upds.top().ff] = upds.top().ss;
        upds.pop();
    }
}

int n;
void dfs(int node,int p,int der = 0) {
    d[node] = der;
    if (node > 1) dp[node] = 1LL*s[node]+1LL*v[node]*d[node]+query(1,1,n,idx(v[node]));
    else dp[node] = 0;
    int crea = upds.size();
    Line toadd = {-d[node],dp[node]};
    update(1,1,n,toadd);
    int crea2 = upds.size();
    for (auto it : edges[node]) {
        if (it.ff == p) continue;
        dfs(it.ff,node,der+it.ss);
    }
    rollback(crea2-crea);
}

void solve() {
    cin >> n;
    for (int i = 1;i<=4*n;i++) lines[i] = {inf,inf};
    for (int i=1;i<n;i++) {
        int a,b,c;
        cin >> a >> b >> c;
        edges[a].push_back({b,c});
        edges[b].push_back({a,c});
    }
    for (int i=2;i<=n;i++) cin >> s[i] >> v[i];
    for (int i=2;i<=n;i++) vals.push_back(v[i]);
    sort(all(vals));
    vals.erase(unique(all(vals)),vals.end());
    int nn = n;
    n = vals.size();
    dfs(1,1);
    for (int i=2;i<=nn;i++) cout << dp[i] << ' ';
    cout << '\n';
} 

signed main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    #ifdef Dodi
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
    #endif
    int t = 1;
    //cin >> t;
    while (t --> 0) solve();
}