Submission #1124662

#	Time	Username	Problem	Language	Result	Execution time	Memory
1124662		Marko2604	Harbingers (CEOI09_harbingers)	C++20	100 / 100	127 ms	32700 KiB

harbingers

#include<bits/stdc++.h>
#define ll long long
#define MAXN 100003
using namespace std;
vector<vector<pair<int,int>>>T(MAXN);
int s[MAXN], v[MAXN];
struct line
{
    int node;
    ll k,n;
};
ll eval(ll x, line *l) 
{
    return l->k*x+l->n;
}
ll depth[MAXN];
void depth_dfs(int node, int p)
{
    for(auto i:T[node])
    {
        if(i.first!=p)
        {
            depth[i.first]=(ll)i.second+depth[node];
            depth_dfs(i.first, node);
        }
    }
}
vector<vector<line*>>lichao(262151);
vector<vector<int>>loc(MAXN);
vector<int>xx;
int sz;
void make_lichao(int n)
{
    sz = (1<<((int)ceil(log2(n))));
    for(int i=1;i<=n;i++) xx.push_back(v[i]);
    while(xx.size()<sz) xx.push_back(0);
    sort(xx.begin(),xx.end());
}
void add_line(line *ln, int node, int l, int r)
{
    if(lichao[node].empty())
    {
        lichao[node].push_back(ln);
        loc[ln->node].push_back(node);
        return;
    }
    line *lo = lichao[node].back();
    ll lold = eval(xx[l], lo), rold = eval(xx[r], lo);
    ll lnew = eval(xx[l], ln), rnew = eval(xx[r], ln);
    if(lnew>=lold && rnew>=rold) return;
    if(lnew<=lold && rnew<=rold)
    {
        lichao[node].push_back(ln);
        loc[ln->node].push_back(node);
        return;
    }
    int mid = (l+r)/2;
    ll mold = eval(xx[mid], lo), mnew = eval(xx[mid], ln);
    if(lnew<=lold)
    {
        if(mnew<=mold)
        {
            lichao[node].push_back(ln);
            loc[ln->node].push_back(node);
            add_line(lo, 2*node+1, mid+1, r);
            return;
        }
        else
        {
            add_line(ln, 2*node, l, mid);
            return;
        }
    }
    else
    {
        if(mnew<=mold)
        {
            lichao[node].push_back(ln);
            loc[ln->node].push_back(node);
            add_line(lo, 2*node, l, mid);
            return;
        }
        else
        {
            add_line(ln, 2*node+1, mid+1, r);
            return;
        }
    }
    return;
}
void pop_line(line *ln) 
{
    while(!loc[ln->node].empty())
    {
        lichao[loc[ln->node].back()].pop_back();
        loc[ln->node].pop_back();
    }
    return;
}
ll get_val(int x)
{
    ll res = 100000000000000000;
    int l=0, r=sz-1, node=1;
    while(l<=r)
    {
        if(!lichao[node].empty()) res=min(res, eval(x, lichao[node].back()));
        int mid=(l+r)/2;
        if(xx[mid]<=x) 
        {
            l=mid+1;
            node=node*2+1;
        }
        else 
        {
            r=mid-1;
            node=node*2;
        }
    }
    return res;
}
ll dp[MAXN];
void dp_dfs(int node, int p)
{
    if(node != 1 ) dp[node]=(ll)(s[node])+(ll)(v[node])*depth[node]+get_val(v[node]);

    line l;
    l.node=node;
    l.k=-depth[node];
    l.n=dp[node];
    add_line(&l, 1, 0, sz-1);
    for(auto i:T[node])
    {
        if(i.first!=p)
        {
            dp_dfs(i.first,node);
        }
    }
    pop_line(&l);
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    int n;
    cin>>n;
    for(int i=1;i<n;i++)
    {
        int u1,v1;
        int w;
        cin>>u1>>v1>>w;
        T[u1].emplace_back(v1,w);
        T[v1].emplace_back(u1,w);
    }
    s[1]=0, v[1]=0;
    for(int i=2;i<=n;i++)
        cin>>s[i]>>v[i];
    depth[1]=0;
    depth_dfs(1,1);
    make_lichao(n);
    dp[1]=0;
    dp_dfs(1,1);
    for(int i=2;i<=n;i++)
        cout<<dp[i]<<" ";
    cout<<endl;
    return 0;
}

• Subtask 1: 100 / 100