Submission #474801

#	Time	Username	Problem	Language	Result	Execution time	Memory
474801		aniervs	Harbingers (CEOI09_harbingers)	C++17	0 / 100	83 ms	11976 KiB

harbingers

#ifdef LOCAL
#include <prettyprint.hpp>
#endif
#include<bits/stdc++.h>
#define endl '\n'
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define lg2(x) __lg(x)
#define rem_dupl(x) sort(all(x)); x.erase(unique(all(x)), x.end())
using namespace std;

typedef long long ll;
const int maxn = (int)2e5 + 5;

struct point{
    ll x, y;
    point(){ x = y = 0; }
    point(ll _x, ll _y) : x(_x), y(_y) {}
    
    bool operator <(const point & other){ return make_pair(x, y) < make_pair(other.x, other.y); }
    point operator +(const point &other){ return {x + other.x, y + other.y}; }
    point operator -(const point &other){ return {x + other.x, y + other.y}; }
};

ll dot(const point &a, const point &b){ return a.x * b.x + a.y * b.y; }
ll cross(const point &a, const point &b){ return a.x * b.y  - a.y * b.x; }
ll area2(point a, point b, point c){ return cross(b - a, c - a); }

struct hull : vector<point>{
    void add_point(point p){ // p is bigger than all the previous ones

        for(auto q:*this)
            assert(q < p);

        while(size() > 1 and area2(at(size()-2), at(size()-1), p) >= 0)
            pop_back();
        push_back(p);
    }

    ll max_dot(point p){
        if(empty())
            return LLONG_MIN;
        int l = 0, r = (int)size() - 1;
        while(l < r){
            int mid = (l + r)>>1;
            assert(mid+1 < (int)size());
            assert(mid >= 0);
            if(dot(at(mid), p) <= dot(at(mid + 1), p))
                l = mid + 1;
            else
                r = mid;
        }
        
        assert(l < (int)size());
        assert(l >= 0);

        return dot(at(l), p);
    }

};

vector<pair<int,ll>> G[maxn];
ll speed[maxn], start[maxn], dp[maxn], sumW[maxn];
int n, sz[maxn];

point get_point(int u){
    return {sumW[u], -dp[u]};
}


void dfs(int u){
    sz[u] = 1;
    for(auto [v, w]:G[u]){
        sumW[v] = sumW[u] + w;
        dfs(v);
        sz[u] += sz[v];
    }
}


vector<hull> lights;
hull heavy;

void dfsHLD(int u){

    if(u != 1){
        dp[u] = LLONG_MIN;
        for(auto h:lights){
            dp[u] = max(dp[u], h.max_dot({speed[u], 1}));
        }
        if(!heavy.empty())
            dp[u] = max(dp[u], heavy.max_dot({speed[u], 1}));
        dp[u] = sumW[u] * speed[u] + start[u] - dp[u];
    }

    heavy.push_back(get_point(u));
    
/*
    dp[v] = LLONG_MAX;
    for(int p:ancestors)
        dp[v] = min(dp[v], dot({sumW[p], dp[p]}, {-speed[v], 1});
    dp[v] += sumW[v] * speed[v];
    dp[v] += start[v];
*/

    int bigChild = -1;
    for(auto [v, w]:G[u])
        if(bigChild == -1 or sz[bigChild] < sz[v])
            bigChild = v;
    lights.push_back(heavy);
        
    for(auto [v, w]:G[u])
        if(v != bigChild){
            heavy.clear();
            dfsHLD(v);
        }
    heavy = lights.back();
    lights.pop_back();

    if(bigChild != -1)
        dfsHLD(bigChild);
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);

    cin >> n;
    for(int i = 1; i < n; i++){
        int u, v, w;
        cin >> u >> v >> w;
        G[u].push_back({v, w});
    }

    for(int i = 2; i <= n; i++)
        cin >> start[i] >> speed[i];
    
    dfs(1);

    dfsHLD(1);

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

    
    return 0;
}

• Subtask 1: 0 / 100