Submission #503575

#	Time	Username	Problem	Language	Result	Execution time	Memory
503575		fvogel499	Harbingers (CEOI09_harbingers)	C++14	30 / 100	1084 ms	57628 KiB

harbingers

/*
 * File created on 01/08/2022 at 10:53:58.
 * Link to problem: 
 * Description: 
 * Time complexity: O()
 * Space complexity: O()
 * Status: ---
 * Copyright: Ⓒ 2022 Francois Vogel
*/

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <functional>

using namespace std;
using namespace __gnu_pbds;

#define pii pair<int, int>
#define f first
#define s second

#define vi vector<int>
#define all(x) x.begin(), x.end()
#define size(x) (int)((x).size())
#define pb push_back
#define ins insert
#define cls clear

#define int ll
#define ll long long
#define ld long double

typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

const int siz = 1e5+40;
const int inf = 1e18;

vector<pii> graph [siz];
int height [siz];
int dp [siz];
int prep [siz];
int speed [siz];
map<ld, int> opt;
vi q;

ld xIntercept(int a1, int b1, int a2, int b2) {
    if (a1-a2 == 0) return (ld)(b2-b1)*(ld)(inf);
    return (ld)(b2-b1)/(ld)(a1-a2);
}

void dfs(int x, int p = -1) {
    if (p == -1) dp[x] = 0;
    else {
        auto it = opt.upper_bound(speed[x]);
        it = prev(it);
        dp[x] = -height[(*it).s]*speed[x]+dp[(*it).s];
        dp[x] += height[x]*speed[x]+prep[x];
    }
    vector<pair<ld, int>> rem;
    while (size(q) >= 2 && xIntercept(-height[q.back()], dp[q.back()], -height[q[size(q)-2]], dp[q[size(q)-2]]) >= xIntercept(-height[x], dp[x], -height[q.back()], dp[q.back()])) {
        rem.pb(*(prev(opt.end())));
        opt.erase(prev(opt.end()));
        q.pop_back();
    }
    reverse(all(rem)); // first in rem is now deepest in stack q
    ld fromX = -inf;
    if (!q.empty()) {
        fromX = ceil(xIntercept(-height[x], dp[x], -height[q.back()], dp[q.back()]));
    }
    opt[fromX] = x;
    q.pb(x);
    for (pii y : graph[x]) if (y.f != p) {
        height[y.f] = height[x]+y.s;
        dfs(y.f, x);
    }
    q.pop_back();
    opt.erase(prev(opt.end()));
    for (pair<ld, int> i : rem) {
        q.pb(i.s);
        opt[i.f] = i.s;
    }
}

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

    int n;
    cin >> n;
    for (int i = 0; i < n-1; i++) {
        int na, nb, lw;
        cin >> na >> nb >> lw;
        na--;
        nb--;
        graph[na].pb(pii(nb, lw));
        graph[nb].pb(pii(na, lw));
    }
    for (int i = 1; i < n; i++) cin >> prep[i] >> speed[i];
    dfs(0);
    for (int i = 1; i < n; i++) cout << dp[i] << ' ';

    cout.flush();
    int d = 0;
    d++;
}

• Subtask 1: 30 / 100