#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
#define sz(x) (int)x.size()
#define all(x) begin(x),end(x)
#define lb(x,y) lower_bound(all(x),y)-begin(x)
mt19937 rng;
struct Line {
mutable ll k, m, p;
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
static const ll inf = LLONG_MAX;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) return x->p = inf, 0;
if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(ll k, ll m) {
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
ll query(ll x) {
assert(!empty());
auto l = *lower_bound(x);
return l.k * x + l.m;
}
};
void solve() {
int N; cin >> N;
vector<vector<pair<int, int>>> adj(N);
for (int i = 0; i < N - 1; i++) {
int u, v, k; cin >> u >> v >> k; u--; v--;
adj[u].pb({v, k});
adj[v].pb({u, k});
}
vector<int> S(N), V(N);
for (int i = 1; i < sz(S); i++) cin >> S[i] >> V[i];
queue<int> q; q.push(0);
vector<int> p(N, 0);
vector<LineContainer> lc(N);
for (int i = 0; i < N; i++) lc[i].add(0, 0);
vector<int> srt;
while (!q.empty()) {
int u = q.front(); q.pop();
srt.pb(u);
for (auto &edge : adj[u]) {
int v = edge.first, k = edge.second;
for (int i = 0; i < sz(adj[v]); i++) if (adj[v][i].first == u) adj[v].erase(adj[v].begin() + i);
p[v] = p[u] + k;
q.push(v);
}
}
reverse(all(srt));
vector<int> cnt(N, 1);
for (int u : srt) {
for (auto &edge : adj[u]) {
int v = edge.first;
cnt[u] += cnt[v];
}
}
reverse(all(srt));
vector<ll> res(N, LLONG_MAX);
for (int u : srt) {
res[u] = min(res[u], -lc[u].query(V[u]) + S[u] + (ll)V[u] * p[u]);
lc[u].add(p[u], -res[u]);
for (auto &edge : adj[u]) {
int v = edge.first;
if (cnt[v] * 2 < cnt[u]) {
q.push(v);
while (!q.empty()) {
int u2 = q.front(); q.pop();
res[u2] = min(res[u2], -lc[u].query(V[u2]) + S[u2] + (ll)V[u2] * p[u2]);
for (auto &edge : adj[u2]) {
int v2 = edge.first;
q.push(v2);
}
}
}
}
for (auto &edge : adj[u]) {
int v = edge.first;
if (cnt[v] * 2 >= cnt[u]) swap(lc[u], lc[v]);
}
}
for (int i = 1; i < sz(res); i++) {
cout << res[i] << (i == sz(res) - 1 ? "\n" : " ");
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
rng = mt19937(chrono::steady_clock::now().time_since_epoch().count());
solve();
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
2 ms |
860 KB |
Output is correct |
| 3 |
Correct |
34 ms |
9016 KB |
Output is correct |
| 4 |
Correct |
48 ms |
13524 KB |
Output is correct |
| 5 |
Correct |
67 ms |
16592 KB |
Output is correct |
| 6 |
Correct |
87 ms |
20540 KB |
Output is correct |
| 7 |
Correct |
54 ms |
15060 KB |
Output is correct |
| 8 |
Correct |
106 ms |
25804 KB |
Output is correct |
| 9 |
Correct |
106 ms |
27524 KB |
Output is correct |
| 10 |
Correct |
101 ms |
26828 KB |
Output is correct |
