#include <bits/stdc++.h>
using namespace std;
const int N = 100'000 + 1;
int n;
vector<pair<int, int>> ad[N];
int s[N], velocity[N];
int d[N];
struct Line {
long long a, b;
double x(const auto& rhs) { return 1.0 * (rhs.b - b) / (a - rhs.a); }
};
struct CHT {
int top;
array<Line, N> hull;
vector<pair<int, Line>> save;
void add(Line line) {
int preTop = top;
Line preLine;
while (top > 1 && hull[top].x(hull[top - 1]) >= hull[top].x(line)) {
preLine = hull[top--];
}
save.push_back({preTop, preLine});
hull[++top] = line;
}
long long query(int u) {
auto cal = [&](int it) {
return hull[it].a * velocity[u] + hull[it].b + 1ll * d[u] * velocity[u] + s[u];
};
int l = 1, r = top - 1, it = 1;
while (l <= r) {
int mid = l + r >> 1;
if (cal(mid) >= cal(mid + 1)) l = it = mid + 1;
else r = mid - 1;
}
return cal(it);
}
} convex;
long long dp[N];
void dfs(int u, int p = 0) {
auto& ret = dp[u];
ret = min(ret, convex.query(u));
convex.add({-d[u], ret});
for (const auto& [v, w] : ad[u]) {
if (v == p) continue;
d[v] = d[u] + w;
dfs(v, u);
}
if (convex.save.size()) {
auto[top, line] = convex.save.end()[-1];
convex.hull[convex.top] = line;
convex.top = top;
convex.save.pop_back();
}
}
int32_t main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n;
for (int i = 2; i <= n; ++i) {
int u, v, w; cin >> u >> v >> w;
ad[u].push_back({v, w});
ad[v].push_back({u, w});
}
for (int i = 2; i <= n; ++i) cin >> s[i] >> velocity[i];
memset(dp, 40, sizeof dp);
dfs(1);
for (int i = 2; i <= n; ++i) cout << dp[i] << " \n"[i == n];
}
Compilation message
harbingers.cpp:13:18: warning: use of 'auto' in parameter declaration only available with '-fconcepts-ts'
13 | double x(const auto& rhs) { return 1.0 * (rhs.b - b) / (a - rhs.a); }
| ^~~~
harbingers.cpp: In member function 'long long int CHT::query(int)':
harbingers.cpp:36:19: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
36 | int mid = l + r >> 1;
| ~~^~~
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Incorrect |
2 ms |
6232 KB |
Output isn't correct |
2 |
Correct |
3 ms |
6748 KB |
Output is correct |
3 |
Correct |
27 ms |
13436 KB |
Output is correct |
4 |
Correct |
37 ms |
16984 KB |
Output is correct |
5 |
Correct |
49 ms |
20936 KB |
Output is correct |
6 |
Correct |
62 ms |
23496 KB |
Output is correct |
7 |
Incorrect |
36 ms |
13012 KB |
Output isn't correct |
8 |
Execution timed out |
1071 ms |
14916 KB |
Time limit exceeded |
9 |
Execution timed out |
1048 ms |
17624 KB |
Time limit exceeded |
10 |
Execution timed out |
1077 ms |
16592 KB |
Time limit exceeded |