#include <bits/stdc++.h>
#define X first
#define Y second
const int N = 100005;
const long long INF = (long long)1e18;
using namespace std;
typedef pair<int, int> Line;
struct operation {
int pos, top;
Line overwrite;
operation(int _p, int _t, Line _o) {
pos = _p; top = _t; overwrite = _o;
}
};
vector<operation> undoLst;
Line lines[N];
int n, top;
long long eval(Line line, long long x) {return line.X * x + line.Y;}
bool bad(Line A,Line B,Line C)
{
Line ab = {B.X - A.X,B.Y - A.Y};
Line ac = {C.X - A.X,C.Y - A.Y};
return (ab.X*ac.Y-ab.Y*ac.X >= 0);
}
long long getMin(long long coord) {
int l = 0, r = top - 1; long long ans = eval(lines[l], coord);
while (l < r) {
int mid = l + r >> 1;
long long x = eval(lines[mid], coord);
long long y = eval(lines[mid + 1], coord);
if (x > y) l = mid + 1; else r = mid;
ans = min(ans, min(x, y));
}
return ans;
}
bool insertLine(Line newLine) {
int l = 1, r = top - 1, k = top;
while (l <= r) {
int mid = l + r >> 1;
if (bad(lines[mid - 1], lines[mid], newLine)) {
k = mid; r = mid - 1;
}
else l = mid + 1;
}
undoLst.push_back(operation(k, top, lines[k]));
top = k + 1;
lines[k] = newLine;
return 1;
}
void undo() {
operation ope = undoLst.back(); undoLst.pop_back();
top = ope.top; lines[ope.pos] = ope.overwrite;
}
long long f[N], S[N], V[N], d[N];
vector<Line> a[N];
void dfs(int u, int par) {
if (u > 1)
f[u] = getMin(V[u]) + S[u] + V[u] * d[u];
insertLine(make_pair(-d[u], f[u]));
for (vector<Line>::iterator it = a[u].begin(); it != a[u].end(); ++it) {
int v = it->X;
int uv = it->Y;
if (v == par) continue;
d[v] = d[u] + uv;
dfs(v, u);
}
undo();
}
int main() {
ios::sync_with_stdio(0); cin.tie(0);
cin >> n;
int u, v, c;
for (int i = 1; i < n; ++i) {
cin >> u >> v >> c;
a[u].push_back(make_pair(v, c));
a[v].push_back(make_pair(u, c));
}
for (int i = 2; i <= n; ++i) cin >> S[i] >> V[i];
dfs(1, 0);
for (int i = 2; i <= n; ++i) cout << f[i] << ' ';
return 0;
}
/*
5
1 2 20
2 3 12
2 4 1
4 5 3
26 9
1 10
500 2
2 30
*/
Compilation message
harbingers.cpp: In function 'long long int getMin(long long int)':
harbingers.cpp:33:21: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
33 | int mid = l + r >> 1;
| ~~^~~
harbingers.cpp: In function 'bool insertLine(Line)':
harbingers.cpp:45:21: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
45 | int mid = l + r >> 1;
| ~~^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
4696 KB |
Output is correct |
| 2 |
Incorrect |
2 ms |
4956 KB |
Output isn't correct |
| 3 |
Incorrect |
24 ms |
9892 KB |
Output isn't correct |
| 4 |
Incorrect |
43 ms |
12436 KB |
Output isn't correct |
| 5 |
Incorrect |
47 ms |
15308 KB |
Output isn't correct |
| 6 |
Incorrect |
61 ms |
17860 KB |
Output isn't correct |
| 7 |
Incorrect |
34 ms |
10572 KB |
Output isn't correct |
| 8 |
Incorrect |
53 ms |
13648 KB |
Output isn't correct |
| 9 |
Incorrect |
55 ms |
15004 KB |
Output isn't correct |
| 10 |
Incorrect |
57 ms |
14404 KB |
Output isn't correct |
