#include <bits/stdc++.h>
using namespace std;
struct LinearFn
{
int64_t m, t;
LinearFn(int64_t m_, int64_t t_) { m = m_, t = t_; }
int64_t operator()(int64_t x) { return m * x + t; }
};
bool intersects_earlier(LinearFn f, LinearFn g, LinearFn h)
{
return (double)(h.t - f.t) / (double)(f.m - h.m) <
(double)(g.t - f.t) / (double)(f.m - g.m);
}
#define N 100000
int64_t s[N], v[N], d[N], ans[N];
vector<pair<size_t, int64_t>> g[N];
void find_shortest_route(size_t u, size_t p, deque<LinearFn> &q)
{
vector<LinearFn> removed;
if (!q.empty())
{
size_t a = 0, b = q.size() - 1;
while (a < b)
{
size_t mid = (a + b) / 2;
if (mid < q.size() - 1)
{
if (q[mid](v[u]) <= q[mid + 1](v[u]))
b = mid;
else
a = mid + 1;
}
else
{
if (mid && q[mid - 1](v[u]) <= q[mid](v[u]))
b = mid - 1;
else
a = mid;
}
}
ans[u] = q[a](v[u]) + d[u] * v[u] + s[u];
LinearFn f(-d[u], ans[u]);
while (q.size() >= 2 && intersects_earlier(*(q.rbegin() + 1), *q.rbegin(), f))
{
removed.push_back(q.back());
q.pop_back();
}
q.emplace_back(-d[u], ans[u]);
}
else
{
q.emplace_back(0, 0);
}
for (auto [x, w] : g[u])
{
if (x != p)
{
d[x] = d[u] + w;
find_shortest_route(x, u, q);
}
}
q.pop_back();
for (auto it = removed.rbegin(); it != removed.rend(); it++)
q.push_back(*it);
}
int main()
{
size_t n;
cin >> n;
for (size_t i = 0; i + 1 < n; i++)
{
size_t u, v, w;
cin >> u >> v >> w;
g[u - 1].emplace_back(v - 1, w);
g[v - 1].emplace_back(u - 1, w);
}
for (size_t i = 1; i < n; i++)
cin >> s[i] >> v[i];
deque<LinearFn> q;
find_shortest_route(0, SIZE_MAX, q);
for (size_t i = 1; i < n; i++)
cout << ans[i] << ' ';
cout << '\n';
}
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
2 ms |
2644 KB |
Output is correct |
2 |
Correct |
5 ms |
3284 KB |
Output is correct |
3 |
Correct |
84 ms |
13772 KB |
Output is correct |
4 |
Correct |
128 ms |
19116 KB |
Output is correct |
5 |
Correct |
170 ms |
24460 KB |
Output is correct |
6 |
Correct |
176 ms |
29716 KB |
Output is correct |
7 |
Correct |
137 ms |
13780 KB |
Output is correct |
8 |
Execution timed out |
1090 ms |
19880 KB |
Time limit exceeded |
9 |
Execution timed out |
1072 ms |
15348 KB |
Time limit exceeded |
10 |
Execution timed out |
1083 ms |
21164 KB |
Time limit exceeded |