#include <bits/stdc++.h>
#define st first
#define nd second
using lint = int64_t;
constexpr int mod = int(1e9) + 7;
constexpr int inf = 0x3f3f3f3f;
constexpr int ninf = 0xcfcfcfcf;
constexpr lint linf = 0x3f3f3f3f3f3f3f3f;
const long double pi = acosl(-1.0);
// Returns -1 if a < b, 0 if a = b and 1 if a > b.
int cmp_double(double a, double b = 0, double eps = 1e-9) {
return a + eps > b ? b + eps > a ? 0 : 1 : -1;
}
using namespace std;
struct Line{
mutable lint k, m, p;
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(lint x) const {return p < x; }
};
struct LineContainer : multiset<Line, less<>>{
static const lint inf = LLONG_MAX;
lint div(lint a, lint b){
return a / b - ((a ^ b) < 0 && a % b);
}
bool isect(iterator x, iterator y){
if(y == end()){ x->p = inf; return false; }
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(lint k, lint 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));
}
lint query(lint x){
assert(!empty());
auto l = *lower_bound(x);
return l.k * x + l.m;
}
};
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
int n;
cin>>n;
vector<vector<pair<int, int>>>g(n);
for(int i=1;i<n;i++){
int a, b, c;
cin>>a>>b>>c;
a--, b--;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
vector<lint>s(n), v(n);
for(int i=1;i<n;i++) cin>>s[i]>>v[i];
int sz = sqrt(n * log(n));
vector<lint>dist(n), dp(n, linf);
dp[0] = 0;
vector<int>par(n);
vector<LineContainer>st;
auto dfs = [&](auto& self, int u, int p, int d)->void{
par[u] = p;
if(d && d % sz == 0){
st.push_back(LineContainer());
LineContainer& cht = st.back();
for(int i=0,x=par[u];i<sz;i++,x=par[x]){
cht.add(dist[x], -dp[x]);
}
}
{
// calculate ans
lint cnt = dist[u] * v[u] + s[u];
dp[u] = cnt;
for(int i=0,x=par[u];i<d%sz;i++,x=par[x]){
dp[u] = min(dp[u], cnt - dist[x] * v[u] + dp[x]);
}
for(auto& cht : st){
dp[u] = min(dp[u], cnt - cht.query(v[u]));
}
}
for(auto [nxt, c] : g[u]){
if(nxt == p) continue;
dist[nxt] = dist[u] + c;
self(self, nxt, u, d+1);
}
if(d && d % sz == 0) st.pop_back();
};
dfs(dfs, 0, 0, 0);
for(int i=1;i<n;i++) cout<<dp[i]<<" ";
cout<<"\n";
return 0;
}
/*
[ ]Leu o problema certo???
[ ]Ver se precisa de long long
[ ]Viu o limite dos fors (é n? é m?)
[ ]Tamanho do vetor, será que é 2e5 em vez de 1e5??
[ ]Testar sample
[ ]Testar casos de borda
[ ]1LL no 1LL << i
[ ]Testar mod (é 1e9+7, mesmo?, será que o mod não ficou negativo?)
*/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
3 ms |
980 KB |
Output is correct |
| 3 |
Correct |
161 ms |
11872 KB |
Output is correct |
| 4 |
Correct |
333 ms |
17744 KB |
Output is correct |
| 5 |
Correct |
473 ms |
22064 KB |
Output is correct |
| 6 |
Correct |
699 ms |
27356 KB |
Output is correct |
| 7 |
Correct |
357 ms |
12020 KB |
Output is correct |
| 8 |
Correct |
754 ms |
20216 KB |
Output is correct |
| 9 |
Execution timed out |
1063 ms |
24480 KB |
Time limit exceeded |
| 10 |
Correct |
990 ms |
22408 KB |
Output is correct |
