#include<bits/stdc++.h>
#define fast ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL)
#define pb push_back
#define F first
#define S second
#define int long long
using namespace std;
const int N = 1e5 + 5, MOD = 1e9 + 7;
vector<pair<int, int> > g[N];
int n, par[N], dis[N], dp[N], s[N], d[N];
struct Line{
int m, c;
int val(int x){
return m*x + c;
}
};
vector<Line> hulls(N);
int cur_hullsize = 1;
long double intersect(Line l1, Line l2){
return (long double)(l2.c - l1.c) / (long double)(l1.m - l2.m);
}
int pos(int mm, int cc){
Line cur;
cur.m = mm;
cur.c = cc;
if(cur_hullsize < 2 or (intersect(cur, hulls[cur_hullsize - 1]) >= intersect(hulls[cur_hullsize - 1], hulls[cur_hullsize - 2])))
return cur_hullsize;
int low = 1, high = cur_hullsize - 1, ans = 0;
while(low <= high){
int mid = (low + high) / 2;
if(intersect(cur, hulls[mid]) < intersect(hulls[mid], hulls[mid - 1])){
ans = mid;
high = mid - 1;
}
else
low = mid + 1;
}
return ans;
}
int get(int x){
int low = 0, high = cur_hullsize - 1;
while(low < high){
int mid = (low + high) / 2;
if(hulls[mid].val(x) < hulls[mid + 1].val(x))
high = mid;
else
low = mid + 1;
}
return hulls[high].val(x);
}
void dfs(int node, int p, int sum){
dis[node] = sum;
par[node] = p;
for(auto k : g[node]){
if(k.F == p) continue;
dfs(k.F, node, sum + k.S);
}
}
/*
we want to find the position in the convex hull where the current line will go
we will replace that position with the current line
we will change it back once I go up from that node
*/
void dfs1(int node){
dp[node] = get(d[node]) + s[node] + dis[node] * d[node];
int cur, here = cur_hullsize;
Line pre;
if(node != 1){
cur = cur_hullsize = pos(-dis[node], dp[node]);
Line neww;
neww.m = -dis[node];
neww.c = dp[node];
pre = hulls[cur];
hulls[cur] = neww;
cur_hullsize++;
}
for(auto k : g[node]){
if(k.F == par[node])
continue;
dfs1(k.F);
}
if(node != 1){
cur_hullsize = here;
hulls[cur] = pre;
}
}
void solve(){
cin >> n;
for(int i = 1; i < n; ++i){
int u, v, c;
cin >> u >> v >> c;
g[u].pb({v, c});
g[v].pb({u, c});
}
for(int i = 1; i < n; ++i)
cin >> s[i + 1] >> d[i + 1];
dfs(1, 0, 0);
Line wut;
wut.m = 0, wut.c = 0;
hulls[0] = wut;
dfs1(1);
for(int i = 2; i <= n; ++i)
cout << dp[i] << " ";
}
int32_t main(){
fast;
int t = 1;
// cin >> t;
while(t--)
solve();
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
4180 KB |
Output is correct |
| 2 |
Correct |
4 ms |
4728 KB |
Output is correct |
| 3 |
Correct |
38 ms |
11648 KB |
Output is correct |
| 4 |
Correct |
59 ms |
15168 KB |
Output is correct |
| 5 |
Correct |
73 ms |
18604 KB |
Output is correct |
| 6 |
Correct |
104 ms |
21916 KB |
Output is correct |
| 7 |
Correct |
49 ms |
13088 KB |
Output is correct |
| 8 |
Correct |
103 ms |
17784 KB |
Output is correct |
| 9 |
Correct |
103 ms |
19000 KB |
Output is correct |
| 10 |
Correct |
82 ms |
17868 KB |
Output is correct |
