/**
* Author: Anil Byar
**/
#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
using namespace std;
// template<class T>
// using ordered_set = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)(x).size()
#define uniq(v) v.erase(unique(all(v)), v.end())
#define ft first
#define sd second
#define pb push_back
// Source: https://codeforces.com/blog/entry/68809
// { start
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '"' << x << '"';}
void __print(const string &x) {cerr << '"' << x << '"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
// } end
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii> vii;
typedef vector<ll> vl;
typedef vector<pll> vll;
typedef vector<vi> vvi;
typedef vector<vii> vvii;
typedef vector<vl> vvl;
#define dbg if(0)
const ll MOD = 1e9+7;
const ll MOD9 = 998244353;
const ll INFLL = 1e18+5;
const int INF = 1e9;
void printbit(int x, int len) {string s="\n";while(len--){s=((x%2)?'1':'0')+s;x/=2;} cout<<s;}
ll power(ll x, ll y, ll mod){if (y==0) return 1;ll ret = power(x, y/2, mod);ret *= ret;ret%=mod;if (y&1) ret *= x;return ret%mod;}
ll modinv(ll x, ll mod = MOD) {return power(x, mod-2, mod);}
template<class T>
istream& operator>>(istream&in, vector<T>&v){
for (T& x:v) in>>x;
return in;
}
template<class T>
ostream& operator<<(ostream&out, vector<T>&v){
for (T& x:v) out<<x<<' ';
cout<<'\n';
return out;
}
// use ?: with brackets (?:)
// check for overflow
// think about dp
// Read the statement carefully
struct Line{
ll m, c;
Line(ll mm, ll cc):m(mm), c(cc){}
Line(){}
ll at(ll x){
return m*x+c;
}
friend ostream& operator<<(ostream&out, Line l){
out<<l.m<<"x + "<<l.c<<' ';
return out;
}
};
double intersection(const Line& l1, const Line& l2) {
return (l2.c-l1.c)/(double)(l1.m-l2.m);
}
#define sq(x) ((x)*(x))
const int maxN = 1e5+5; // change this
const int maxK = 8001;
ll dep[maxN];
ll dp[maxN];
ll V[maxN], S[maxN];
vii adj[maxN];
pair<double, Line> d[maxN];
int stkptr;
Line getline(int x, int ind){
int l = 0, r = ind+1;
while(r-l>1){
int m = (l+r)/2;
if (d[m].first<=x) l = m;
else r = m;
}
return d[l].second;
}
int getreplaceIdx(const Line& line, int ptr){
int l = 0, r = ptr+1;
while(r-l>1){
int mid = (l+r)/2;
if (intersection(line, d[mid].second)>d[mid].first) l = mid;
else r = mid;
}
return r;
}
void dfs(int node, int par, int ind){
pair<double, Line> tmp;
if (node==1){
dp[node] = 0;
Line curr = {0, 0};
d[ind] = {0, curr};
} else {
dp[node] = V[node]*dep[node]+S[node] + getline((int)V[node], ind).at(V[node]);
Line curr(-dep[node], dp[node]);
int newind = getreplaceIdx(curr, ind);
tmp = d[newind];
d[newind] = {intersection(curr, d[newind-1].second), curr};
ind = newind;
}
for (pii x:adj[node]){
if (x.ft==par) continue;
dep[x.ft] = dep[node] + x.sd;
dfs(x.first, node, ind);
}
d[ind] = tmp;
}
void solve(){
int n;cin>>n;
for (int i = 0;i<n-1;i++){
int u, v, w;cin>>u>>v>>w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
for (int i = 2;i<=n;i++){
cin>>S[i]>>V[i];
}
dfs(1, 0, 0);
for (int i = 2;i<=n;i++) cout<<dp[i]<<' ';
return;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
#define ONLINE_JUDGE
#ifndef ONLINE_JUDGE
freopen("input.in", "r", stdin);
freopen("output.out", "w", stdout);
freopen("debug.dbg", "w", stderr);
int tt = clock();
#endif
int t=1, i = 1;
// cin>>t;
while(t--){
// cout<<"Case #"<<i++<<": ";
solve();
cout<<"\n"[t!=0];
}
#ifndef ONLINE_JUDGE
cerr << "TIME = " << (float)(clock() - tt)/CLOCKS_PER_SEC << endl;
tt = clock();
#endif
}
Compilation message
harbingers.cpp: In function 'int main()':
harbingers.cpp:199:14: warning: unused variable 'i' [-Wunused-variable]
199 | int t=1, i = 1;
| ^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
5024 KB |
Output is correct |
| 2 |
Correct |
5 ms |
5544 KB |
Output is correct |
| 3 |
Correct |
54 ms |
15664 KB |
Output is correct |
| 4 |
Correct |
79 ms |
20508 KB |
Output is correct |
| 5 |
Correct |
102 ms |
25512 KB |
Output is correct |
| 6 |
Correct |
98 ms |
30176 KB |
Output is correct |
| 7 |
Correct |
74 ms |
16152 KB |
Output is correct |
| 8 |
Correct |
145 ms |
21444 KB |
Output is correct |
| 9 |
Correct |
133 ms |
24436 KB |
Output is correct |
| 10 |
Correct |
102 ms |
22776 KB |
Output is correct |
