#include <bits/stdc++.h>
using namespace std;
#define int int64_t //be careful about this
#define pr pair
#define ar array
#define f first
#define s second
#define vt vector
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define SZ(x) ((int)(x).size())
#define all(a) (a).begin(),(a).end()
#define allr(a) (a).rbegin(),(a).rend()
#define mem(a,b) memset(a, b, sizeof(a))
template<class A> void rd(vt<A>& v);
template<class T> void rd(T& x){ cin >> x;}
template<class H, class... T> void rd(H& h, T&... t) { rd(h); rd(t...);}
template<class A> void rd(vt<A>& x) { for(auto& a : x) rd(a);}
template<class T> bool ckmin(T& a, const T b) { return b < a ? a = b, 1 : 0;}
template<class T> bool ckmax(T& a, const T b) { return a < b ? a = b, 1 : 0;}
template<typename T>
void __p(T a) {
cout<<a;
}
template<typename T, typename F>
void __p(pair<T, F> a) {
cout<<"{";
__p(a.first);
cout<<",";
__p(a.second);
cout<<"}\n";
}
template<typename T>
void __p(std::vector<T> a) {
cout<<"{";
for(auto it=a.begin(); it<a.end(); it++)
__p(*it),cout<<",}\n"[it+1==a.end()];
}
template<typename T, size_t N>
void __p(array<T,N> a){
cout<<"{";
for(int i = 0; i < N; ++i)
__p(a[i]),cout<<",}\n"[i+1==N];
}
template<typename T, typename ...Arg>
void __p(T a1, Arg ...a) {
__p(a1);
__p(a...);
}
template<typename Arg1>
void __f(const char *name, Arg1 &&arg1) {
cout<<name<<" : ";
__p(arg1);
cout<<endl;
}
template<typename Arg1, typename ... Args>
void __f(const char *names, Arg1 &&arg1, Args &&... args) {
int bracket=0,i=0;
for(;; i++)
if(names[i]==','&&bracket==0)
break;
else if(names[i]=='(')
bracket++;
else if(names[i]==')')
bracket--;
const char *comma=names+i;
cout.write(names,comma-names)<<" : ";
__p(arg1);
cout<<" | ";
__f(comma+1,args...);
}
#define trace(...) cout<<"Line:"<<__LINE__<<" ", __f(#__VA_ARGS__, __VA_ARGS__)
void setIO(string s = "") {
ios_base::sync_with_stdio(0); cin.tie(0);
cout.precision(20); cout << fixed;
if(SZ(s)){
freopen((s+".in").c_str(),"r",stdin);
freopen((s+".out").c_str(),"w",stdout);
}
}
const auto start_time = std::chrono::high_resolution_clock::now();
void output_run_time(){
// will work for ac,cc&&cf.
#ifndef ONLINE_JUDGE
auto end_time = std::chrono::high_resolution_clock::now();
std::chrono::duration<double> diff = end_time-start_time;
cout << "\n\n\nTime Taken : " << diff.count();
#endif
}
/*/--------------------------------------------------look below-----------------------------------------------------------------------------------/*/
/*
* Description :- monotonic convex hull trick.
* Source :- https://codeforces.com/blog/entry/63823.
* Verf :- DMOJ APIO 10' 1.
*/
// F = true means queries are in arbitary order else they are in non-increasing order.
// add(m,c) has m in non-increasing order.
// return max value for m*x+c.
template<bool F>
struct monotonic_cht{
static int floor_div(int a,int b){
return a/b-((a^b)<0&&a%b);
}
struct line{
int m,c;
int eval(int x){
return m*x+c;
}
long double isect(const line& l){
return (c-l.c)/(l.m-m);
}
};
deque<line> dq;
void init(){
dq.clear();
}
vector<vector<line>> change;
void add(int m,int c){
line cur = {m,c};
vector<line> rem;
if(dq.size() >= 1 && dq.front().m == m){
if(dq.front().c >= c){
change.pb(rem);return;
}
rem.pb(dq.front());
dq.pop_front();
}
while(dq.size() >= 2 && cur.isect(dq[0]) >= dq[0].isect(dq[1]))
rem.pb(dq.front()),dq.pop_front();
dq.push_front(cur);
change.pb(rem);return;
}
void roll_back(){
dq.pop_front();
auto rem = change.back(); change.pop_back();
reverse(all(rem));
for(auto l : rem)
dq.push_front(l);
return;
}
int query(int x){
if(F){
assert(!dq.empty());
if(dq.size() == 1 || dq[0].isect(dq[1]) > x)
return dq[0].eval(x);
int lo = 0, hi = dq.size() - 1;
while(hi - lo > 1){
int mid = (hi + lo)/2;
dq[mid].isect(dq[mid+1]) < (long double)x ? lo = mid : hi = mid;
}
return dq[lo+1].eval(x);
}else{
while(dq.size() >= 2 && end(dq)[-1].eval(x) <= end(dq)[-2].eval(x))
dq.pop_back();
return dq.back().eval(x);
}
}
};
signed main(){
setIO();
int n;
rd(n);
vt<vt<pr<int,int>>> g(n);
for(int e = 0; e < n-1; ++e){
int u,v,w; rd(u,v,w); --u,--v;
g[u].eb(v,w);
g[v].eb(u,w);
}
vt<int> p(n,0),s(n,0);
for(int i = 1; i < n; ++i)
rd(p[i],s[i]);
monotonic_cht<true> cht;
vt<int> t(n);
int offset = 0;
t[0] = 0;
cht.add(0,0);
function<void(int,int)> dfs = [&](int i,int par)->void{
for(auto [j,w] : g[i])
if(j != par){
t[j] = p[j] + w * s[j] - cht.query(-s[j]) + offset * s[j];
cht.add(-offset-w,-t[j]);
offset += w;
dfs(j,i);
cht.roll_back();
offset -= w;
}
};
dfs(0,-1);
for(int i = 1; i < n; ++i)
cout << t[i] << " ";
//output_run_time();
return 0;
}
// tips to avoid bugs.
/*
* be careful of whats happening you dont want a continue statement to miss imp line of code.
* be careful when to update what since it might be needed in next segment of code.
* dont get stuck on one idea.
* dont use too much space bar so that code is written quickly as possible.
*/
Compilation message
harbingers.cpp: In function 'void setIO(std::string)':
harbingers.cpp:87:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
87 | freopen((s+".in").c_str(),"r",stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
harbingers.cpp:88:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
88 | freopen((s+".out").c_str(),"w",stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
204 KB |
Output is correct |
| 2 |
Incorrect |
2 ms |
1100 KB |
Output isn't correct |
| 3 |
Incorrect |
47 ms |
12996 KB |
Output isn't correct |
| 4 |
Incorrect |
68 ms |
19116 KB |
Output isn't correct |
| 5 |
Incorrect |
83 ms |
25084 KB |
Output isn't correct |
| 6 |
Incorrect |
119 ms |
31156 KB |
Output isn't correct |
| 7 |
Incorrect |
57 ms |
13128 KB |
Output isn't correct |
| 8 |
Execution timed out |
1101 ms |
19948 KB |
Time limit exceeded |
| 9 |
Execution timed out |
1085 ms |
15096 KB |
Time limit exceeded |
| 10 |
Execution timed out |
1091 ms |
21640 KB |
Time limit exceeded |
