#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
#define int long long
const int maxv = (int) 4e18;
const int maxn = 100005;
int n,dst[maxn],dp[maxn],rmv[maxn],s[maxn],v[maxn],ncnt = 0,rcnt = 0;
pair<int,int> nconn[maxn],rmvd[maxn];
vector<pair<int,int> > conn[maxn],cht;
inline void fdp(int pos) {
int l = -5, r = cht.size()+5;
while(l+1 < r) {
int mid = (l+r)/2;
bool isDecr;
if(mid < 0) isDecr = true;
else if(mid >= cht.size()-1) isDecr = false;
else {
int vl1 = cht[mid].second-v[pos]*cht[mid].first;
int vl2 = cht[mid+1].second-v[pos]*cht[mid+1].first;
isDecr = (vl2 < vl1);
}
if(isDecr == true) l = mid;
else r = mid;
}
dp[pos] = cht[r].second-v[pos]*cht[r].first+v[pos]*dst[pos]+s[pos];
}
inline void prmv(int pos) {
int l = -5, r = cht.size()+5;
while(l+1 < r) {
int mid = (l+r)/2;
bool isV;
if(mid < 0) isV = true;
else if(mid >= ((int) cht.size())-1) isV = false;
else {
__int128_t x1 = cht[mid].first;
__int128_t y1 = cht[mid].second;
__int128_t x2 = cht[mid+1].first;
__int128_t y2 = cht[mid+1].second;
__int128_t x3 = dst[pos];
__int128_t y3 = dp[pos];
__int128_t v1 = (y3-y2)*(x2-x1);
__int128_t v2 = (y2-y1)*(x3-x2);
isV = (v1 > v2);
}
if(isV) l = mid;
else r = mid;
}
rmv[pos] = r+1;
}
void dfs(int pos, int prevP) {
int ncl = ncnt;
for(int i = 0; i < conn[pos].size(); i++) {
int targP = conn[pos][i].first;
int newV = conn[pos][i].second;
if(targP != prevP) {
dst[targP] = dst[pos]+newV;
fdp(targP);
prmv(targP);
nconn[ncnt].first = rmv[targP];
nconn[ncnt].second = targP;
ncnt++;
}
}
int ncr = ncnt;
sort(nconn+ncl,nconn+ncr);
int rcl = rcnt;
for(int i = ncr-1; i >= ncl; i--) {
while(cht.size() > nconn[i].first) {
rmvd[rcnt] = cht.back();
rcnt++;
cht.pop_back();
}
int targP = nconn[i].second;
cht.push_back(make_pair(dst[targP],dp[targP]));
dfs(targP,pos);
cht.pop_back();
}
int rcr = rcnt;
for(int i = rcr-1; i >= rcl; i--) {
cht.push_back(rmvd[i]);
}
}
signed main () {
scanf("%lld",&n);
for(int i = 0; i < n-1; i++) {
int a,b,c;
scanf("%lld%lld%lld",&a,&b,&c);
conn[a].push_back(make_pair(b,c));
conn[b].push_back(make_pair(a,c));
}
for(int i = 2; i <= n; i++) {
scanf("%lld%lld",&s[i],&v[i]);
}
cht.push_back(make_pair(0,0));
dfs(1,-1);
for(int i = 2; i <= n; i++) {
printf("%lld ",dp[i]);
}
printf("\n");
return 0;
}
Compilation message (stderr)
harbingers.cpp: In function 'int main()':
harbingers.cpp:85:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
85 | scanf("%lld",&n);
| ~~~~~^~~~~~~~~~~
harbingers.cpp:88:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
88 | scanf("%lld%lld%lld",&a,&b,&c);
| ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
harbingers.cpp:93:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
93 | scanf("%lld%lld",&s[i],&v[i]);
| ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
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