This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define fi first
#define se second
using namespace std;
typedef long long ll;
typedef double db;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<db,db> pdb;
typedef tuple<int,int,int> tii;
typedef vector<vector<ll>> mat;
const ll mod=1e9+7;
const int N=2e5+5;
int n,ans,dp1[N],dp2[N],dp3[N],dp4[N];
vector<pii> g[N];
void dfs(int x,int p){
vector<int> v1,v2;
dp2[x]=dp3[x]=dp4[x]=-1e9;
int s=0;
for(auto &it : g[x]) if(it.fi!=p){
int u=it.fi,c=it.se;
dfs(u,x);
v1.emplace_back(dp1[u]+c-max({dp1[u],dp2[u],dp3[u]+c}));
v2.emplace_back(dp2[u]+c-max({dp1[u],dp2[u],dp3[u]+c}));
dp1[x]+=max({dp1[u],dp2[u],dp3[u]+c,dp4[u]+c});
s+=max({dp1[u],dp2[u],dp3[u]+c});
}
if(p){
for(auto &it : g[x]) if(it.fi!=p){
int u=it.fi,c=it.se;
dp3[x]=max(dp3[x],s-max({dp1[u],dp2[u],dp3[u]+c})+dp1[u]+c);
dp4[x]=max(dp4[x],s-max({dp1[u],dp2[u],dp3[u]+c})+dp2[u]+c);
}
}
sort(v1.begin(),v1.end()); reverse(v1.begin(),v1.end());
sort(v2.begin(),v2.end()); reverse(v2.begin(),v2.end());
if(v1.size()>=2){
dp2[x]=max(dp2[x],s+v1[0]+v1[1]);
for(auto &it : g[x]) if(it.fi!=p){
int u=it.fi,c=it.se;
int c1=dp1[u]+c-max({dp1[u],dp2[u],dp3[u]+c}),c2=dp2[u]+c-max({dp1[u],dp2[u],dp3[u]+c});
if(c1==v1[0]) dp2[x]=max(dp2[x],s+v1[1]+c2);
else dp2[x]=max(dp2[x],s+v1[0]+c2);
if(c2==v2[0]) dp2[x]=max(dp2[x],s+c1+v2[1]);
else dp2[x]=max(dp2[x],s+c1+v2[0]);
}
}
//cout<<x<<" : "<<dp1[x]<<" "<<dp2[x]<<" "<<dp3[x]<<" "<<dp4[x]<<"\n";
}
int main(){
ios::sync_with_stdio(false); cin.tie(0);
cin>>n;
for(int u,v,c,i=1;i<n;i++){
cin>>u>>v>>c;
g[u].emplace_back(v,c);
g[v].emplace_back(u,c);
}
dfs(1,0);
cout<<max(dp1[1],dp2[1]);
return 0;
}
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