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>
#pragma GCC target("sse,sse2,avx2")
#pragma GCC optimize("unroll-loops,O2")
#define rep(i,l,r) for (int i = l; i < r; i++)
#define repr(i,r,l) for (int i = r; i >= l; i--)
#define X first
#define Y second
#define all(x) (x).begin() , (x).end()
#define pb push_back
#define endl '\n'
#define debug(x) cerr << #x << " : " << x << endl;
using namespace std;
typedef long long ll;
typedef pair<int,int> pll;
constexpr int N = 2e5+10,mod = 1e9+7,maxm = 210;
constexpr ll inf = 1e9+10;
inline int mkay(int a,int b){
if (a+b >= mod) return a+b-mod;
// if (a+b < 0) return a+b+mod;
return a+b;
}
inline int poww(int a,int k){
if (k < 0) return 0;
int z = 1;
while (k){
if (k&1) z = 1ll*z*a%mod;
a = 1ll*a*a%mod;
k >>= 1;
}
return z;
}
vector<pll> adj[N];
int dp[N][2];
void dfs(int v,int p){
if ((int) adj[v].size() == 1 && p != 0){
dp[v][1] = -2*inf;
dp[v][0] = 0;
return;
}
int s = 0,mx = -2*inf;
for (auto [u,w] : adj[v]){
if (u == p) continue;
dfs(u,v);
int val = max(dp[u][0],dp[u][1]+w);
s += val;
mx = max(mx,dp[u][0]-val+w);
}
dp[v][0] = s;
dp[v][1] = s + mx;
}
bool cmp(int i,int j){
return adj[i][0].Y > adj[j][0].Y;
}
int main(){
ios :: sync_with_stdio(0); cin.tie(0);
int n;
cin >> n;
int mx = -1,U = -1,V = -1;
rep(i,1,n){
int u,v,w;
cin >> u >> v >> w;
if (w > mx){
mx = w;
U = u;
V = v;
}
adj[u].pb({v,w});
adj[v].pb({u,w});
}
if (n <= 2){
cout << 0 << endl;
return 0;
}
vector<int> leaf;
rep(i,1,n+1){
if ((int)adj[i].size() == 1) leaf.pb(i);
}
sort(all(leaf),cmp);
int t = min(1800,(int)leaf.size()),ans = 0;
rep(i,0,t){
dfs(leaf[i],0);
ans = max(ans,dp[leaf[i]][0]);
}
dfs(U,0);
ans = max(ans,dp[U][0]);
dfs(V,0);
ans = max(ans,dp[V][0]);
cout << ans;
}
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