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>
using namespace std;
#define all(x) x.begin(), x.end()
#define pb push_back
#define ln '\n'
#define int long long
template <class _T>
bool chmin(_T &x, const _T &y){
bool flag = false;
if ( x > y ){
x = y; flag |= true;
}
return flag;
}
template <class _T>
bool chmax(_T &x, const _T &y){
bool flag = false;
if ( x < y ){
x = y; flag |= true;
}
return flag;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n; cin >> n;
vector <pair<int,int>> g[n];
for ( int i = 1; i < n; i++ ){
int x, y, w; cin >> x >> y >> w;
g[--x].pb({--y, w});
g[y].pb({x, w});
}
vector <array<int,2>> dp(n);
const int inf = 1e15 + 1;
function <void(int,int,int)> dfs = [&](int x, int par, int prev){
int cnt = 0, l = -inf, r = -inf;
for ( auto [to, w]: g[x] ){
if ( to == par ) continue;
dfs(to, x, w);
cnt += dp[to][1];
int v = dp[to][0] - dp[to][1] + w;
if ( l <= v ){
r = l; l = v;
}
else chmax(r, v);
}
if ( r != -inf ){
chmax(dp[x][0], cnt + l + r);
}
chmax(dp[x][0], cnt);
for ( auto [to, w]: g[x] ){
if ( to == par ) continue;
chmax(dp[x][1], cnt - dp[to][1] + dp[to][0] + w + prev);
}
chmax(dp[x][1], dp[x][0]);
};
dfs(0, 0, 0);
cout << dp[0][0];
cout << '\n';
}
/*
10
4 10 2
1 2 21
1 3 13
6 7 1
7 9 5
2 4 3
2 5 8
1 6 55
6 8 34
*/
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