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>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
#define ll long long int
#define F first
#define S second
#define pb push_back
#define v00 dp[0][0][v]
#define v01 dp[0][1][v]
#define v10 dp[1][0][v]
#define v11 dp[1][1][v]
#define u00 dp[0][0][u]
#define u01 dp[0][1][u]
#define u10 dp[1][0][u]
#define u11 dp[1][1][u]
const ll M = 5;
const ll N = 2e5 + 5;
const ll LOG = 20;
const int MOD = 1e9 + 7;
const ll INF = 1e9 + 5;
ll n, dp[M][M][N];
vector < pair <int, ll> > adj[N];
// dp[0][0][v] : (in sub[v] down : 0) && (v up_dn : 0) -> ok : v is emp
// dp[0][1][v] : (in sub[v] down : 0) && (v up_dn : 1) -> ok : v is up_dn
// dp[1][0][v] : (in sub[v] down : 1) && (v up_dn : 0) -> ok : v is dn || v is emp
// dp[1][1][v] : (in sub[v] down : 1) && (v up_dn : 1) -> ok : v is up_dn
void dfs(int v = 1, int p = 0, ll up = -INF){
v00 = 0;
v01 = v10 = v11 = -INF;
ll hlp[] = {0, -INF, -INF, -INF};
for (auto i : adj[v]){
int u = i.F;
ll dn = i.S;
if (u == p) continue;
dfs(u, v, i.S);
v11 = max({v11 + max(u00, u01), v00 + up + dn + u10});
v10 = max({v10 + max(u00, u01), v00 + max(u10, u11)});
v01 = max(v01 + max(u00, u01), v00 + up + dn + u00);
v00 = v00 + max(u00, u01);
hlp[3] = max({hlp[3] + max(u00, u01), hlp[2] + dn + u00, hlp[1] + dn + max(u00, u10)});
hlp[2] = max(hlp[2] + max(u00, u01), hlp[0] + dn + max(u00, u10));
hlp[1] = max(hlp[1] + max(u00, u01), hlp[0] + dn + u00);
hlp[0] = hlp[0] + max(u00, u01);
}
v10 = max(v10, hlp[3]);
return;
}
int main() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
cin >> n;
for (int i = 0; i < n - 1; i ++){
int u, v, w;
cin >> u >> v >> w;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
dfs();
cout << max(dp[0][0][1], dp[1][0][1]) << '\n';
return 0;
}
/*
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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