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 ii pair < int , int >
#define fi first
#define se second
using namespace std;
const int maxn = 200010;
const int inf = 0x3f3f3f3f;
vector < ii > g[maxn];
int dp[maxn][3] , f[maxn];
void DFS(int u,int p,int wp) {
for (auto v : g[u])
if (v.fi != p)
DFS(v.fi , u , v.se);
for (auto v : g[u])
if (v.fi != p)
dp[u][0] += max(dp[v.fi][0] , dp[v.fi][1]);
for (auto v : g[u])
if (v.fi != p)
dp[u][1] = max(dp[u][1] , dp[u][0] - max(dp[v.fi][0] , dp[v.fi][1]) + dp[v.fi][0] + wp + v.se);
dp[u][2] = dp[u][0];
int ma1 , ma2;
ma1 = ma2 = -inf;
for (auto v : g[u])
if (v.fi != p) {
int cur = dp[v.fi][2] - max(dp[v.fi][0] , dp[v.fi][1]) + v.se;
if (cur > ma1) {
ma2 = ma1;
ma1 = cur;
} else ma2 = max(ma2 , cur);
}
for (auto v : g[u])
if (v.fi != p) {
int cur = ma1;
if (cur == dp[v.fi][0] - max(dp[v.fi][0] , dp[v.fi][1]) + v.se) cur = ma2;
dp[u][2] = max(dp[u][2] , dp[u][0] - max(dp[v.fi][0] , dp[v.fi][1]) + dp[v.fi][2]);
dp[u][2] = max(dp[u][2] , dp[u][0] - max(dp[v.fi][0] , dp[v.fi][1]) + dp[v.fi][2] + cur + v.se);
dp[u][2] = max(dp[u][2] , dp[u][0] - max(dp[v.fi][0] , dp[v.fi][1]) + f[v.fi] + v.se);
}
f[u] = -inf;
for (auto v : g[u])
if (v.fi != p)
f[u] = max(f[u] , dp[v.fi][2] + v.se + dp[u][0] - max(dp[v.fi][0] , dp[v.fi][1]));
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
int n;
cin >> n;
for (int i = 1 ; i < n ; ++i) {
int u , v , w;
cin >> u >> v >> w;
g[u].emplace_back(v , w);
g[v].emplace_back(u , w);
}
DFS(1 , 0 , 0);
cout << dp[1][2];
}
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