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;
using ll = long long;
const int N = 200200;
const ll INF = 2e9;
vector<pair<int, int>> adj[N];
ll dp[5][N];
void dfs(int v, int p = -1) {
ll mx0 = 0, mx2 = -INF, mx3 = -INF;
pair<ll, int> mxf[3] = { {-INF,0}, {-INF,0}, {-INF,0} };
pair<ll, int> mxs[3] = { {-INF,0}, {-INF,0}, {-INF,0} };
for (auto& [x, w] : adj[v]) {
if (x == p) continue;
dfs(x, v);
ll val = max(dp[1][x], dp[2][x] + w);
// 0
dp[0][v] += val;
mx0 = max(mx0, max(dp[0][x], dp[3][x] + w) - val);
// 1
dp[1][v] += val;
// 2
dp[2][v] += val;
mx2 = max(mx2, dp[1][x] + w - val);
// 3
dp[3][v] += val;
mx3 = max(mx3, dp[4][x] + w - val);
// 4
dp[4][v] += val;
mxs[0] = max(mxs[0], { dp[1][x] + w - val, x });
mxs[1] = max(mxs[1], { dp[0][x] + w - val, x });
mxs[2] = max(mxs[2], { dp[4][x] + w - val, x });
if (mxf[0] < mxs[0]) swap(mxf[0], mxs[0]);
if (mxf[1] < mxs[1]) swap(mxf[1], mxs[1]);
if (mxf[2] < mxs[2]) swap(mxf[2], mxs[2]);
}
dp[0][v] += mx0;
dp[2][v] += mx2;
dp[3][v] += mx3;
ll res = 0;
if (mxf[0].second != mxf[1].second) res = max(res, mxf[0].first + mxf[1].first);
else res = max({ res, mxf[0].first + mxs[1].first, mxs[0].first + mxf[1].first });
if (mxf[0].second != mxf[2].second) res = max(res, mxf[0].first + mxf[2].first);
else res = max({ res, mxf[0].first + mxs[2].first, mxs[0].first + mxf[2].first });
dp[4][v] += res;
}
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
int n;
cin >> n;
for (int i = 1;i < n;i++) {
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({ v, w });
adj[v].push_back({ u, w });
}
dfs(1);
cout << max(dp[0][1], dp[4][1]);
return 0;
}
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