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 Loop(x,l,r) for (ll x = (l); x < (ll)(r); ++x)
#define LoopR(x,l,r) for (ll x = (r)-1; x >= (ll)(l); --x)
typedef long long ll;
typedef std::pair<int, int> pii;
typedef std::pair<ll , ll > pll;
using namespace std;
const int N = 200'010;
vector<pii> A[N];
int n;
array<int, 4> dfs(int v, int p, int w)
{
int sum0 = 0;
vector<pii> v20, v10w, v30w;
for (auto [u, e] : A[v]) {
if (u == p)
continue;
auto x = dfs(u, v, e);
v20.emplace_back(x[2] - x[0], u);
v10w.emplace_back(x[1] - x[0] + e, u);
v30w.emplace_back(x[3] - x[0] + e, u);
sum0 += x[0];
}
v20.push_back({-1e9, -1}); v20.push_back({-1e9, -2});
v10w.push_back({-1e9, -3}); v10w.push_back({-1e9, -4});
v30w.push_back({-1e9, -5}); v30w.push_back({-1e9, -6});
sort(v20.rbegin(), v20.rend());
sort(v10w.rbegin(), v10w.rend());
sort(v30w.rbegin(), v30w.rend());
array<int, 4> ans = {};
ans[0] = sum0 + v10w[0].first + w;
ans[1] = 0;
if (v30w[0].second != v10w[0].second) {
ans[3] = sum0 + v30w[0].first + v10w[0].first;
} else {
ans[3] = sum0 + max(v30w[0].first + v10w[1].first,
v30w[1].first + v10w[0].first);
}
ans[2] = max(ans[3], sum0 + v30w[0].first + w);
ans[0] = max(ans[0], sum0);
ans[1] = max(ans[1], sum0);
ans[2] = max(ans[2], sum0 + v20[0].first);
ans[3] = max(ans[3], sum0 + v20[0].first);
Loop (i,0,4)
ans[i] = max(ans[i], 0);
return ans;
}
int main()
{
cin.tie(0) -> sync_with_stdio(false);
cin >> n;
Loop (i,1,n) {
int v, u, w;
cin >> v >> u >> w;
--v; --u;
A[v].push_back({u, w});
A[u].push_back({v, w});
}
cout << dfs(0, -1, 0)[3] << '\n';
}
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