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 all(vec) vec.begin(), vec.end()
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
constexpr ll INF = (1LL << 40) - 1LL;
constexpr ll LINF = (1LL << 60) - 1LL;
constexpr double eps = 1e-9;
constexpr ll MOD = 1000000007LL;
template <typename T>
bool chmin(T& a, T b) {
if(a > b) {
a = b;
return true;
}
return false;
};
template <typename T>
bool chmax(T& a, T b) {
if(a < b) {
a = b;
return true;
}
return false;
};
template <typename T>
ostream& operator<<(ostream& os, vector<T> v) {
for(int i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "\n" : " ");
}
return os;
}
template <typename T>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T& t, const V& v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T& t, const V& v) {
for(auto& e : t) {
fill_v(e, v);
}
};
int n;
vector<vector<P>> G;
vector<vector<ll>> dp;
ll dfs(int i, int f, int p) {
if(dp[i][f] != -1) {
return dp[i][f];
}
ll sum = 0, m21 = -LINF, m22 = -LINF;
for(auto pe : G[i]) {
int e = pe.first;
ll c = pe.second;
if(e == p) {
continue;
}
dfs(e, 0, i);
dfs(e, 1, i);
dfs(e, 2, i);
ll t = max(dp[e][1] + c, dp[e][0]);
sum += t;
if(m21 < dp[e][2] + c - t) {
m22 = m21;
m21 = dp[e][2] + c - t;
} else if(m22 < dp[e][2] + c - t) {
m22 = dp[e][2] + c - t;
}
}
ll res = -LINF;
if(f == 0) {
chmax(res, sum + m21 + m22);
chmax(res, sum);
} else if(f == 1) {
chmax(res, sum + m21);
} else {
chmax(res, sum);
chmax(res, sum + m21 + m22);
}
return dp[i][f] = res;
}
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
cin >> n;
G.resize(n);
dp.resize(n);
for(int i = 0; i < n; i++) {
dp[i].resize(3, -1);
}
for(int i = 0; i < n - 1; i++) {
int u, v, c;
cin >> u >> v >> c;
--u;
--v;
G[u].push_back(P(v, c));
G[v].push_back(P(u, c));
}
cout << dfs(0, 0, -1) << endl;
}
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