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/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
read some solution ideas, found them non-intuitive
trying to build upon my previous idea
*/
const int MOD = 1e9 + 7;
const int N = 2e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
vector<pii> adj[N];
vector<int> dp[N];
vector<int> best(N,-inf1);
void dfs(ll u, ll p){
for(auto [v,w] : adj[u]){
if(v == p) conts;
dfs(v,u);
}
ll sum = 0;
rep(i,sz(adj[u])){
auto [v,w] = adj[u][i];
if(v == p) conts;
// ll curr_val = -inf2;
// rep(j,sz(adj[v])){
// auto [v2,w2] = adj[v][j];
// if(v2 == u) conts;
// ll val = w+w2+dp[v2][0]+dp[v][j+1];
// amax(curr_val,val);
// }
// amax(curr_val,dp[v][0]);
ll curr_val = max(w+best[v],dp[v][0]);
dp[u][i+1] = -curr_val;
sum += curr_val;
}
rep(i,sz(adj[u])+1){
dp[u][i] += sum;
}
best[u] = -inf1;
rep(j,sz(adj[u])){
auto [v,w] = adj[u][j];
if(v == p) conts;
amax(best[u],w+dp[u][j+1]+dp[v][0]);
}
}
void solve(int test_case)
{
int n; cin >> n;
rep1(i,n-1){
int u,v,c; cin >> u >> v >> c;
adj[u].pb({v,c}), adj[v].pb({u,c});
}
int ans = -inf1;
rep1(u,n){
dp[u] = vector<int>(sz(adj[u])+1);
}
rep1(i,n){
vector<pii> ord;
queue<pii> q;
q.push({i,-1});
while(!q.empty()){
auto [u,p] = q.front();
q.pop();
ord.pb({u,p});
for(auto [v,w] : adj[u]){
if(v == p) conts;
q.push({v,u});
}
}
reverse(all(ord));
for(auto [u,p] : ord){
int sum = 0;
rep(i,sz(adj[u])){
auto [v,w] = adj[u][i];
if(v == p) conts;
// ll curr_val = -inf2;
// rep(j,sz(adj[v])){
// auto [v2,w2] = adj[v][j];
// if(v2 == u) conts;
// ll val = w+w2+dp[v2][0]+dp[v][j+1];
// amax(curr_val,val);
// }
// amax(curr_val,dp[v][0]);
int curr_val = max(w+best[v],dp[v][0]);
dp[u][i+1] = -curr_val;
sum += curr_val;
}
dp[u][0] = 0;
rep(i,sz(adj[u])+1){
dp[u][i] += sum;
}
best[u] = -inf1;
rep(j,sz(adj[u])){
auto [v,w] = adj[u][j];
if(v == p) conts;
amax(best[u],w+dp[u][j+1]+dp[v][0]);
}
}
amax(ans,dp[i][0]);
// dfs(i,-1);
// amax(ans,dp[i][0]);
}
cout << ans << endl;
}
int main()
{
fastio;
int t = 1;
// cin >> t;
rep1(i, t) {
solve(i);
}
return 0;
}
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