#include "dreaming.h"
#include <bits/stdc++.h>
// mrrrow meeow :3
// go play vivid/stasis now! it's free on steam
#define fo(i, a, b) for (auto i = (a); i < (b); i++)
#define of(i, a, b) for (auto i = (b); i-- > (a);)
#define f first
#define s second
#define pb push_back
#define pob pop_back
#define lb lower_bound
#define ub upper_bound
#define be(a) a.begin(), a.end()
using namespace std;
int ____init = [] {
ios::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
return 0;
}();
struct Component {
int diameter;
int longest;
Component(int diameter, int longest) : diameter(diameter), longest(longest) {}
};
int vis[100000];
vector<pair<int, int>> adj[100000];
pair<int, int> dfs1(int i) {
pair<int, int> res;
queue<pair<int, int>> q;
q.push({i, 0});
while (q.size()) {
auto [i, d] = q.front();
q.pop();
res = max(res, {d, i});
vis[i] = 1;
for (auto [j, t] : adj[i]) {
if (vis[j] == 1) continue;
q.push({j, d + t});
}
}
return res;
}
pair<int, int> par[100000];
Component dfs2(int i) {
int diameter = 0;
vector<int> diameter_ends = {i};
par[i] = {i, 0};
queue<pair<int, int>> q;
q.push({i, 0});
while (q.size()) {
auto [i, d] = q.front();
q.pop();
if (d > diameter) {
diameter = d;
diameter_ends = {i};
} else if (d == diameter) diameter_ends.pb(i);
vis[i] = 2;
for (auto [j, t] : adj[i]) {
if (vis[j] == 2) continue;
par[j] = {i, t};
q.push({j, d + t});
}
}
int longest = 2000000000;
for (int i : diameter_ends) {
int d = 0;
for (; i != par[i].f; d += par[i].s, i = par[i].f) longest = min(longest, max(d, diameter - d));
longest = min(longest, max(d, diameter - d));
}
return Component(diameter, longest);
}
int travelTime(int n, int m, int l, int a[], int b[], int t[]) {
fo(i, 0, m) {
adj[a[i]].pb({b[i], t[i]});
adj[b[i]].pb({a[i], t[i]});
}
vector<Component> comps;
fo(i, 0, n) if (!vis[i]) {
comps.pb(dfs2(dfs1(i).s));
}
sort(be(comps), [](Component &a, Component &b) { return a.longest < b.longest; });
Component res = comps.back();
comps.pop_back();
for (Component i : comps) {
res.diameter = max(max(res.diameter, i.diameter), res.longest + l + i.longest);
res.longest = max(res.longest, i.longest + l);
}
return res.diameter;
}
