#include "dreaming.h"
#include <bits/stdc++.h>
using namespace std;
int n;
const int N = 1e5+5;
bool used[N];
vector<pair<int, int>> edges[N];
// dfs for calculating maximum depth. (V[i] - distance from the root)
int mx, mxind;
vector<int> vertex;
void dfs(int u, int p, int dist, vector<int> &V, bool flag = 0){
used[u] = true;
if(flag)vertex.push_back(u);
V[u] = dist;
if(dist > mx){
mx = dist;
mxind = u;
}
for(auto X : edges[u]){
int v = X.first;
int cost = X.second;
if(v == p)continue;
dfs(v, u, dist + cost, V, flag);
}
}
//calculate best center for the tree
int max_diameter;
int calculate_center(int u){
vertex.clear();
mx = -1;
vector<int> no_need(n);
dfs(u, u, 0, no_need, 1);
mx = -1;
int ind1 = mxind;
vector<int> a(n);
dfs(ind1, ind1, 0, a);
int ind2 = mxind;
vector<int> b(n);
dfs(ind2, ind2, 0, b);
max_diameter = max(max_diameter, mx);
int mn = INT_MAX;
for(auto x : vertex){
mn = min(mn, max(a[x], b[x]));
}return mn;
}
int travelTime(int _N, int M, int L, int A[], int B[], int T[]) {
n = _N;
for(int i=0;i<M;i++){
edges[A[i]].push_back({B[i], T[i]});
edges[B[i]].push_back({A[i], T[i]});
}
vector<int> v;
for(int i=0;i<n;i++){
if(!used[i]){
v.push_back(calculate_center(i));
}
}
sort(v.begin(), v.end());
reverse(v.begin(), v.end());
if(v.size() == 1){
return max_diameter;
}else {
return max(max(max_diameter, v[0]+v[1]+L), ((v.size() > 2)? v[1]+v[2]+L*2 : 0));
}
}
/*
12 8 2
0 8 4
8 2 2
2 7 4
5 11 3
5 1 7
1 3 1
1 9 5
10 6 3
*/
