#include <bits/stdc++.h>
#include "dreaming.h"
using namespace std;
const int MAXN = 1e6 + 5;
vector<vector<pair<int, int>>> adj(MAXN);
vector<int> parent(MAXN, -1); // use parent and distance pointers
vector<int> dist(MAXN, 0); // to construct graph and find radius node
vector<int> color(MAXN, 0);
int max_dist = 0;
int end_node = 0;
void dfs(int u, int c) {
color[u] = c;
if (dist[u] > max_dist) {
max_dist = dist[u];
end_node = u;
}
for (auto [v, w] : adj[u]) {
if (color[v] != c) {
parent[v] = u;
dist[v] = dist[u] + w;
dfs(v, c);
}
}
}
int travelTime(int N, int M, int L, int A[], int B[], int T[]) {
if (N == 1) return 0; // no bridges need
for (int i = 0; i < M; i++) {
adj[A[i]].emplace_back(B[i], T[i]);
adj[B[i]].emplace_back(A[i], T[i]);
}
vector<int> radii;
int max_diameter = 0;
int color_id = 1;
for (int i = 0; i < N; i++) {
if (!color[i]) {
max_dist = -1; //
dist[i] = 0; //
dfs(i, color_id); //
// Double dfs to find diameter
int start = end_node; //
max_dist = -1; //
parent[start] = -1; //
dist[start] = 0; //
dfs(start, color_id + 1); //
int diameter = max_dist;
max_diameter = max(max_diameter, diameter);
int radius = diameter; //
for (int u = end_node; u != -1; u = parent[u]) { // trace back eccentricities: radius = min(all eccentricity values)
radius = min(radius, max(dist[u], diameter - dist[u])); // of connectected compoennts
}
radii.push_back(radius);
color_id += 2;
}
}
sort(radii.rbegin(), radii.rend());
if (radii.size() == 1) {
return max_diameter;
}
if (radii.size() == 2) {
return max(max_diameter, radii[0] + radii[1] + L);
}
return max({max_diameter, radii[0] + radii[1] + L, radii[1] + radii[2] + 2 * L});
}
/*
int main() {
int N = 12;
int M = 8;
int L = 2;
int A[] = {0, 8, 2, 5, 5, 1, 1, 10};
int B[] = {8, 2, 7, 11, 1, 3, 9, 6};
int T[] = {4, 2, 4, 3, 7, 1, 5, 3};
cout << travelTime(N, M, L, A, B, T) << endl;
return 0;
}
*/
