#include <bits/stdc++.h>
#include "dreaming.h"
using namespace std;
int k = 0, M;
void DFS_sum(int node, int p, vector<int> &sum, vector<vector<int>> &vec, vector<vector<int>> &cost, vector<int> &col)
{
col[node] = k;
for (int i = 0; i < vec[node].size(); i++)
{
if (vec[node][i] == p)
continue;
DFS_sum(vec[node][i], node, sum, vec, cost, col);
sum[node] = max(sum[node], sum[vec[node][i]] + cost[node][i]);
}
}
void DFS_main(int node, int p, int main, int sec, vector<int> &sum, int &ans, vector<vector<int>> &vec, vector<vector<int>> &cost)
{
M = max(M, main + sec);
ans = min(ans, max(main, sec));
if (main == 0)
return;
int nr = 0;
for (int i = 0; i < vec[node].size(); i++)
{
if (vec[node][i] == p)
continue;
int temp = sum[vec[node][i]] + cost[node][i];
if (temp == main && nr == 0)
{
nr++;
continue;
}
if (temp > sec && (temp != main || nr >= 1))
sec = temp;
}
M = max(M, main + sec);
for (int i = 0; i < vec[node].size(); i++)
{
if (vec[node][i] == p)
continue;
int temp = sum[vec[node][i]] + cost[node][i];
if (temp == main)
DFS_main(vec[node][i], node, main - cost[node][i], sec + cost[node][i], sum, ans, vec, cost);
}
}
int trace(int node, int p, int main, vector<int> &sum, vector<vector<int>> &vec, vector<vector<int>> &cost)
{
for (int i = 0; i < vec[node].size(); i++)
{
if (vec[node][i] == p)
continue;
if (sum[vec[node][i]] + cost[node][i] == main)
return trace(vec[node][i], node, main - cost[node][i], sum, vec, cost);
}
return node;
}
pair<int, int> graph_hub(int node, vector<vector<int>> &vec, vector<vector<int>> &cost, vector<int> &col)
{
vector<int> sum(vec.size(), 0);
DFS_sum(node, -1, sum, vec, cost, col);
M = 0;
int MAX = 0, sec = 0;
for (int i = 0; i < vec[node].size(); i++)
{
int temp = sum[vec[node][i]] + cost[node][i];
if (temp > MAX)
{
sec = MAX;
MAX = temp;
}
else
sec = max(sec, temp);
}
int ans = sum[node];
DFS_main(node, -1, MAX, sec, sum, ans, vec, cost);
return make_pair(ans, M);
}
int travelTime(int N, int M, int L, int A[], int B[], int C[])
{
vector<int> col(N, -1);
vector<vector<int>> vec(N), cost(N);
for (int i = 0; i < M; i++)
{
vec[A[i]].push_back(B[i]);
vec[B[i]].push_back(A[i]);
cost[A[i]].push_back(C[i]);
cost[B[i]].push_back(C[i]);
}
if (M == N - 1)
{
vector<int> sum(N, 0);
DFS_sum(0, -1, sum, vec, cost, col);
int colt = trace(0, -1, sum[0], sum, vec, cost);
vector<int> new_sum(vec.size(), 0);
DFS_sum(colt, -1, new_sum, vec, cost, col);
return new_sum[colt];
}
vector<pair<int, int>> hub_l;
for (int i = 0; i < N; i++)
if (col[i] == -1)
{
hub_l.push_back(graph_hub(i, vec, cost, col));
k++;
}
int unos = 0, dos = 0, tres = 0;
for (int i = 0; i < hub_l.size(); i++)
{
int p = hub_l[i].first;
if (p > unos)
{
tres = dos;
dos = unos;
unos = p;
}
else
if (p > dos)
{
tres = dos;
dos = p;
}
else
tres = max(tres, p);
}
int Max = 0;
for (int i = 0; i < hub_l.size(); i++)
Max = max(Max, hub_l[i].second);
if (M == N - 2)
return max(unos + L + dos, Max);
return max(unos + L + dos, max(Max, dos + 2 * L + tres));
}
