#include <bits/stdc++.h>
#include "dreaming.h"
using namespace std;
const int MAX_N = 1e5 + 5;
vector<vector<pair<int, int>>> g(MAX_N);
vector<vector<pair<int, int>>> tree(MAX_N);
vector<int> par(MAX_N);
bitset<MAX_N> vis;
pair<int, int> best_way = {-1, -1};
void find_diam(const vector<vector<pair<int, int>>>& graph, int node, int p, int w) {
par[node] = p;
vis[node] = 1;
best_way = max(best_way, {w, node});
for (auto [to, cost] : graph[node]) {
if (to != p) {
find_diam(graph, to, node, w + cost);
}
}
}
vector<int> dp_down(MAX_N);
vector<int> dp_up(MAX_N);
int calc_down(const vector<vector<pair<int, int>>>& graph, int node, int p) {
for (auto [to, cost] : graph[node]) {
if (to != p) {
dp_down[node] = max(dp_down[node], calc_down(graph, to, node) + cost);
}
}
return dp_down[node];
}
void calc_up(const vector<vector<pair<int, int>>>& graph, int node, int p) {
int best = -1, second_best = -1;
for (auto [to, cost] : graph[node]) {
if (to != p) {
const int w = dp_down[to] + cost;
if (w > best) {
swap(best, second_best);
best = w;
} else {
second_best = max(second_best, w);
}
}
}
for (auto [to, cost] : graph[node]) {
if (to != p) {
const int w = dp_down[to] + cost;
dp_up[to] = max({dp_up[to], cost + dp_up[node], cost + (w == best ? second_best : best)});
calc_up(graph, to, node);
}
}
}
pair<int, int> opt = {2e9, 2e9};
void find_optimal(const vector<vector<pair<int, int>>>& graph, int node, int p) {
opt = min(opt, { max(dp_down[node], dp_up[node]), node } );
//~ cout << node << ' ' << dp_down[node] << ' ' << dp_up[node] << '\n';
for (auto [to, cost] : graph[node]) {
if (to != p) {
find_optimal(graph, to, node);
}
}
//~ return mn;
}
tuple<int, int, int> find_center(const vector<vector<pair<int, int>>>& graph, int node) {
best_way = {-1, -1};
find_diam(graph, node, -1, 0);
int L = best_way.second;
best_way = {-1, -1};
find_diam(graph, L, -1, 0);
int longest_path = best_way.first;
calc_down(graph, node, -1);
calc_up(graph, node, -1);
opt = {2e9, 2e9};
find_optimal(graph, node, -1);
//~ cout << opt.second << ' ' << longest_path << '\n';
return make_tuple(opt.first, opt.second, longest_path);
}
int travelTime(int N, int M, int L, int A[], int B[], int T[]) {
for (int i = 0; i < M; i++) {
//~ cout << A[i] << ' ' << B[i] << ' ' << T[i] << '\n';
g[A[i]].emplace_back(B[i], T[i]);
g[B[i]].emplace_back(A[i], T[i]);
tree[A[i]].emplace_back(B[i], T[i]);
tree[B[i]].emplace_back(A[i], T[i]);
}
int nxt = -1;
vector<tuple<int, int, int>> best;
for (int i = 0; i < N; i++) {
if (!vis[i]) {
best.emplace_back(find_center(g, i));
//~ auto w = ;
//~ if (nxt != -1) {
//~ cout << nxt << ' ' << w.first << '\n';
//~ tree[nxt].emplace_back(w.first, L);
//~ tree[w.first].emplace_back(nxt, L);
//~ }
//~ nxt = w.first;
//~ return 0;
}
}
sort(best.begin(), best.end(), [&](auto a, auto b) {
return get<0>(a) < get<0>(b);
});
const int root = get<1>(best.back());
for (int i = 0; i < (int) best.size() - 1; i++) {
//~ cout << get<1>(best[i - 1]) << ' ' << get<1>(best[i]) << '\n';
tree[ get<1>(best[i]) ].emplace_back( root , L);
tree[ root ].emplace_back( get<1>(best[i]), L);
}
return get<2>(find_center(tree, 0));
}
