#include <bits/stdc++.h>
#include "grader.h"
using namespace std;
vector<int> adj[513];
vector<int> dfs_order;
// Standard DFS to get a connected ordering
void dfs(int u, int p) {
dfs_order.push_back(u);
for (int v : adj[u]) {
if (v != p) {
dfs(v, u);
}
}
}
int findEgg(int N, vector<pair<int, int>> bridges) {
// 1. Reset/Clear for multiple test cases
for (int i = 1; i <= N; i++) adj[i].clear();
dfs_order.clear();
// 2. Build adjacency list
for (auto edge : bridges) {
adj[edge.first].push_back(edge.second);
adj[edge.second].push_back(edge.first);
}
// 3. Generate the connected sequence
dfs(1, 0);
// 4. Binary Search on the DFS order
int low = 0, high = N - 1;
int ans = dfs_order[0];
while (low <= high) {
int mid = low + (high - low) / 2;
// Construct the query set: a prefix of the DFS order (always connected)
vector<int> query_set;
for (int i = 0; i <= mid; i++) {
query_set.push_back(dfs_order[i]);
}
if (query(query_set)) {
ans = dfs_order[mid]; // The egg is within this prefix.
high = mid - 1;
} else {
low = mid + 1; // The egg is further down the DFS order
}
}
return ans;
}
