Connect cities

#include <iostream>
#include <vector>

using namespace std;

void depth_search(int start, vector<bool> &visited, vector<vector<int>> &cities) {
    if (visited[start]) return;
    visited[start] = true;
    for (auto next : cities[start]) {
        depth_search(next, visited, cities);
    }
}

int all_visited(vector<bool> &visited, int n) {
    for (int i = 0; i < n; i++) {
        if (!visited[i]) {
            return i;
        }
    }
    return n+1;
}

int main() {
    int n, m;
    cin >> n >> m;

    vector<vector<int>> cities(n);

    for (int i = 0; i < m; i++) {
        int r1, r2;
        cin >> r1 >> r2;
        cities[r1-1].push_back(r2-1);
        cities[r2-1].push_back(r1-1);
    }
    
    vector<bool> visited(n, false);
    depth_search(0, visited, cities);

    int non_visited = all_visited(visited, n);
    while (non_visited != n+1) {
        cities[0].push_back(non_visited);
        cities[non_visited].push_back(0);
        cout << 1 << " " << non_visited+1;
        depth_search(0, visited, cities);
    }

    return 0;
}

Test 1

Verdict: TIME LIMIT EXCEEDED

Test 2

Verdict: TIME LIMIT EXCEEDED

Test 3

Verdict: WRONG ANSWER

Test 4

Verdict: TIME LIMIT EXCEEDED

Test 5

Verdict: WRONG ANSWER

Test 6

Verdict: TIME LIMIT EXCEEDED

Test 7

Verdict: TIME LIMIT EXCEEDED

Test 8

Verdict: TIME LIMIT EXCEEDED

Test 9

Verdict: TIME LIMIT EXCEEDED

Test 10

Verdict: TIME LIMIT EXCEEDED

Test 11

Verdict: TIME LIMIT EXCEEDED

Test 12

Verdict: TIME LIMIT EXCEEDED