Connect cities

from collections import deque


def task1(n, roads):
    vis = [False] * n
    graph = [[] for _ in range(n)]

    for a, b in roads:
        graph[b - 1].append(a - 1)  # connect b->a
        graph[a - 1].append(b - 1)  # connect a->b

    subgraphs = []
    for i in range(n):
        if not vis[i]:
            subgraph = bfs(i, graph)  # conectivty check
            subgraphs.append(subgraph)
            for node in subgraph:
                vis[node] = True
    added_roads = []

    for i in range(len(subgraphs) - 1):  # we connect deepest node in each subgrph
        added_roads.append([subgraphs[i][-1] + 1, subgraphs[i + 1][-1] + 1])

    return added_roads


def bfs(start, adj):
    N = len(adj)
    visited = [False] * N
    subgraph = []
    q = deque([start])
    visited[start] = True
    while q:
        node = q.popleft()
        subgraph.append(node)
        for neighbor in adj[node]:
            if not visited[neighbor]:
                visited[neighbor] = True
                q.append(neighbor)

    return subgraph


if __name__ == "__main__":
    n, m = map(int, input().split())
    roads = []
    for i in range(m):
        a, b = map(int, input().split())
        roads.append([a, b])
    added_roads = task1(n, roads)

    print(len(added_roads))
    for road in added_roads:
        print(road[0], road[1])

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

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: ACCEPTED