BFS Traversal in a Graph

Given an undirected and disconnected graph G(V, E) where V vertices are numbered from 0 to V-1, and E represents edges, your task is to output the BFS traversal starting from the 0th vertex.

Explanation:

BFS, or Breadth-First Traversal, is an algorithm for visiting all nodes of a graph by exploring neighbor nodes first before moving to the next level neighbors. An undirected graph means each edge is bidirectional. In a disconnected graph, not all pairs of vertices have paths connecting them.

Input:

V E Edge1A Edge1B ... EdgeEA EdgeEB

Output:

BFS Traversal for each test case in a separate line.

Example:

Consider this graph:

Starting from vertex 0, BFS traverses nodes 1 and 2 directly connected to 0. Thus, the traversal sequence becomes [0, 1, 2]. Since vertex 2 is connected to 3, the sequence extends to [0, 1, 2, 3].

Constraints:

0 ≤ V ≤ 10^4

0 ≤ E ≤ (V * (V - 1)) / 2

0 ≤ A ≤ V - 1

0 ≤ B ≤ V - 1

Note:

Ensure the BFS path starts from vertex 0. In a situation where node-order matters, connected nodes are printed in numerical sort order.

Question

BFS Traversal in a Graph

Given an undirected and disconnected graph G(V, E) where V vertices are numbered from 0 to V-1, and E represents edges, your task is to output the BFS traversal starting from the 0th vertex.

Explanation:

BFS, or Breadth-First Traversal, is an algorithm for visiting all nodes of a graph by exploring neighbor nodes first before moving to the next level neighbors. An undirected graph means each edge is bidirectional. In a disconnected graph, not all pairs of vertices have paths connecting them.

Input:

V  E
Edge1A  Edge1B
...
EdgeEA  EdgeEB

Output:

BFS Traversal for each test case in a separate line.

Example:

Consider this graph:

Starting from vertex 0, BFS traverses nodes 1 and 2 directly connected to 0. Thus, the traversal sequence becomes [0, 1, 2]. Since vertex 2 is connected to 3, the sequence extends to [0, 1, 2, 3].

Constraints:

0 ≤ V ≤ 10^4
0 ≤ E ≤ (V * (V - 1)) / 2
0 ≤ A ≤ V - 1
0 ≤ B ≤ V - 1

Note:

Ensure the BFS path starts from vertex 0. In a situation where node-order matters, connected nodes are printed in numerical sort order.

Accepted Answer

BFS traversal of an undirected and disconnected graph starting from vertex 0.

Implement BFS algorithm to traverse the graph starting from vertex 0.
Use a queue to keep track of visited nodes and their neighbors.
Ensure the traversal starts from vertex 0 and follows the BFS order.
Output the BFS traversal sequence for each test case in a separate line.
Handle disconnected components by checking for unvisited nodes.
Consider the constraints for the number of vertices and edges in the graph.
Print connected nodes in numerical sort order if node-order matters.