What is the time complexity of BFS in terms of the number of vertices V and edge

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Question: What is the time complexity of BFS in terms of the number of vertices V and edges E?

Options:

Correct Answer: O(V + E)

Solution:

The time complexity of BFS is O(V + E) because it visits each vertex and edge once.

What is the time complexity of BFS in terms of the number of vertices V and edges E?

What is the time complexity of BFS in terms of the number of vertices V and edges E?

Step 1: Understand that BFS stands for Breadth-First Search, which is a way to explore graphs or trees.
Step 2: Identify that in a graph, there are two main components: vertices (V) and edges (E).
Step 3: Realize that BFS starts at a specific vertex and explores all its neighbors before moving to the next level of vertices.
Step 4: Note that during the BFS process, each vertex is visited once.
Step 5: Also, each edge is considered once when exploring the neighbors of a vertex.
Step 6: Combine the visits: since we visit each vertex (V) and each edge (E) once, the total time taken is proportional to V + E.
Step 7: Conclude that the time complexity of BFS is O(V + E).

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