What is the time complexity of a breadth-first search (BFS) on a graph with V ve

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Question: What is the time complexity of a breadth-first search (BFS) on a graph with V vertices and E edges?

Options:

Correct Answer: O(V + E)

Solution:

BFS visits each vertex and edge once, leading to a time complexity of O(V + E).

What is the time complexity of a breadth-first search (BFS) on a graph with V vertices and E edges?

What is the time complexity of a breadth-first search (BFS) on a graph with V vertices and E edges?

Step 1: Understand that a graph consists of vertices (V) and edges (E).
Step 2: Recognize that in a breadth-first search (BFS), we explore all the vertices and edges connected to the starting vertex.
Step 3: Note that during BFS, each vertex is visited once.
Step 4: Also note that each edge is considered once when exploring the vertices.
Step 5: Combine the visits: since we visit each vertex (V) and each edge (E) once, the total work done is proportional to V + E.
Step 6: Therefore, the time complexity of BFS is expressed as O(V + E).

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