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

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Question: What is the time complexity of a breadth-first search (BFS) on a graph?

Options:

Correct Answer: O(V + E)

Solution:

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

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

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

Step 1: Understand that BFS is a way to explore all the vertices in a graph.
Step 2: Know that a graph consists of vertices (nodes) and edges (connections between nodes).
Step 3: Realize that during BFS, we visit each vertex once.
Step 4: Also, during BFS, we look at each edge that connects the vertices.
Step 5: Count the total number of vertices in the graph as V.
Step 6: Count the total number of edges in the graph as E.
Step 7: Since we visit each vertex and each edge once, we add these counts together.
Step 8: The total time taken for BFS is proportional to the sum of vertices and edges, which is expressed as O(V + E).

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