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

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

Options:

Correct Answer: O(V + E)

Solution:

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

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

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

Step 1: Understand that BFS is a way to explore all the nodes (vertices) in a graph.
Step 2: Know that in a graph, there are two main components: vertices (V) and edges (E).
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: Since we visit each vertex once and each edge once, we can add these together.
Step 6: This gives us the total time taken as V (for vertices) + E (for edges).
Step 7: Therefore, the time complexity of BFS is O(V + E).

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