What is the time complexity of BFS in a graph with V vertices and E edges?

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Question: What is the time complexity of BFS in a graph with V vertices and E edges?

Options:

Correct Answer: O(V + E)

Solution:

The time complexity of BFS is O(V + E), where V is the number of vertices and E is the number of edges in the graph.

What is the time complexity of BFS in a graph with V vertices and E edges?

What is the time complexity of BFS in a graph with V vertices and E edges?

Step 1: Understand that BFS stands for Breadth-First Search, which is a way to explore a graph.
Step 2: Identify that a graph consists of vertices (points) and edges (connections between points).
Step 3: Realize that in BFS, we visit each vertex and each edge to explore the graph.
Step 4: Note that visiting each vertex takes O(V) time, where V is the number of vertices.
Step 5: Understand that traversing each edge takes O(E) time, where E is the number of edges.
Step 6: Combine the time taken to visit all vertices and edges, which gives us O(V + E).
Step 7: Conclude that the overall time complexity of BFS is O(V + E).

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