What is the time complexity of Breadth-First Search (BFS) in a graph with V vert

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Question: What is the time complexity of Breadth-First Search (BFS) in a graph with V vertices and E edges?

Options:

Correct Answer: O(V + E)

Solution:

BFS explores all vertices and edges, leading to a time complexity of O(V + E).

What is the time complexity of Breadth-First Search (BFS) in a graph with V vertices and E edges?

What is the time complexity of Breadth-First Search (BFS) in a graph with V vertices and E edges?

Step 1: Understand that BFS is an algorithm used to explore all the vertices and edges in a graph.
Step 2: Identify that a graph has 'V' vertices (points) and 'E' edges (connections between points).
Step 3: Realize that during BFS, each vertex is visited once, which contributes to the 'O(V)' part of the time complexity.
Step 4: Note that BFS also examines each edge to find connected vertices, contributing to the 'O(E)' part of the time complexity.
Step 5: Combine the contributions from vertices and edges to conclude that the total time complexity of BFS is O(V + E).

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