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

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

Step 1: Understand that BFS 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 during BFS, we visit each vertex to explore it.
Step 4: Note that we also look at each edge to see which vertices are connected.
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: Understand that BFS will visit each vertex once and each edge once.
Step 8: Combine the visits: the total time taken is proportional to the number of vertices plus the number of edges.
Step 9: Conclude that the time complexity of BFS is O(V + E).

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