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

Practice Questions

Q1
What is the time complexity of a breadth-first search (BFS) in a graph?
  1. O(V)
  2. O(E)
  3. O(V + E)
  4. O(V^2)

Questions & Step-by-Step Solutions

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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