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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the time complexity of 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 once to see which vertices are connected.
  • Step 5: Combine the visits: since we visit each vertex (V) and each edge (E) once, we add them together.
  • Step 6: This gives us the total time complexity of BFS as O(V + E).
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