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What is the time complexity of BFS in terms of the number of vertices V and edge

Practice Questions

Q1
What is the time complexity of BFS in terms of the number of vertices V and edges E?
  1. O(V + E)
  2. O(V^2)
  3. O(E log V)
  4. O(V log V)

Questions & Step-by-Step Solutions

What is the time complexity of BFS in terms of the number of vertices V and edges E?
  • Step 1: Understand that BFS stands for Breadth-First Search, which is a way to explore graphs or trees.
  • Step 2: Identify that in a graph, there are two main components: vertices (V) and edges (E).
  • Step 3: Realize that BFS starts at a specific vertex and explores all its neighbors before moving to the next level of vertices.
  • Step 4: Note that during the BFS process, each vertex is visited once.
  • Step 5: Also, each edge is considered once when exploring the neighbors of a vertex.
  • Step 6: Combine the visits: since we visit each vertex (V) and each edge (E) once, the total time taken is proportional to V + E.
  • Step 7: Conclude that the time complexity of BFS is O(V + E).
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