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What is the time complexity of performing a breadth-first search (BFS) on a grap

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

Options:

  1. O(V)
  2. O(E)
  3. O(V + E)
  4. O(V * E)

Correct Answer: O(V + E)

Solution: 

The time complexity of performing a breadth-first search (BFS) on a graph is O(V + E), where V is the number of vertices and E is the number of edges.

What is the time complexity of performing a breadth-first search (BFS) on a grap

Practice Questions

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

Questions & Step-by-Step Solutions

What is the time complexity of performing a breadth-first search (BFS) on a graph?
  • Step 1: Understand what BFS is. BFS is a way to explore all the nodes (or vertices) in a graph level by level.
  • Step 2: Identify the components of a graph. A graph consists of vertices (V) and edges (E). Vertices are the points, and edges are the connections between them.
  • Step 3: Realize that during BFS, each vertex is visited once. This means we will look at all V vertices.
  • Step 4: Understand that for each vertex, we may need to look at all its edges to find connected vertices. This means we will also consider all E edges.
  • Step 5: Combine the two parts. Since we visit each vertex and check each edge, the total time taken is proportional to the number of vertices plus the number of edges.
  • Step 6: Write the final time complexity. The time complexity of BFS is O(V + E).
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