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What is the time complexity of finding the shortest path in an unweighted graph

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Question: What is the time complexity of finding the shortest path in an unweighted graph using BFS?

Options:

  1. O(n)
  2. O(n^2)
  3. O(m + n)
  4. O(log n)

Correct Answer: O(m + n)

Solution: 

Breadth-first search (BFS) explores all vertices and edges, resulting in a time complexity of O(m + n), where m is the number of edges and n is the number of vertices.

What is the time complexity of finding the shortest path in an unweighted graph

Practice Questions

Q1
What is the time complexity of finding the shortest path in an unweighted graph using BFS?
  1. O(n)
  2. O(n^2)
  3. O(m + n)
  4. O(log n)

Questions & Step-by-Step Solutions

What is the time complexity of finding the shortest path in an unweighted graph using BFS?
  • Step 1: Understand what BFS (Breadth-First Search) is. It is an algorithm used to explore nodes and edges in a graph.
  • Step 2: Identify the components of a graph: 'n' represents the number of vertices (or nodes) and 'm' represents the number of edges (connections between nodes).
  • Step 3: Realize that BFS visits each vertex once and checks each edge once to explore the graph.
  • Step 4: Calculate the total time taken by BFS. Since it visits all 'n' vertices and checks all 'm' edges, the total time complexity is O(m + n).
  • Step 5: Conclude that the time complexity of finding the shortest path in an unweighted graph using BFS is O(m + n).
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