20.3.6. Complexity Analysis of BFS

Try these first

1. 1.

   What does BFS stand for?

   Hint

   Remember the first part of the name!

2. 2.

   Name one way to represent a graph.

   Hint

   Think about how we discussed graphs in class.

3. 3.

   What is the time complexity of BFS using an adjacency list?

   • O(n)
   • O(n + m)
   • O(n²)

   Hint

   Think about the connections in sparse graphs.

4. 4.

   True or False: BFS can only find the shortest path in weighted graphs.

   • True
   • False

   Hint

   Consider the nature of BFS's exploration.

5. 5.

   You have a graph with 10 vertices and the edges {(1,2), (2,3), (3,4), (4,5), (1,6), (6,7), (6,8), (5,9)}. Describe the BFS traversal starting from vertex 1.

   Hint

   Keep track of the levels while traversing!

6. 6.

   Given an example of both an adjacency matrix and list for the edges mentioned above, calculate the time complexity of BFS for both representations.

   Hint

   Make sure to consider the number of edges and how they relate.