20.2. Recap of the Naive Algorithm

Try these first

1. 1.

   What is the time complexity of the naive algorithm for computing transitive closure?

   Hint

   Think about the number of operations in relation to the size of the input set.

2. 2.

   Define transitive closure in your own words.

   Hint

   Consider how paths connect nodes.

3. 3.

   What is the time complexity of Warshall's algorithm?

   • O(n)
   • O(n^2)
   • O(n^3)
   • O(n^4)

   Hint

   Consider how many layers of iterations it incorporates.

4. 4.

   True or False: The naive algorithm can find all connections in a sparse graph efficiently.

   • True
   • False

   Hint

   Think about the relation to connectivity in dense vs. sparse.

5. 5.

   Given a graph with nodes A, B, C, D, represent it using a connectivity matrix. Apply Warshall's algorithm step-by-step.

   Hint

   Begin with direct connections then add nodes incrementally.

6. 6.

   Discuss the implications of using Warshall’s algorithm over other graph algorithms. When might it be preferred?

   Hint

   Reflect on strengths concerning different graph characteristics.