1.6. Example to Illustrate Floyd-Warshall Algorithm

Try these first

1. 1.

   What does the Floyd-Warshall algorithm compute?

   Hint

   Think about which pairs are considered.

2. 2.

   What happens when there are negative cycles in a graph?

   Hint

   Consider the implications of getting lower costs.

3. 3.

   What is the primary function of the Floyd-Warshall algorithm?

   • Find minimum spanning tree
   • Find all pairs shortest paths
   • Find Eulerian path

   Hint

   Consider what kind of paths it is typically applied to.

4. 4.

   True or False: The Floyd-Warshall algorithm can handle negative edge weights.

   • True
   • False

   Hint

   Think about the types of weights involved in various edges.

5. 5.

   Given a directed graph with the following edges: A -> B (weight 2), B -> C (weight 3), A -> C (weight 5), C -> B (weight -4). Determine the shortest paths between all pairs using the Floyd-Warshall algorithm.

   Hint

   Visualize the graph and iteratively apply the Floyd-Warshall updates.

6. 6.

   Explain how the Floyd-Warshall algorithm can identify graphs with negative cycles, and outline an approach to modify the algorithm for cycle detection.

   Hint

   Think about how paths get calculated and where each vertex sits in their transitions.