28.1.2. Department of Computer Science and Engineering

Try these first

1. 1.

   What is the primary purpose of the Bellman-Ford algorithm?

   Hint

   Consider the situations where Dijkstra's algorithm fails.

2. 2.

   Define negative cycles in the context of graphs.

   Hint

   Think of paths that can reduce distance continuously.

3. 3.

   What is the main restriction of the Bellman-Ford algorithm?

   • Allows negative cycles
   • Requires positive edges only
   • Allows negative edges but not cycles
   • None of the above

   Hint

   Review the importance of negative cycles in graphs.

4. 4.

   True or False? The Dijkstra's algorithm can be applied to graphs with negative weights.

   • True
   • False

   Hint

   Think about the assumptions each algorithm makes.

5. 5.

   Given a graph with vertices and edges including both negative and positive weights, illustrate the processes of the Bellman-Ford algorithm showing each iteration's distance updates until stabilization.

   Hint

   Be methodical and label each vertex clearly to track distances.

6. 6.

   Consider a graph that includes a negative cycle. Describe how Bellman-Ford would behave and the ultimate impact this has on finding the shortest paths.

   Hint

   Reflect on the definition of shortest paths in relation to negative cycles.