28.2.4. Characteristics of the Bellman-Ford Algorithm

Try these first

1. 1.

   What does the Bellman-Ford algorithm do?

   Hint

   Think about what you learned regarding path weights.

2. 2.

   What is the significance of detecting negative cycles in graphs?

   Hint

   Consider the implications of endlessly reducing path lengths.

3. 3.

   What does the Bellman-Ford algorithm accommodate that Dijkstra's does not?

   • Only positive weights
   • Negative weights
   • No weights

   Hint

   Recall what types of edge weights each algorithm is suited for.

4. 4.

   True or False: The shortest path in a graph can include negative edge weights as long as there are no negative cycles.

   • True
   • False

   Hint

   Think about the difference between weight types.

5. 5.

   You have a directed graph with vertices A, B, C, and D. The edges are A -> B (weight 2), A -> C (weight -1), B -> D (weight 3), and C -> D (weight 4). Use the Bellman-Ford algorithm to find the shortest paths from A to all other vertices.

   Hint

   Follow through the iterations carefully, check each edge's weight for updates.

6. 6.

   Given a set of weights in a directed graph containing negative edges and no cycles, describe how you would apply the Bellman-Ford algorithm in terms of the expected outcomes of each iteration.

   Hint

   Think about how each vertex assesses potential paths from its neighbors.