28.1.4. Lecture - 27

Try these first

1. 1.

   What does a negative edge in a graph signify?

   Hint

   Think about how weights affect paths.

2. 2.

   Why is it important to avoid negative cycles?

   Hint

   Consider the impact of looping in paths.

3. 3.

   Which algorithm can handle negative edge weights?

   • A) Dijkstra's Algorithm
   • B) Bellman-Ford Algorithm
   • C) A* Algorithm

   Hint

   Remember which algorithms are designed for certain conditions.

4. 4.

   True or False: A negative cycle guarantees a shortest path.

   • True
   • False

   Hint

   Recap the definition of negative cycles.

5. 5.

   Consider a graph with vertices A, B, C, and D where A connects to B with weight 1, B to C with weight -2, and C to D with weight 2. How do the distances from A to all vertices evolve through the Bellman-Ford algorithm?

   Hint

   Iterate through all edges and update distances accordingly.

6. 6.

   Design a strange graph where negative cycles appear yet ensure Bellman-Ford can’t find them. What is their impact on path calculations?

   Hint

   Use examples of loops to draw a clear distinction.