Practice Design And Analysis Of Algorithms, Chennai Mathematical Institute (28.1)

Practice: Design and Analysis of Algorithms, Chennai Mathematical Institute

Lesson 28.1Module – 03

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8 questions

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6 sample questions

Question 1.
What does the Bellman-Ford algorithm specifically handle that Dijkstra's does not?
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Think about edge weights in graphs.
Question 2.
True or False: A shortest path can have loops.
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Recall the properties of shortest paths and loops.
3Question 3.
What does the Bellman-Ford algorithm do?
- Finds paths with positive weights only
- Finds shortest paths with negative weights
- Finds all longest paths
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Consider the capabilities of both the Bellman-Ford and Dijkstra’s algorithms.
4Question 4.
True or False: The Bellman-Ford algorithm can handle negative cycles.
- True
- False
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Think about the implications of negative cycles.
Question 5.
In a graph with vertices A, B, C, and D, where edges are weighted A->B(2), B->C(-3), A->C(4), and C->D(1). Determine the shortest path from A to D using the Bellman-Ford algorithm.
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Implement the updates as per Bellman-Ford, observing each iteration's effect.
Question 6.
Create your own graph with at least one negative cycle and explain in detail how it affects the path calculations when running Bellman-Ford.
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Draw the graph out and calculate distances after each iteration to see the cycle's effect.

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