Practice Warshall's Algorithm And Transitive Closure (1.10)

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6 sample questions

Question 1.
What is Warshall's Algorithm used for?
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Think about connectivity between vertices.
Question 2.
What is the typical initial state of an adjacency matrix?
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Consider how edges are represented.
3Question 3.
What does Warshall's Algorithm compute?
- Shortest paths
- Transitive Closure
- Graph coloring
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Think about how reachability is defined.
4Question 4.
True or False: Floyd-Warshall's algorithm can handle graphs with negative cycles.
- True
- False
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Consider the implications of a negative cycle.
Question 5.
Given a directed graph with weights, apply the Floyd-Warshall algorithm to find all pairs shortest paths. Write down each step leading to the final matrix.
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Keep track of how weights update as you consider intermediate vertices.
Question 6.
Construct an example with a negative cycle and demonstrate what happens when using Floyd-Warshall.
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Think about what happens if a path gets shorter with each iteration through the cycle.

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