Practice Complexity Analysis Of Floyd-warshall Algorithm (1.7) - All-pairs Shortest Paths

Practice: Complexity Analysis of Floyd-Warshall Algorithm

Lesson 1.7All-pairs Shortest Paths

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9 questions

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6 sample questions

Question 1.
What does the Floyd-Warshall algorithm compute?
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Think about what problems you can solve with pathfinding.
Question 2.
Can the Floyd-Warshall algorithm handle negative weights?
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Consider the implications of negative cycles on pathfinding.
3Question 3.
What is the primary purpose of the Floyd-Warshall algorithm?
- Find minimum spanning tree
- Compute shortest paths between all pairs
- Sort the vertices
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Recall what this algorithm is designed for in the context of graphs.
4Question 4.
True or False: The Floyd-Warshall algorithm can handle graphs with negative weights.
- True
- False
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Think about the rules concerning weights in graphs.
Question 5.
Create a weighted graph with at least 5 vertices containing both negative and positive weights. Apply the Floyd-Warshall algorithm to find the shortest paths and discuss the results.
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Make sure to include the edges and their weights clearly.
Question 6.
Analyze a scenario where the Floyd-Warshall fails due to a negative cycle present in the graph. Explain the consequences.
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Reflect on what a negative cycle does to pathweight over cycles.

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