Practice Space Complexity Considerations - 1.8 | 1. All-pairs Shortest Paths | Design & Analysis of Algorithms - Vol 2
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Space Complexity Considerations

1.8 - Space Complexity Considerations

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does the Floyd-Warshall algorithm compute?

💡 Hint: Think about what you want to find in the graph.

Question 2 Easy

Does the Floyd-Warshall algorithm work with negative edge weights?

💡 Hint: Consider what negative cycles do to path calculations.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the time complexity of the Floyd-Warshall algorithm?

O(n)
O(n²)
O(n³)

💡 Hint: Think about how many vertices are involved in the updates.

Question 2

True or False: The Floyd-Warshall algorithm can handle graphs with negative cycles.

True
False

💡 Hint: Remember that negative cycles alter path finding.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a directed graph with vertices A, B, C, and D. The edges are as follows: A to B (3), A to C (5), B to D (2), and C to D (1). Compute the shortest paths between all pairs using the Floyd-Warshall method.

💡 Hint: Use the initial weight matrix to track distances through each step.

Challenge 2 Hard

Design an example graph that contains a negative cycle. Explain why the Floyd-Warshall algorithm cannot provide a valid solution for this graph.

💡 Hint: Focus on how negative edge weights contribute to cycles when combined.

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