Practice Example to Illustrate Floyd-Warshall Algorithm - 1.6 | 1. All-pairs Shortest Paths | Design & Analysis of Algorithms - Vol 2
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1.6 - Example to Illustrate Floyd-Warshall Algorithm

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does the Floyd-Warshall algorithm compute?

💡 Hint: Think about which pairs are considered.

Question 2

Easy

What happens when there are negative cycles in a graph?

💡 Hint: Consider the implications of getting lower costs.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the primary function of the Floyd-Warshall algorithm?

  • Find minimum spanning tree
  • Find all pairs shortest paths
  • Find Eulerian path

💡 Hint: Consider what kind of paths it is typically applied to.

Question 2

True or False: The Floyd-Warshall algorithm can handle negative edge weights.

  • True
  • False

💡 Hint: Think about the types of weights involved in various edges.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a directed graph with the following edges: A -> B (weight 2), B -> C (weight 3), A -> C (weight 5), C -> B (weight -4). Determine the shortest paths between all pairs using the Floyd-Warshall algorithm.

💡 Hint: Visualize the graph and iteratively apply the Floyd-Warshall updates.

Question 2

Explain how the Floyd-Warshall algorithm can identify graphs with negative cycles, and outline an approach to modify the algorithm for cycle detection.

💡 Hint: Think about how paths get calculated and where each vertex sits in their transitions.

Challenge and get performance evaluation