Practice Challenges With Arbitrary Graphs (25.1.11)

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10 questions

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6 sample questions

Question 1.
Define a Directed Acyclic Graph (DAG).
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Think about the property of cycles in graphs.
Question 2.
What does topological sorting achieve?
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Consider how tasks might depend on one another.
3Question 3.
What is the primary characteristic of a Directed Acyclic Graph?
- It has cycles
- It has no cycles
- It can be undirected
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Recall the definition of a DAG.
4Question 4.
Is it NP-hard to find the longest path in arbitrary graphs?
- True
- False
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Think about the implications of cycles.
Question 5.
Given a directed acyclic graph of 5 vertices and the following edges: (1,2), (1,3), (2,4), (3,4), (4,5). Calculate the longest path and describe how you computed it.
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Draw the graph to visualize all potential paths.
Question 6.
An arbitrary graph includes cycles: If a vertex connects back to itself multiple times, how would you begin to analyze the longest path?
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Think about how to handle vertices that lead back to previous nodes.

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