Practice Unique Path Property (2.4.3) - Minimum Cost Spanning Trees - Design & Analysis of Algorithms - Vol 2

Practice: Unique Path Property

Lesson 2.4.3Minimum Cost Spanning Trees

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9 questions

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4 cards from this section. Quick, good the night before a test.
Exercise
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is a Minimum Cost Spanning Tree?
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Think about how these trees are formed and what they contain.
Question 2.
How many edges does a tree with n vertices contain?
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Consider how removing an edge impacts the connectivity of a tree.
3Question 3.
What is the primary objective of a Minimum Cost Spanning Tree?
- To connect all vertices with the fewest edges
- To minimize the total edge weight
- To create a cycle
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Think about the keyword 'minimum' in the context of costs.
4Question 4.
True or False: A spanning tree can have cycles.
- True
- False
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Consider the properties that define a tree.
Question 5.
Given a graph with vertices A, B, C, and D and edges (A-B, 3), (A-C, 4), (B-D, 5), (C-D, 1), determine the Minimum Cost Spanning Tree and justify your edges.
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Consider the edge weights carefully before selecting.
Question 6.
Construct an acyclic graph with 8 vertices and demonstrate the unique path property between any two vertices.
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Draw out the graph and label the paths clearly.

5 more questions in this section. Enroll free to practise them all.