Practice Building a Minimum Cost Spanning Tree - 2.5 | 2. Minimum Cost Spanning Trees | Design & Analysis of Algorithms - Vol 2
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Building a Minimum Cost Spanning Tree

2.5 - Building a Minimum Cost Spanning Tree

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a spanning tree?

💡 Hint: Think about how trees connect branches.

Question 2 Easy

Name one application of Minimum Cost Spanning Trees.

💡 Hint: Consider situations that involve connectivity.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which of the following statements is true regarding Minimum Cost Spanning Trees?

Every spanning tree has cycles.
A Minimum Cost Spanning Tree is the most expensive spanning tree.
A Minimum Cost Spanning Tree connects all vertices without cycles.

💡 Hint: Recall the definition of a spanning tree.

Question 2

Prim's algorithm builds an MST by:

Connecting random edges.
Adding edges in descending order of cost.
Expanding from the smallest edge incrementally.

💡 Hint: Think about the strategy of growth in this algorithm.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a graph with vertices A, B, C, and D having edges AB (weight 5), AC (weight 3), AD (weight 4), BC (weight 2), and BD (weight 1). Find the Minimum Cost Spanning Tree using both Prim’s and Kruskal’s algorithms. Illustrate each step.

💡 Hint: Visualize the graph as you proceed to understand better.

Challenge 2 Hard

Construct a real-world scenario involving travel routes and use Kruskal's algorithm to minimize the costs of travel while ensuring all points are accessible. Illustrate with steps.

💡 Hint: Ensure to account for cost efficiency in your scenario.

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