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

2.5 - Building a Minimum Cost Spanning Tree

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

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.

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

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.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation