Practice Building A Minimum Cost Spanning Tree (2.5) - Minimum Cost Spanning Trees

Practice: Building a Minimum Cost Spanning Tree

Lesson 2.5Minimum Cost Spanning Trees

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is a spanning tree?
Show hintHide hint
Think about how trees connect branches.
Question 2.
Name one application of Minimum Cost Spanning Trees.
Show hintHide hint
Consider situations that involve connectivity.
3Question 3.
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.
Show hintHide hint
Recall the definition of a spanning tree.
4Question 4.
Prim's algorithm builds an MST by:
- Connecting random edges.
- Adding edges in descending order of cost.
- Expanding from the smallest edge incrementally.
Show hintHide hint
Think about the strategy of growth in this algorithm.
Question 5.
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.
Show hintHide hint
Visualize the graph as you proceed to understand better.
Question 6.
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.
Show hintHide hint
Ensure to account for cost efficiency in your scenario.

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