Practice Spanning Trees - 2.2 | 2. Minimum Cost Spanning Trees | Design & Analysis of Algorithms - Vol 2
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2.2 - Spanning Trees

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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 what it means to connect all points without returning to the same point.

Question 2

Easy

How many edges does a spanning tree with n vertices have?

💡 Hint: Relate it to the number of vertices.

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

What is the definition of a spanning tree?

  • A cycle in a graph
  • A connected
  • acyclic graph covering all vertices
  • A disconnected graph

💡 Hint: Consider the properties of trees in graph theory.

Question 2

True or False: A minimum spanning tree for a graph can have cycles.

  • True
  • False

💡 Hint: Think about the definition of a tree.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a complete graph with 5 nodes and the following edge weights: (A-B: 2, A-C: 3, A-D: 1, A-E: 4, B-C: 5, B-D: 3, B-E: 2, C-D: 4, C-E: 1, D-E: 6), find the minimum spanning tree and compute its total weight.

💡 Hint: Look for the smallest edges that keep the tree connected.

Question 2

Design a road restoration plan for a small town affected by a natural disaster. You have the costs of repairing each road between towns. Describe how you would apply Prim's or Kruskal's algorithm.

💡 Hint: Outline the costs and visualize the connections before applying the algorithm.

Challenge and get performance evaluation