Practice Checking for Cycles - 5.3.1 | 5. Kruskal's Algorithm | Design & Analysis of Algorithms - Vol 2
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5.3.1 - Checking for Cycles

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is a minimum cost spanning tree?

💡 Hint: Think about the total weights of connecting all nodes.

Question 2

Easy

What does Kruskal's algorithm start with?

💡 Hint: Consider the importance of edge weights in the algorithm.

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 first step in Kruskal's algorithm?

  • Add edges to the spanning tree
  • Sort all edges by weight
  • Check for cycles

💡 Hint: Remember the order of operations in Kruskal's algorithm.

Question 2

True or False: Kruskal's algorithm can result in cycles in the spanning tree.

  • True
  • False

💡 Hint: Think about how the algorithm maintains tree properties.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a weighted graph with the following edges and weights: { (A, B, 1), (B, C, 2), (A, C, 3), (C, D, 4) }, apply Kruskal's algorithm to determine the minimum spanning tree and calculate its total weight.

💡 Hint: Start by sorting edges based on their weights.

Question 2

Consider a graph where there are 6 vertices and 7 edges. If you apply Kruskal's algorithm, what is the maximum number of edges you can add to the spanning tree without creating a cycle?

💡 Hint: Recall the property of trees regarding edges and vertices.

Challenge and get performance evaluation