Practice Union and Find Operations - 6.2 | 6. Union-Find Data Structure | Design & Analysis of Algorithms - Vol 2
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6.2 - Union and Find Operations

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What are the two primary operations of the Union-Find data structure?

💡 Hint: Think about what these operations do to a set.

Question 2

Easy

What is the worst-case time complexity for the naive union operation?

💡 Hint: Consider the number of elements you may have to visit in a union operation.

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 does the find operation in the Union-Find structure do?

  • Merges two components
  • Determines the component an element belongs to
  • Creates a new set

💡 Hint: Think about the purpose of checking components.

Question 2

True or False: The union by size technique merges the larger tree into the smaller tree.

  • True
  • False

💡 Hint: Consider what it means for trees to be balanced.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a set of cities represented as nodes and roads as edges connecting them, explain how you would implement a Union-Find structure to detect cycles when planning a new road network.

💡 Hint: Consider the implications of connecting components when checking for cycles.

Question 2

Implement a Union-Find algorithm with path compression and union by size. Analyze its complexity over a series of operations.

💡 Hint: Look at how merging impacts future operations and their costs.

Challenge and get performance evaluation