Practice Improving Union Operations (6.7) - Union-Find Data Structure - Design & Analysis of Algorithms

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9 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What are the two main operations of the Union-Find data structure?
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Think about the operations that help in managing components.
Question 2.
How does the find operation work?
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It queries the component label.
3Question 3.
What is the main challenge with basic union operations?
- They take constant time
- They require scanning all elements
- They merge components instantly
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Think about what happens during a merge.
4Question 4.
Amortized complexity refers to:
- True
- False
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Consider how operations accumulate cost over time.
Question 5.
You have 1,000 elements and perform 750 union operations. Analyze how union-find could handle this efficiently.
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Focus on the efficiency that comes with clever data structuring.
Question 6.
Assuming a scenario where you frequently merge small components into a large one, explain how that impacts time complexity.
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Consider how the component sizes change over repeated operations.

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