Practice Using Union-find In Kruskal's Algorithm (6.10) - Union-Find Data Structure

Practice: Using Union-Find in Kruskal's Algorithm

Lesson 6.10Union-Find Data Structure

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9 questions

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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 what you do to find out which group an element belongs to.
Question 2.
In Kruskal's algorithm, what do we ensure when adding an edge?
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Consider the relationship of the vertices in the edge.
3Question 3.
What does the 'find' operation do in Union-Find?
- Merges two sets
- Finds the component of a set
- Counts the number of elements
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Think about how you verify if two elements are in the same group.
4Question 4.
True or False: In Kruskal's algorithm, we can add an edge if it creates a cycle.
- True
- False
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Consider what happens when you connect nodes that are already connected.
Question 5.
Given a connected graph with 6 vertices and 7 edges, use Union-Find to apply Kruskal's algorithm to find the MST. List the edges included and those excluded from the MST.
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Make sure to track which nodes are connected to avoid cycles.
Question 6.
Consider a scenario where you have to perform a sequence of union operations. Analyze how the structure of your Union-Find will change over these operations, and explain the final configuration.
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Focus on how merging smaller into larger affects the overall structure.

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