6.10. Using Union-Find in Kruskal's Algorithm

Try these first

1. 1.

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

   Hint

   Think about what you do to find out which group an element belongs to.

2. 2.

   In Kruskal's algorithm, what do we ensure when adding an edge?

   Hint

   Consider the relationship of the vertices in the edge.

3. 3.

   What does the 'find' operation do in Union-Find?

   • Merges two sets
   • Finds the component of a set
   • Counts the number of elements

   Hint

   Think about how you verify if two elements are in the same group.

4. 4.

   True or False: In Kruskal's algorithm, we can add an edge if it creates a cycle.

   • True
   • False

   Hint

   Consider what happens when you connect nodes that are already connected.

5. 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.

   Hint

   Make sure to track which nodes are connected to avoid cycles.

6. 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.

   Hint

   Focus on how merging smaller into larger affects the overall structure.