6. Union-Find Data Structure

Try these first

1. 1.

   What does the find operation do in Union-Find?

   Hint

   Think about how you check for a group or a team.

2. 2.

   How does the union operation affect two disjoint sets?

   Hint

   Imagine combining two groups into one larger group.

3. 3.

   What is the primary function of the union operation?

   • A) To find the size of a component
   • B) To split a component into two
   • C) To merge two components
   • D) To check if elements are in the same component

   Hint

   Think about what happens during a team merger.

4. 4.

   True or False: Path compression only applies during the union operation.

   • True
   • False

   Hint

   Remember where path compression is most helpful.

5. 5.

   Given a list of edges in a graph, demonstrate how the Union-Find structure can be used to detect cycles.

   Hint

   Start with each vertex in its own set, and apply union carefully.

6. 6.

   Develop an alternative implementation of Union-Find that uses linked lists instead of arrays, and analyze its efficiency.

   Hint

   Think about the operations in linked lists and how to traverse them.