7.1. Operations of Union-Find Data Structure

Try these first

1. 1.

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

   Hint

   Think of the operations as initializing, discovering, and merging.

2. 2.

   What is path compression in Union-Find?

   Hint

   It's about making paths shorter.

3. 3.

   What operation does Union-Find use to initialize single element partitions?

   • Union
   • Find
   • Make

   Hint

   Think about how we start the groups.

4. 4.

   True or False: The union operation combines two partitions into one.

   • True
   • False

   Hint

   Consider what merging means.

5. 5.

   Given a series of union operations on elements, demonstrate the state of the Union-Find structure at each step and compute the resulting sizes of components.

   Hint

   Map out each element and ensure to reflect on which joins which component.

6. 6.

   Implement a simple Union-Find structure with path compression and demonstrate it using a few find and union operations, explaining the changes in structure.

   Hint

   Keep track of the structures before and after each operation!