7.4. Make Union Find Initialization

Try these first

1. 1.

   What does the 'make union-find' operation do?

   Hint

   Think about how each element relates to others initially.

2. 2.

   What key operation allows us to merge two components together?

   Hint

   Consider the goal of combining disjoint sets.

3. 3.

   What does the 'make union-find' operation establish?

   • Merges all components
   • Creates separate components for each element
   • Tracks component sizes

   Hint

   Consider what happens at the very start of the process.

4. 4.

   Path compression is used primarily to optimize which operation?

   • True
   • False

   Hint

   Think about which operations rely on following paths.

5. 5.

   Consider a set of numbers {1, 2, 3, 4, 5}. After executing a series of union operations: union(1, 2), union(2, 3), and union(4, 5), describe the pointer structure.

   Hint

   Visualize each operation step-by-step.

6. 6.

   If you perform find(2) on the structure created above with path compression enabled, what would be the new structure?

   Hint

   Consider how paths change after each 'find' operation.