7.5. Merging Components

Try these first

1. 1.

   What does the union operation do in the union-find data structure?

   Hint

   Think about how groups combine.

2. 2.

   What is the purpose of the find operation?

   Hint

   This is like checking which group someone is in.

3. 3.

   What is the time complexity of the find operation with path compression?

   • O(n)
   • O(log n)
   • amortized O(α(n))

   Hint

   Think about how the tree structure changes.

4. 4.

   True or False: The union operation can be performed in constant time.

   • True
   • False

   Hint

   Consider what the union operation entails.

5. 5.

   Implement your own union-find structure in Python that supports union, find, and path compression. Analyze the time taken for a large number of operations.

   Hint

   Focus on implementing proper data structures and optimizing for find operations.

6. 6.

   Create a visualization of union-find operations showing how paths change with path compression.

   Hint

   Detail the process and highlight the differences before and after path compression.