7.2. Array Based Implementation

Try these first

1. 1.

   What is the purpose of the union-find data structure?

   Hint

   Think about group management and connections.

2. 2.

   Which operation checks the component of an element?

   Hint

   This operation helps you know where an element's group is.

3. 3.

   What is the initial time complexity for the find operation in union-find?

   • O(n)
   • O(log n)
   • O(1)

   Hint

   Consider what happens during a direct lookup.

4. 4.

   Is the amortized complexity for the union operation O(log m)?

   • True
   • False

   Hint

   Think about the sequence of operations and how they merge.

5. 5.

   Given a sequence of union operations, illustrate how the data structure looks after each operation. Describe what happens to the find operations for the involved elements.

   Hint

   Use a diagram to represent the sequence and changes.

6. 6.

   Suppose you implement path compression in the union-find structure. Analyze the implications of this on the time complexity of find operations across multiple sequences.

   Hint

   Sketch out how the path updates during the process.