7.8. Find Operation Complexity

Try these first

1. 1.

   What is the time complexity of the find operation in an array-based implementation?

   Hint

   Think about how quickly you can retrieve the component.

2. 2.

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

   Hint

   Consider what happens to each element initially.

3. 3.

   What is the amortized time complexity for union operations in a pointer-based union-find?

   • O(1)
   • O(log n)
   • O(n)

   Hint

   Think about how unions are formed in the data structure.

4. 4.

   True or False: The find operation can be accomplished in constant time in a pointer-based implementation.

   • True
   • False

   Hint

   Consider how trees are structured.

5. 5.

   Given a union-find data structure with elements 1 through 10, perform a series of unions and a find operation. Calculate the time complexity for each operation based on the implementation type.

   Hint

   Make note of unions performed and the resulting structure.

6. 6.

   Design a new optimization technique for union-find and compare it against path compression in terms of efficiency.

   Hint

   Consider methods used in graph algorithms.