16.1.2. Partitioning and Efficiency

Try these first

1. 1.

   What is the time complexity of the best case for Quicksort?

   Hint

   Think about how the pivot divides the array.

2. 2.

   What is the purpose of partitioning in Quicksort?

   Hint

   What happens to elements relative to the chosen pivot?

3. 3.

   What is the average case time complexity of Quicksort?

   • O(n)
   • O(n log n)
   • O(n^2)

   Hint

   Think about the efficient partitioning.

4. 4.

   True or False: Quicksort always uses the first element as the pivot.

   • True
   • False

   Hint

   What strategies exist for selecting pivots?

5. 5.

   Given a set of random numbers, apply the Quicksort algorithm with detailed steps for choosing a pivot at each stage.

   Hint

   Keep track of how your pivot choice influences subsequent partitions.

6. 6.

   Analyze the sorting time for a partially sorted array using Quicksort. What is the expected performance?

   Hint

   Consider how close to sorted the initial arrangement is.