During Quicksort, for the array A = [3,7,2,9,14,0,8]; the line of code "pivotIndex = PARTITION( A, left = 0, right = 6)" is called. Assume PARTITION uses "left&qu…

Question

During Quicksort, for the array A = [3,7,2,9,14,0,8]; the line of code "pivotIndex = PARTITION( A, left = 0, right = 6)" is called. Assume PARTITION uses "left" to select the element value to pivot about. What are the element values for the left hand array and right hand array split around the new pivotIndex after PARTITION returns?

Answer 1

After PARTITION returns in the Quicksort algorithm, assuming 'left' is the pivot and the pivot value is 3, the left side will contain elements less than or equal to 3 (e.g., [2, 0, 3]), and the right side will contain elements greater than 3 (e.g., [7, 9, 14, 8]).

Step-by-step explanation:

When the PARTITION function is called in the Quicksort algorithm with the array A = [3,7,2,9,14,0,8] using 'left' as the pivot, the partition operation will organize elements around the pivot value 3. As PARTITION uses the leftmost element to pivot around, after PARTITION returns, elements on the left side of the pivot are less than or equal to the pivot, and elements on the right side are greater than the pivot. The exact distribution of elements can vary based on the specific iteration steps implemented by PARTITION, but the goal is to place 3 in such a way that it would be positioned if the array were sorted.

Assuming a typical PARTITION algorithm and the initial pivot being the first element, 3, the resulting array might look something like the following:

1. Left hand array (values <= pivot): [2, 0, 3]
2. Right hand array (values > pivot): [7, 9, 14, 8]

The element values listed here are representative and the actual result could be slightly different based on the behavior of the PARTITION algorithm since elements equal to the pivot can be on either side. However, the pivot value 3 will be in its correct sorted position.