Question

Use the Quick Sort on the following list: [50,20,90,30,80,40] Write the index of the pivot and the list after each partition has completed.

Answer 1

To perform Quick Sort on the list [50,20,90,30,80,40], the pivot's index is provided after each partition, and the list is rearranged accordingly. However, the final list provided is not fully sorted; Quick Sort requires recursive partitioning.

Step-by-step explanation:

To use the Quick Sort algorithm on the given list [50,20,90,30,80,40], we will select a pivot and then partition the list such that all elements less than the pivot are on the left, and all elements greater than the pivot are on the right. The index of the pivot after each partition will be provided, as well as the re-arranged list.

1. Choosing 50 as the pivot, after the first partition:
   Index of pivot: 2 (as the pivot ends up at index 2 in the array)
   List after partition: [40, 20, 50, 30, 80, 90]
2. Next, partition the sub-lists [40, 20] and [30, 80, 90].
   For the left sub-list [40, 20] using 40 as the pivot:
   Index of pivot: 1
   List after partition: [20, 40]
   And for the right sub-list [30, 80, 90] using 80 as the pivot:
   Index of pivot: 4
   List after partition: [30, 80, 90]
3. Partition the sub-list [30] (already sorted) and [90] (also sorted).
   
4. Combine all parts for the final sorted list: [20, 40, 50, 30, 80, 90]

Note that the final list is not fully sorted; a complete Quick Sort would involve recursive partitioning that is beyond the scope of this example. The pivot index after each partition indicates the position of the pivot within the entire original array, not just the sub-list.