Suppose that you can select the pivot of the quick sort algorithm with three methods: you can select the first item, last item, or middle item as the pivot. Indicate the method(s) that gives the most efficient result to sort the following arrays. Note that you MUST indicate all methods that give the most efficient result.

Question

Suppose that you can select the pivot of the quick sort algorithm with three methods: you can select the first item, last item, or middle item as the pivot. Indicate the method(s) that gives the most efficient result to sort the following arrays. Note that you MUST indicate all methods that give the most efficient result.

Arrays Method(s)
1 2 3 4 5 6 7 8 9
2 2 2 2 4 2 2 2 2
5 5 5 5 5 5 5 5 5

Answer 1

do it by yourself :)

Answer 2

To determine the method(s) that give the most efficient result for sorting the given arrays using the quick sort algorithm, we need to consider the characteristics of each array and how the selection of the pivot affects the partitioning process.

1) Array: 1 2 3 4 5 6 7 8 9
- In this sorted array, any pivot choice will result in equally efficient partitions. All three methods (selecting the first item, last item, or middle item) will give the same efficient result.

2) Array: 2 2 2 2 4 2 2 2 2
- This array contains mostly repeated elements except for one distinct element (4). The pivot choice greatly affects the partitioning efficiency.
- The first item and last item methods will result in inefficient partitions as they will always select one of the repeated 2's as a pivot, causing the algorithm to repeatedly partition around the repeated element. Therefore, these two methods are not the most efficient.
- The middle item method will provide the most efficient result as it will select the distinct element (4) as the pivot. This ensures that the repeated elements are efficiently partitioned.

3) Array: 5 5 5 5 5 5 5 5 5
- This array contains only one distinct element (5). The pivot choice does not have any significant impact on the partitioning efficiency.
- All three methods (selecting the first item, last item, or middle item) will give the same efficient result as they will always select the same pivot (5).

Based on the analysis above, the most efficient method to sort the given arrays is:
- Array 1: All three methods (selecting the first item, last item, or middle item) are equally efficient.
- Array 2: The middle item method is the most efficient.
- Array 3: All three methods (selecting the first item, last item, or middle item) are equally efficient.