Final answer:
The student's question involves modifying the quicksort algorithm to use insertion sort for sub-lists with less than 10 items. A Python code example is provided to demonstrate the hybrid approach. To compare performance, timing the sorting process for both the original and modified algorithms on datasets of 20 and 30 items is needed.
Step-by-step explanation:
Modified Quicksort with Insertion Sort
To improve the performance of quicksort for smaller sub-lists, we can integrate insertion sort into the algorithm. This hybrid approach takes advantage of the efficiency of insertion sort for small datasets. Below is a Python code that demonstrates this modified version of quicksort:
def insertion_sort(arr):
for i in range(1, len(arr)):
key = arr[i]
j = i-1
while j >=0 and key < arr[j]:
arr[j+1] = arr[j]
j -= 1
arr[j+1] = key
return arr
def quicksort(arr, low, high):
if (high - low) < 10 and low < high:
insertion_sort(arr[low:high+1])
elif low < high:
pi = partition(arr, low, high)
quicksort(arr, low, pi-1)
quicksort(arr, pi+1, high)
def partition(arr, low, high):
# ...partition logic...
return pi
The output will vary based on the input array. To compare the performance of this modified quicksort with the original, you will need to time the sorting process over various datasets of 20 and 30 items, using the time module in Python for example. It's typically seen that the hybrid approach of using insertion sort for smaller partitions improves the overall sorting time for quicksort, but the actual performance gain can vary based on many factors.