When the list gets large, quicksort is clearly the fastest comparison sorting algorithm $($hence the name$).$ However, when the lists are small enough, quicksort runs slower that some of the $(n^2)$ algorithms. This might not seem important until you note that when sorting a large list with quicksort, many small sub lists must be sorted. While the savings on sorting one small list with a faster algorithm is negligible, sorting hundreds of small lists with a faster algorithm can make a difference in the overall efficiency of the sort. For this, you will combine quicksort with another sorting algorithm to build the fastest possible sorting algorithm.

You have several options $--$Use quicksort until the list gets small enough, and then use another sort to sort the small lists

a$)$ Explore how different sorting methods behave when handling various amounts of data to distinguish their efficiency in terms of time and space complexity.

b$)$ Devise and implement a hybrid sorting algorithm by combining quicksort with another sorting method.

c$)$ Evaluate the performance of the hybrid algorithm on various types of input list including sorted, inverse sorted, and random lists.