Final answer:
All four sorting algorithms: Quick sort, Bubble sort, Merge sort, and Insertion sort can technically be performed on a doubly-linked list, but Quick sort is generally more challenging because it requires random access to elements.
Step-by-step explanation:
The student has asked which of the following sorting algorithms cannot be performed on a doubly-linked list: a) Quick sort, b) Bubble sort, c) Merge sort, d) Insertion sort. In theory, all four sorting algorithms can be applied to a doubly-linked list. However, the algorithm that is generally more challenging to implement efficiently on a doubly-linked list is Quick sort.
Quick sort typically requires random access to elements for partitioning, which is not as easily done in a linked list where sequential access is required. Bubble sort, Merge sort, and Insertion sort can be applied to doubly-linked lists with some modifications to algorithm steps designed for array-based data structures.
For instance, Bubble sort and Insertion sort can be performed by swapping the element's data, instead of swapping the nodes themselves, and taking advantage of a doubly-linked list's capability to traverse in both directions. Merge sort is also well-suited for linked lists as it doesn't need random access and is based on the divide-and-conquer strategy.