Merge sort is preferred over quick sort for sorting linked lists due to several key reasons related to the nature of linked lists and the operational characteristics of these sorting algorithms:
Sequential Access vs. Random Access
Sequential Access: Linked lists are inherently sequential data structures, meaning that accessing elements in a linked list requires traversing from the head node to the desired node. Merge sort works well with sequential access because it divides the list into smaller sublists and merges them sequentially, which aligns with the linked list's structure[1][4][5].
Random Access: Quick sort, on the other hand, relies heavily on random access to elements for partitioning around a pivot. This is efficient in arrays where elements can be accessed directly via indices, but in linked lists, it requires traversing the list repeatedly, which is inefficient and increases the overhead[1][3][4].
Space Complexity
In-Place Sorting: Quick sort is an in-place sorting algorithm for arrays, meaning it does not require additional memory for sorting. However, implementing quick sort for linked lists is complex and often requires additional space for managing pointers, which negates its in-place advantage[3][6].
Merge Sort's Space Efficiency: Merge sort can be implemented in a way that requires only O(1) extra space for linked lists. This is because the merge operation can be done by simply adjusting the pointers in the linked list, without needing additional arrays or significant extra memory[1][4][5].
Stability
Stability: Merge sort is a stable sorting algorithm, meaning it preserves the relative order of elements with equal values. This is often a desirable property in sorting, especially for linked lists where maintaining the order of nodes with equal values can be important[2][6].
Quick Sort's Instability: Quick sort is not inherently stable, and making it stable requires additional modifications, which can further complicate its implementation for linked lists[6][7].
Consistent Performance
Consistent Time Complexity: Merge sort has a consistent time complexity of O(n log n) in all cases (best, average, and worst). This predictability is beneficial when dealing with linked lists, as it ensures reliable performance regardless of the initial order of elements[2][6].
Variable Performance of Quick Sort: Quick sort's performance can degrade to O(n^2) in the worst case, particularly if the pivot selection is poor. Although this can be mitigated with techniques like randomized pivot selection, it still introduces variability that is less desirable for linked lists[3][6].
