Sorting a linked list

Question

I have written a basic linked list class in C#. It has a Node object, which (obviously) represents every node in the list.

The code does not use IEnumerable, however

Answer 1

If you want to really utilize the fact that you're using a linked list, as opposed to working around it, I would suggest insertion sort.

Normally an insertion sort is not very efficient - O(n^2) in the worst case, but with linked list this can be improved to O(n log n)

pseudo:

for i in range (1,n):
    item = arr[i]
    location = binary_search(l=root, r=i, value=item.val)  // O(log i)
    insert_item_before(arr[location], item) // O(1)

In the regular algorithm the insert part takes O(i) because we may need to shift all the items that are larger then item. because a linked list enables us to do the insertion without shifting, we can search for the location with a binary search and so the insertion part takes only O(log i)

note: usually an insertion sort has O(n) performance in the best case (if the array is sorted). Unfortunately this isn't the case here because binary search takes always O(log n) steps.