Is the single linked list already sorted, so identical elements are adjacent?
If its an sorted array that makes it easy.
But my question is incase of Unsorted array.
I know one method is liner search method. Where each indivual element is check once with all elements. But the complexity is O(n*n)
Basically, you use the hash to answer the "doesElementExist" test. If it doesn't, copy it to the unique list.
Or you could just insert the whole list into a balanced binary tree, then flatten it into a list when you're done. The inserts will be O(log2(n)) on average, either finding the item already present or finding where to insert it.