Question

adding an element to a linked list is known to be O(1).

However, adding it in position X is O(X)
and if i want to add R elements in this position the total running time would be O(R*X).

but there must be an O(X+R) solution.

And the question is how to do the O(R+X) in java?

Answer 1

You have a list of pairs (element, X) where X is an index and element is the item you want to put under that index. Sort this list by X and add elements one after another using an Iterator. Here is an example:

Your input is: [(E1, 5), (E2, 3), (E3, 7)].

1. Sort it by index: [(E2, 3), (E1, 5), (E3, 7)]

2. Create an iterator and advance it by 3.

3. Add E2 using an iterator.

4. Advance the same iterator by 2 (5 - 3).

5. Add E1.

6. …

Notice that this algorithm has an of-by-one bug. It should be relatively easy to fix it.

UPDATE: just noticed that your problem is much simpler. In your case just create an iterator, advance it X times and add elements one by one using that iterator.