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For the method add of the ArrayList Java API states:
The add operation runs in amortized constant time, that is, adding n elements requires O(n) time.
I wonder if it is the same time complexity, linear, when using the add method of a LinkedList.
This depends on where you’re adding. E.g. if in an ArrayList you add to the front of the list, the implementation will have to shift all items every time, so adding n elements will run in quadratic time.
Similar for the linked list, the implementation in the JDK keeps a pointer to the head and the tail. If you keep appending to the tail, or prepending in front of the head, the operation will run in linear time for n elements. If you append at a different place, the implementation will have to search the linked list for the right place, which might give you worse runtime. Again, this depends on the insertion position; you’ll get the worst time complexity if you’re inserting in the middle of the list, as the maximum number of elements have to be traversed to find the insertion point.
The actual complexity depends on whether your insertion position is constant (e.g. always at the 10th position), or a function of the number of items in the list (or some arbitrary search on it). The first one will give you O(n) with a slightly worse constant factor, the latter O(n^2).