Question

Does the Collections.sort(list) check if the list is already sorted or is it maybe O(1) for some other reason?
Or, is it a good idea to have a flag sorted and set it to true/false upon calling sort()/adding an element to the list?

Answer 1

How can you determine if any list is sorted without looking at it? It wont be O(1). Determining if a list is sorted takes at least O(n).

That would mean If Collections.sortdid bother to check if a list was sorted first each sorting operation would take an average of O(n) + O(n log n).