putIfAbsent is not atomic relative to other operations on the List. But I think "synchronized" preventing multithreads enter putIfAbsent
This is true but there is no guarantees that there are other ways threads are accessing the list. The list field is public (which is always a bad idea) which means that other threads can call methods on the list directly. To properly protect the list, you should make it private and add add(...) and other methods to your ListHelper that are also synchronized to fully control all access to the synchronized-list.
// we are synchronizing the list so no reason to use Collections.synchronizedList
private List<E> list = new ArrayList<E>();
...
public synchronized boolean add(E e) {
return list.add(e);
}
If the list is private and all of the methods are synchronized that access the list then you can remove the Collections.synchronizedList(...) since you are synchronizing it yourself.
if there are other methods that do other operations on the List, key word synchronized should also be as the method atttribute. So following this way, should it be thread safe?
Not sure I fully parse this part of the question. But if you make the list be private and you add other methods to access the list that are all synchronized then you are correct.
Under what case "it is not atomic"?
putIfAbsent(...) is not atomic because there are multiple calls to the synchronized-list. If multiple threads are operating on the list then another thread could have called list.add(...) between the time putIfAbsent(...) called list.contains(x) and then calls list.add(x). The Collections.synchronizedList(...) protects the list against corruption by multiple threads but it cannot protect against race-conditions when there are multiple calls to list methods that could interleave with calls from other threads.