By "list", is this a linked list? I don't see what other type of list makes sense. Actually, I'm pretty sure it's not O(n^2). If there is a loop, the worst case is that it loops back to the last element (this means the faster pointer will take the longest to reach the slow pointer). By the time the slow pointer reaches the point in the list where it loops back, the fast pointer will have caught up to it. So it's O(n).

the above is O(n^2), you can do much better. Single iterator plus a hash table (insert each value into hash table after searching for it in there). You get O(n).