how to connect circular doubly-linked lists - algorithm

Question

Consider, I have given 2 items of the circular doubly-linked lists A and B. I want to implement a function which connects both of the lists.
This task is simple. However, I want to handle the case where A and B are the members of the same linked list. In this case it would just do nothing. Is it possible to implement it in O(1)? Do I need to check whether A and B are from the same list first? Or can I somehow magically swap/mix the pointers?
IMO it is not possible, but I'm unable to prove it.
thanks

Answer 1

You can. Being curious myself, I sketched an implementation in Java. Assuming a linked list as follows
public class CLinkedList {
class Node {
Node prev, next;
int val;
public Node(int v) {
val = v;
}
}
Node s;
public CLinkedList(Node node) {
s = node;
}
void traverse() {
if (s == null)
return;
Node n = s;
do {
System.out.println(n.val);
n = n.next;
} while (n != s);
}
...
}
a merging method would look like
void join(CLinkedList list) {
Node prev = list.s.prev;
Node sprev = s.prev;
prev.next = s;
sprev.next = list.s;
s.prev = prev;
list.s.prev = sprev;
}
which works just fine when the lists are different.
If they're not, all this does is just split the original list into two perfectly valid, different linked lists. All you should do is just join them again.
Edit: The join method joins (lol) two lists if they are different or (contrary to its name) splits the list if the nodes belong to the same list. Applying join twice thus has no effect, indeed. But you can make use of this property in other ways. The method below works fine:
public void merge(CLinkedList list) {
CLinkedList nList = new CLinkedList(s.next);
join(nList);
nList.join(list);
join(nList);
}
public static void main(String[] args) {
CLinkedList list = new CLinkedList(new int[] {1,2,3});
CLinkedList nlist = new CLinkedList(list.s.next);
list.merge(nlist);
list.traverse();
}
Still O(1) :) Keeping the small disclaimer - not the best quality code, but you get the picture.