how to reverse a list with O(1) space and O(n) time?

Question

I am looking for a method that reverses the same instance of a given list, with O(1) additional space and O(n) time.
this is not HW nor I am looking for some library me

Answer 1

   public LinkedList Reverse(LinkedList head)
{
    if (head == null) return null; // first question

    if (head.Next == null) return head; // second question

    // third question
    // so we grab the second element (which will be the last after we reverse it)

    LinkedList secondElem = head.Next;

    // bug fix - need to unlink list from the rest or you will get a cycle
    head.Next = null;

    // then we reverse everything from the second element on
    LinkedList reverseRest = Reverse(secondElem);

    // then we join the two lists
    secondElem.Next = head;

    return reverseRest;
}

Answer 2

using ListIterators:

ListIterator<T> head = list.listIterator();
ListIterator<T> tail = list.listIterator(size);//assuming this can be done in O(1) though O(n) doesn't hurt that much and total is still O(n)
while(head.nextIndex()<tail.previousIndex()){
    T tmp = head.next();
    head.set(tail.previous());
    tail.set(tmp);
}