When inserting a new node at the head of a circular singly linked list with a tail pointer, which sequence is correct?

• A. If the list is empty, create one node pointing to itself; otherwise set new.next to head, tail.next to new, and head to new.
• B. Only set head to new; update tail to new.
• C. Set new.next to head, then set head to new.
• D. Create new node and insert after tail; nothing about head.

Answer: (A)

Inserting at the front of a circular singly linked list with a tail pointer requires preserving the circular connection and keeping tail pointing to the last node whose next links to the head. The correct approach starts by handling the empty list: create a single node that points to itself and set both head and tail to that node. This establishes the circular structure right away.

For a non-empty list, you link the new node to the current head (new.next = head), then you update the tail’s next pointer to point to the new node (tail.next = new) so the circle remains closed with the new node at the front, and finally you update the head reference to the new node (head = new). This sequence ensures the head moves to the new node, the circle remains intact, and the tail continues to reference the last node.

Why the other approaches don’t fit as cleanly: simply changing the head without updating tail.next breaks the circular link, because the tail wouldn’t point to the new head. Creating a new node and linking it after the tail without updating the head leaves the front of the list unchanged, so you haven’t actually inserted at the head. Making changes that touch only one part of the pointers disrupts the invariant that tail.next should always refer to the current head.