Insert at End of Circular Linked List in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a circular linked list?

A circular linked list is a linked list where the last node points back to the first node, forming a circle with no null end.

beginner

Why do we need a special method to insert at the end of a circular linked list?

Because the last node points to the first node, we must update the last node's next pointer to the new node and the new node's next pointer to the first node to keep the circle intact.

beginner

Inserting at the end of an empty circular linked list results in what?

The new node points to itself, making it both the first and last node in the circular linked list.

intermediate

What is the time complexity of inserting at the end of a circular linked list if we do not keep a tail pointer?

O(n), because we need to traverse the list to find the last node before inserting.

intermediate

How can we optimize insertion at the end of a circular linked list?

By maintaining a tail pointer that always points to the last node, insertion at the end can be done in O(1) time.

What does the last node in a circular linked list point to?

A Null

B The first node

C Itself

D The second node

In a circular linked list, the last node's next pointer points back to the first node, forming a circle.

When inserting a new node at the end of an empty circular linked list, what should the new node's next pointer be?

A Itself

B Null

C The head node

D The previous last node

For an empty circular linked list, the new node points to itself to maintain the circular structure.

If you do not maintain a tail pointer, what is the time complexity to insert at the end of a circular linked list?

A O(n)

B O(1)

C O(log n)

D O(n^2)

Without a tail pointer, you must traverse the entire list to find the last node, which takes O(n) time.

Which pointer must be updated when inserting a new node at the end of a circular linked list?

A New node's next to null

B New node's previous to last node

C Head node's next to new node

D Last node's next to new node

The last node's next pointer must point to the new node to insert it at the end.

What is the correct order of pointers after inserting a new node at the end of a circular linked list?

A Head node -> new node -> last node

B New node -> last node -> head node

C Last node -> new node -> head node

D New node -> head node -> last node

After insertion, the last node points to the new node, and the new node points to the head node.

Explain step-by-step how to insert a new node at the end of a circular linked list.

Think about how the circle is maintained after insertion.

Describe the difference in insertion time complexity when using a tail pointer versus not using one in a circular linked list.

Consider how many nodes you must visit before inserting.

Practice

1. What happens when you insert a new node at the end of an empty circular linked list?

easy

A. The new node points to null, ending the list.

B. The new node points to itself, becoming the only node in the list.

C. The list remains empty because insertion is not possible.

D. The new node points to the head, but the list has multiple nodes.

Solution

1. Step 1: Understand empty circular linked list

   An empty circular linked list has no nodes, so inserting the first node means it must point to itself to maintain circularity.

2. Step 2: Insert new node and set its next pointer

   The new node's next pointer is set to itself, making it the only node and the head of the list.

3. Final Answer:

   The new node points to itself, becoming the only node in the list. -> Option B

4. Quick Check:

   Empty list insertion = node points to itself [OK]

Hint: First node in circular list points to itself [OK]

Common Mistakes:

• Setting next pointer to null instead of itself
• Assuming list remains empty after insertion
• Not updating head pointer to new node

2. Which of the following TypeScript code snippets correctly inserts a new node at the end of a circular linked list?

easy

A. newNode.next = head; head.next = newNode; tail = newNode;

B. newNode.next = null; tail.next = newNode; tail = newNode;

C. newNode.next = head; tail.next = newNode; tail = newNode;

D. newNode.next = tail; head.next = newNode; tail = newNode;

Solution

1. Step 1: Set new node's next to head

   In a circular linked list, the last node points to the head, so newNode.next must point to head.

2. Step 2: Update tail's next and tail pointer

   Tail's next is updated to newNode, and tail pointer moves to newNode to mark new end.

3. Final Answer:

   newNode.next = head; tail.next = newNode; tail = newNode; -> Option C

4. Quick Check:

   New node points to head, tail updated [OK]

Hint: New node's next always points to head in circular list [OK]

Common Mistakes:

• Setting newNode.next to null breaks circularity
• Updating head.next instead of tail.next
• Not moving tail pointer to new node

3. Given the circular linked list: 10 -> 20 -> 30 -> (back to 10), what is the list after inserting 40 at the end?

medium

A. 10 -> 20 -> 30 -> 40 -> 10

B. 40 -> 10 -> 20 -> 30 -> 40

C. 10 -> 20 -> 30 -> 40 -> null

D. 10 -> 20 -> 30 -> 10 -> 40

Solution

1. Step 1: Understand circular list structure

   Original list loops from 30 back to 10, so last node 30 points to head 10.

2. Step 2: Insert 40 at end and update pointers

   New node 40 points to head 10, old tail 30 points to 40, maintaining circularity.

3. Final Answer:

   10 -> 20 -> 30 -> 40 -> 10 -> Option A

4. Quick Check:

   New node added before head, tail points to new node [OK]

Hint: New tail points to head, list stays circular [OK]

Common Mistakes:

• Adding null at end breaks circularity
• Inserting new node at head instead of tail
• Incorrect pointer updates causing loops

4. Identify the error in this TypeScript code snippet for inserting at the end of a circular linked list:

function insertEnd(tail: Node | null, data: number): Node {
  const newNode = new Node(data);
  if (!tail) {
    newNode.next = null;
    return newNode;
  }
  newNode.next = tail.next;
  tail.next = newNode;
  return newNode;
}

medium

A. newNode.next should point to itself when list is empty

B. Returning newNode instead of tail breaks list reference

C. newNode.next should point to tail.next, not null when list is empty

D. tail.next should not be updated in insertion

Solution

1. Step 1: Check empty list insertion

   When tail is null (empty list), newNode.next should point to itself to maintain circularity, not null.

2. Step 2: Verify pointer updates for non-empty list

   For non-empty list, newNode.next = tail.next (head), tail.next = newNode is correct.

3. Final Answer:

   newNode.next should point to itself when list is empty -> Option A

4. Quick Check:

   Empty list node points to itself [OK]

Hint: Empty circular list node points to itself, not null [OK]

Common Mistakes:

• Setting newNode.next to null breaks circularity
• Returning newNode instead of updating tail reference
• Not updating tail.next pointer

5. You have a circular linked list with nodes 5 -> 15 -> 25 -> (back to 5). You want to insert 35 at the end and then insert 2 at the beginning. What is the correct final circular linked list?

hard

A. 35 -> 2 -> 5 -> 15 -> 25 -> 35

B. 5 -> 15 -> 25 -> 35 -> 2 -> 5

C. 2 -> 5 -> 15 -> 25 -> 35 -> 5

D. 2 -> 5 -> 15 -> 25 -> 35 -> 2

Solution

1. Step 1: Insert 35 at end

   After inserting 35, list is 5 -> 15 -> 25 -> 35 -> back to 5.

2. Step 2: Insert 2 at beginning

   Insert at beginning means new node 2 points to current head 5, tail's next updated to 2, making 2 the new head.

3. Step 3: Final circular list

   The list is 2 -> 5 -> 15 -> 25 -> 35 -> back to 2, maintaining circularity.

4. Final Answer:

   2 -> 5 -> 15 -> 25 -> 35 -> 2 -> Option D

5. Quick Check:

   New head inserted, tail points to new head [OK]

Hint: Tail's next always points to head in circular list [OK]

Common Mistakes:

• Not updating tail.next after inserting at beginning
• Inserting new node at end but not updating tail
• Breaking circular link by pointing to wrong node