Insert at End of Circular Linked List in DSA Javascript - Time & Space Complexity

Time Complexity: Insert at End of Circular Linked List

O(n)

Understanding Time Complexity

We want to understand how the time to insert a new node at the end of a circular linked list changes as the list grows.

How does the number of steps needed grow when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function insertAtEnd(head, value) {
  const newNode = { data: value, next: null };
  if (!head) {
    newNode.next = newNode;
    return newNode;
  }
  let current = head;
  while (current.next !== head) {
    current = current.next;
  }
  current.next = newNode;
  newNode.next = head;
  return head;
}
    

This code inserts a new node with the given value at the end of a circular linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through nodes to find the last node.
• How many times: It runs once for each node until it reaches the last node, so roughly n times where n is the number of nodes.

How Execution Grows With Input

As the list grows, the loop must check more nodes to find the end.

Input Size (n)	Approx. Operations
10	About 10 steps to find the end
100	About 100 steps to find the end
1000	About 1000 steps to find the end

Pattern observation: The number of steps grows roughly the same as the number of nodes, so it grows linearly.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert at the end grows directly with the size of the list.

Common Mistake

[X] Wrong: "Inserting at the end is always fast and takes constant time."

[OK] Correct: Because we must find the last node by moving through the list, which takes longer as the list grows.

Interview Connect

Understanding this helps you explain how linked list operations scale and shows you can analyze code beyond just writing it.

Self-Check

"What if we kept a pointer to the last node? How would the time complexity change?"

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 itself, becoming the only node in the list.

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

C. The list remains empty because no insertion is possible.

D. The new node points to the head, but the list is not circular.

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 forming a circular link.

3. Final Answer:

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

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 maintaining circular link for single node

2. Which of the following is the correct syntax to insert a new node at the end of a circular linked list in JavaScript?

easy

A. newNode.next = head; lastNode.next = newNode;

B. newNode.next = null; lastNode.next = newNode;

C. newNode.next = lastNode; head.next = newNode;

D. newNode.next = newNode; head = 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 to maintain circularity.

2. Step 2: Update last node's next to new node

   The current last node's next pointer is updated to newNode, inserting it at the end.

3. Final Answer:

   newNode.next = head; lastNode.next = newNode; -> Option A

4. Quick Check:

   New node points to head, last node points to new node [OK]

Hint: New node next points to head, last node next points to new node [OK]

Common Mistakes:

• Setting newNode.next to null breaks circularity
• Swapping pointers incorrectly
• Not updating last node's next pointer

3. What will be the printed circular linked list after inserting a node with value 4 at the end of the list: 1 -> 2 -> 3 -> (back to 1)?

medium

A. 4 -> 1 -> 2 -> 3 -> (back to 4)

B. 1 -> 2 -> 3 -> 4 -> (back to 1)

C. 1 -> 2 -> 3 -> (back to 4)

D. 1 -> 2 -> 3 -> 4 -> null

Solution

1. Step 1: Identify current list structure

   The list currently has nodes 1, 2, 3 linked circularly, so last node 3 points back to 1.

2. Step 2: Insert node with value 4 at end

   New node 4's next points to head (1), and node 3's next points to node 4, extending the circle.

3. Final Answer:

   1 -> 2 -> 3 -> 4 -> (back to 1) -> Option B

4. Quick Check:

   New node added at end, circle maintained [OK]

Hint: New node added after last, points to head [OK]

Common Mistakes:

• Placing new node at start instead of end
• Breaking circular link by pointing to null
• Incorrectly updating pointers causing broken list

4. Given the code snippet below, what is the error when inserting at the end of a circular linked list?

function insertEnd(head, data) {
  let newNode = { value: data, next: null };
  if (!head) {
    head = newNode;
    newNode.next = head;
    return head;
  }
  let temp = head;
  while (temp.next !== head) {
    temp = temp.next;
  }
  temp.next = newNode;
  newNode.next = head;
  return head;
}

medium

A. Head is not updated when list is empty.

B. The while loop condition is incorrect and causes infinite loop.

C. New node is not created properly.

D. New node's next is not set to head, breaking circularity.

Solution

1. Step 1: Check new node's next pointer

   New node's next is initialized to null and never updated to point to head, breaking the circular link.

2. Step 2: Verify circularity after insertion

   Since temp.next points to newNode but newNode.next is null, the list is no longer circular.

3. Final Answer:

   New node's next is not set to head, breaking circularity. -> Option D

4. Quick Check:

   New node next must point to head [OK]

Hint: Always set new node's next to head in circular list [OK]

Common Mistakes:

• Forgetting to link new node back to head
• Incorrect loop condition causing infinite loop
• Not handling empty list properly

5. You have a circular linked list with nodes 10 -> 20 -> 30 -> (back to 10). You want to insert a new node with value 40 at the end, but also keep the list sorted in ascending order. Which approach correctly inserts the node and maintains circularity and order?

hard

A. Insert 40 at the end as usual, then rotate the list to start at 40.

B. Insert 40 at the head and update last node's next to new node.

C. Traverse to find correct position for 40, insert it there, update pointers to keep circularity.

D. Insert 40 at the end and break circularity temporarily.

Solution

1. Step 1: Find correct sorted position for new node

   Traverse the list to find where 40 fits between nodes to keep ascending order.

2. Step 2: Insert new node at found position and update pointers

   Insert new node between nodes, update previous node's next to new node, and new node's next to next node, maintaining circularity.

3. Final Answer:

   Traverse to find correct position for 40, insert it there, update pointers to keep circularity. -> Option C

4. Quick Check:

   Sorted insert requires correct position and pointer updates [OK]

Hint: Insert in sorted order by finding correct spot, update pointers [OK]

Common Mistakes:

• Inserting at end without sorting
• Breaking circularity during insertion
• Not updating last node's next pointer correctly