Delete a Node from Circular Linked List in DSA Javascript - Time & Space Complexity

Time Complexity: Delete a Node from Circular Linked List

O(n)

Understanding Time Complexity

When deleting a node from a circular linked list, we want to know how the time needed changes as the list grows.

We ask: How many steps does it take to find and remove a node?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function deleteNode(head, key) {
  if (!head) return null;
  let curr = head, prev = null;
  do {
    if (curr.data === key) {
      if (prev) prev.next = curr.next;
      else {
        // find last node to update its next
        let last = head;
        while (last.next !== head) last = last.next;
        if (curr.next === head) return null; // only one node
        last.next = curr.next;
        head = curr.next;
      }
      break;
    }
    prev = curr;
    curr = curr.next;
  } while (curr !== head);
  return head;
}
    

This code searches for a node with a given value and removes it from the circular linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through nodes to find the node to delete.
• How many times: Up to n times, where n is the number of nodes in the list.

How Execution Grows With Input

As the list grows, the number of nodes to check grows linearly.

Input Size (n)	Approx. Operations
10	Up to 10 checks
100	Up to 100 checks
1000	Up to 1000 checks

Pattern observation: The steps increase directly with the number of nodes.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete a node grows linearly with the list size.

Common Mistake

[X] Wrong: "Deleting a node is always O(1) because we just change pointers."

[OK] Correct: We must first find the node, which can take up to n steps, so the overall time depends on list size.

Interview Connect

Understanding this helps you explain how linked list operations scale and shows you can analyze real data structure tasks clearly.

Self-Check

"What if the list was doubly linked? How would the time complexity of deletion change?"

Practice

1. What happens when you delete the head node from a circular linked list with multiple nodes?

easy

A. The head moves to the next node and the list remains circular

B. The list becomes empty immediately

C. The last node points to null breaking the circle

D. The list throws an error and stops

Solution

1. Step 1: Understand the head deletion in circular list

   When the head node is deleted, the next node becomes the new head.

2. Step 2: Maintain circular link

   The last node's next pointer is updated to point to the new head, keeping the list circular.

3. Final Answer:

   The head moves to the next node and the list remains circular -> Option A

4. Quick Check:

   Head deletion updates head and last node pointer [OK]

Hint: Head deletion shifts head and keeps circle intact [OK]

Common Mistakes:

• Assuming list becomes empty after head deletion
• Breaking the circular link by setting last node to null
• Not updating the last node's next pointer

2. Which of the following is the correct syntax to delete a node with value `key` from a circular linked list in JavaScript?

easy

A. function deleteNode(head) { /* code */ }

B. function deleteNode(key, head) { /* code */ }

C. function deleteNode(head, key) { /* code */ }

D. function deleteNode() { /* code */ }

Solution

1. Step 1: Identify function parameters for deletion

   The function needs the head of the list and the key value to delete the correct node.

2. Step 2: Confirm correct parameter order

   The common and clear order is (head, key) to access the list and the target value.

3. Final Answer:

   function deleteNode(head, key) { /* code */ } -> Option C

4. Quick Check:

   Parameters: head and key in order [OK]

Hint: Function needs head and key parameters in order [OK]

Common Mistakes:

• Swapping parameter order causing confusion
• Missing key parameter to identify node
• Using no parameters making deletion impossible

3. What will be the output after deleting node with value 3 from this circular linked list: 1 -> 3 -> 5 -> 7 -> (back to 1)?
<pre>function deleteNode(head, key) { if (!head) return null; let curr = head, prev = null; do { if (curr.data === key) { if (prev) prev.next = curr.next; else { let temp = head; while (temp.next !== head) temp = temp.next; head = curr.next; temp.next = head; } break; } prev = curr; curr = curr.next; } while (curr !== head); return head; } // After deletion, print list starting from head

medium

A. 1 -> 5 -> 7 -> (back to 1)

B. 3 -> 5 -> 7 -> (back to 3)

C. 1 -> 3 -> 5 -> 7 -> (back to 1)

D. 5 -> 7 -> 1 -> (back to 5)

Solution

1. Step 1: Locate node with value 3

   The code loops through nodes and finds node with data 3.

2. Step 2: Delete node 3 and update links

   Since node 3 is not head, prev.next skips node 3 and points to node 5, maintaining circular link.

3. Final Answer:

   1 -> 5 -> 7 -> (back to 1) -> Option A

4. Quick Check:

   Node 3 removed, list links updated [OK]

Hint: Skip deleted node by linking previous to next [OK]

Common Mistakes:

• Not updating previous node's next pointer
• Deleting head incorrectly when key is not head
• Breaking circular link by missing last node update

4. Identify the bug in this code snippet for deleting a node from a circular linked list:

function deleteNode(head, key) {
  if (!head) return null;
  let curr = head;
  while (curr.next !== head) {
    if (curr.next.data === key) {
      curr.next = curr.next.next;
      return head;
    }
    curr = curr.next;
  }
  return head;
}

medium

A. Infinite loop due to missing break

B. Does not handle deletion when head node has the key

C. Deletes multiple nodes with the key instead of one

D. Returns null even if list is not empty

Solution

1. Step 1: Analyze loop and deletion logic

   The loop checks curr.next for key but never checks head node itself.

2. Step 2: Identify missing head deletion case

   If head node contains key, this code does not delete it, causing incorrect behavior.

3. Final Answer:

   Does not handle deletion when head node has the key -> Option B

4. Quick Check:

   Head node deletion missing in logic [OK]

Hint: Always check head node separately for deletion [OK]

Common Mistakes:

• Ignoring head node deletion case
• Assuming loop covers all nodes including head
• Not updating head pointer when head is deleted

5. Given a circular linked list with nodes 10 -> 20 -> 30 -> 40 -> (back to 10), how would you delete the last node (40) and maintain the circular structure? Choose the correct approach.

hard

A. Swap last node data with head and delete head

B. Set head to null directly to delete last node

C. Change last node's next to null to break the circle

D. Traverse to node before last, set its next to head, and delete last node

Solution

1. Step 1: Find node before last node

   Traverse list until node.next.next equals head, identifying node before last.

2. Step 2: Update next pointer and delete last node

   Set node before last's next pointer to head, removing last node and keeping list circular.

3. Final Answer:

   Traverse to node before last, set its next to head, and delete last node -> Option D

4. Quick Check:

   Update second last node's next to head [OK]

Hint: Link second last node directly to head [OK]

Common Mistakes:

• Breaking circle by setting next to null
• Deleting head instead of last node
• Not updating pointers causing broken list