Delete a Node from Circular Linked List in DSA Go - 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 the node?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func deleteNode(head *Node, key int) *Node {
    if head == nil {
        return nil
    }
    curr := head
    var prev *Node = nil
    for {
        if curr.data == key {
            if prev != nil {
                prev.next = curr.next
            } else {
                // handle deleting head
                // find last node to update its next pointer
                last := head
                for last.next != head {
                    last = last.next
                }
                if curr.next == head { // only one node
                    return nil
                }
                last.next = curr.next
                head = curr.next
            }
            break
        }
        prev = curr
        curr = curr.next
        if curr == head {
            break
        }
    }
    return head
}
    

This code searches the circular linked list to find a node with the given key and deletes it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through nodes to find the target node.
• 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 steps to find the node grows roughly the same as the list size.

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

Pattern observation: The steps grow linearly with the number of nodes.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete a node grows directly with the list size because we may need to check each node once.

Common Mistake

[X] Wrong: "Deleting a node in a circular linked list always takes constant time O(1)."

[OK] Correct: You 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 code efficiently.

Self-Check

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

Practice

1. What happens when you delete the only node in a circular linked list?

easy

A. The list still contains the deleted node.

B. The list becomes empty (head points to nil).

C. The list forms a linear linked list.

D. The list throws an error automatically.

Solution

1. Step 1: Understand single-node circular list

   A circular linked list with one node points to itself.

2. Step 2: Delete the only node

   Removing this node means no nodes remain, so head becomes nil.

3. Final Answer:

   The list becomes empty (head points to nil). -> Option B

4. Quick Check:

   Single node deleted = empty list [OK]

Hint: Deleting last node empties the list, head = nil [OK]

Common Mistakes:

• Assuming list still has nodes after deleting the only node
• Not updating head to nil
• Confusing circular with linear list after deletion

2. Which Go syntax correctly moves the head pointer when deleting the head node from a circular linked list?

easy

A. head.next = head

B. head = nil.next

C. head = head.next

D. head = head.prev

Solution

1. Step 1: Identify head deletion logic

   Deleting head means moving head pointer to next node.

2. Step 2: Check syntax correctness

   Assigning head = head.next correctly moves head to next node.

3. Final Answer:

   head = head.next -> Option C

4. Quick Check:

   Move head to next node = head = head.next [OK]

Hint: Move head pointer to next node to delete head [OK]

Common Mistakes:

• Using nil.next causes runtime error
• Assigning head.next = head does not delete node
• Using head.prev is invalid for singly circular list

3. Given this circular linked list: 1 -> 2 -> 3 -> (back to 1), what is the list after deleting node with value 2?

medium

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

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

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

D. 3 -> 1 -> (back to 3)

Solution

1. Step 1: Locate node with value 2

   Node 2 is between nodes 1 and 3 in the circular list.

2. Step 2: Remove node 2 by linking 1 to 3

   Update node 1's next pointer to node 3, skipping node 2.

3. Final Answer:

   1 -> 3 -> (back to 1) -> Option A

4. Quick Check:

   Deleted 2, linked 1 to 3 [OK]

Hint: Link previous node to next of deleted node [OK]

Common Mistakes:

• Not updating previous node's next pointer
• Deleting wrong node
• Breaking circular link

4. What is wrong with this Go code snippet for deleting a node from a circular linked list?

func deleteNode(head *Node, key int) *Node {
  if head == nil {
    return nil
  }
  curr := head
  for curr.next != head && curr.next.data != key {
    curr = curr.next
  }
  if curr.next.data == key {
    curr.next = curr.next.next
  }
  return head
}

medium

A. It returns nil always.

B. It causes infinite loop always.

C. It deletes all nodes with the key.

D. It does not handle deleting the head node correctly.

Solution

1. Step 1: Analyze deletion logic

   The code searches for node before target and skips target node.

2. Step 2: Check head deletion case

   If the node to delete is head, head pointer is not updated, causing incorrect list.

3. Final Answer:

   It does not handle deleting the head node correctly. -> Option D

4. Quick Check:

   Head deletion needs head pointer update [OK]

Hint: Update head if deleting head node [OK]

Common Mistakes:

• Ignoring head node deletion
• Not updating head pointer
• Assuming key always exists

5. You have a circular linked list: 10 -> 20 -> 30 -> 40 -> (back to 10). You want to delete node with value 10 (head). Which steps correctly update the list?

hard

A. Find last node (40), set its next to head.next (20), then update head to 20.

B. Set head to nil directly without updating last node.

C. Delete node 10 by setting head.next to nil.

D. Swap data of head and next node, then delete next node.

Solution

1. Step 1: Find last node pointing to head

   Traverse list to find node 40 which points to head (10).

2. Step 2: Update last node's next pointer

   Set node 40's next to head.next (node 20) to maintain circularity.

3. Step 3: Update head pointer

   Set head to head.next (node 20) to delete original head.

4. Final Answer:

   Find last node (40), set its next to head.next (20), then update head to 20. -> Option A

5. Quick Check:

   Update last node and head to delete head node [OK]

Hint: Update last node's next and head to delete head [OK]

Common Mistakes:

• Not updating last node's next pointer
• Setting head to nil breaks list
• Deleting node by setting next to nil