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

Time Complexity: Delete a Node from Circular Linked List

O(n)

Understanding Time Complexity

We want to understand how long it takes to remove a node from a circular linked list.

Specifically, how the time grows as the list gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

def delete_node(head, key):
    if head is None:
        return None
    curr = head
    prev = None
    while True:
        if curr.data == key:
            if prev:
                prev.next = curr.next
            else:
                # Deleting head node
                if head.next == head:
                    return None
                temp = head
                while temp.next != head:
                    temp = temp.next
                temp.next = head.next
                head = head.next
            break
        prev = curr
        curr = curr.next
        if curr == head:
            break
    return head
    

This code deletes a node with a given value from a circular linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Traversing the circular linked list 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 time to find the node grows roughly in a straight line.

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

Pattern observation: The number of steps grows 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 in a circular linked list always takes constant time because it's linked."

[OK] Correct: You must first find the node, which can take time proportional to the list size.

Interview Connect

Understanding this helps you explain how linked lists work and how to handle circular references efficiently.

Self-Check

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

C. The last node is deleted instead

D. The list breaks and becomes linear

Solution

1. Step 1: Understand the head deletion in circular linked 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 keeps circular [OK]

Hint: Deleting head shifts head to next, list stays circular [OK]

Common Mistakes:

• Assuming list becomes empty after head deletion
• Not updating last node's next pointer
• Breaking circular link accidentally

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

easy

A. def deleteNode(head, key):
if head.data == key:
# delete head logic

B. def deleteNode(head, key):
while head.data != key:
head = head.next

C. def deleteNode(head, key):
if head is None:
return None

D. def deleteNode(head, key):
head = None
return head

Solution

1. Step 1: Check for empty list

   Before deleting, check if the list is empty (head is None) to avoid errors.

2. Step 2: Return None if list is empty

   If head is None, return None as there is nothing to delete.

3. Final Answer:

   def deleteNode(head, key): if head is None: return None -> Option C

4. Quick Check:

   Empty list check is essential before deletion [OK]

Hint: Always check if list is empty before deleting [OK]

Common Mistakes:

• Not checking if head is None before deletion
• Incorrectly looping without exit condition
• Setting head to None without condition

3. What will be the output list after deleting node with value 3 from this circular linked list: 1 -> 3 -> 5 -> 7 -> (back to 1)?

medium

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

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

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

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

Solution

1. Step 1: Locate node with value 3

   Traverse the list to find node with value 3 between 1 and 5.

2. Step 2: Remove node 3 and link 1 to 5

   Update node 1's next pointer to node 5, skipping node 3.

3. Final Answer:

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

4. Quick Check:

   Deleted 3, linked 1 to 5 [OK]

Hint: Skip the node with key, link previous to next [OK]

Common Mistakes:

• Not updating previous node's next pointer
• Deleting wrong node or not deleting at all
• Breaking circular link after deletion

4. Given this code snippet to delete a node from a circular linked list, what is the bug?

def deleteNode(head, key):
    if head is None:
        return None
    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. Does not handle deletion if head node contains the key

B. Infinite loop due to missing break

C. Deletes all nodes instead of one

D. Returns None instead of head

Solution

1. Step 1: Analyze deletion logic

   The code checks nodes after head but never checks if head itself has the key.

2. Step 2: Identify missing head deletion handling

   If head contains the key, this code will not delete it, causing incorrect behavior.

3. Final Answer:

   Does not handle deletion if head node contains the key -> Option A

4. Quick Check:

   Head node deletion must be handled separately [OK]

Hint: Always check if head node matches key before loop [OK]

Common Mistakes:

• Ignoring head node in deletion logic
• Assuming loop covers all nodes including head
• Not updating head pointer after deletion

5. You have a circular linked list with only one node containing value 10. What should be the list after deleting node with value 10?

hard

A. List with node 10 pointing to None

B. List with node 10 pointing to itself

C. List unchanged

D. Empty list (None)

Solution

1. Step 1: Identify single node list condition

   When the list has only one node, head.next points to head itself.

2. Step 2: Delete the only node

   Deleting this node means the list becomes empty, so head should be None.

3. Final Answer:

   Empty list (None) -> Option D

4. Quick Check:

   Single node deletion empties the list [OK]

Hint: Deleting sole node results in empty list (None) [OK]

Common Mistakes:

• Leaving node pointing to itself after deletion
• Not setting head to None
• Assuming list still has one node