Delete from Beginning of Doubly Linked List in DSA Python - Time & Space Complexity

Time Complexity: Delete from Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

When we delete the first node from a doubly linked list, we want to know how the time needed changes as the list grows.

We ask: How much work does it take to remove the first item when the list is very long?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

class DoublyLinkedList:
    def __init__(self):
        self.head = None

    def delete_from_beginning(self):
        if not self.head:
            return  # List is empty
        self.head = self.head.next
        if self.head:
            self.head.prev = None

This code removes the first node from a doubly linked list by updating the head pointer and adjusting links.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Updating pointers of the first node and head reference.
• How many times: This happens only once per deletion, no loops or recursion involved.

How Execution Grows With Input

Deleting the first node always takes the same steps, no matter how big the list is.

Input Size (n)	Approx. Operations
10	2-3 pointer updates
100	2-3 pointer updates
1000	2-3 pointer updates

Pattern observation: The number of steps stays the same no matter how large the list is.

Final Time Complexity

Time Complexity: O(1)

This means deleting the first node takes a fixed amount of time regardless of list size.

Common Mistake

[X] Wrong: "Deleting the first node takes longer if the list is bigger because we have to check all nodes."

[OK] Correct: We only change the head and its immediate neighbors, so the list size does not affect the steps needed.

Interview Connect

Knowing that deleting from the start of a doubly linked list is quick helps you explain efficient list operations clearly in interviews.

Self-Check

"What if we changed this to delete from the end of the doubly linked list? How would the time complexity change?"

Practice

1. What happens to the head pointer when you delete the first node from a doubly linked list?

easy

A. It moves to the second node in the list

B. It becomes null immediately

C. It points to the last node in the list

D. It remains pointing to the deleted node

Solution

1. Step 1: Understand the head pointer role

   The head pointer always points to the first node in the list.

2. Step 2: After deleting the first node

   The head must move to the next node, which becomes the new first node.

3. Final Answer:

   It moves to the second node in the list -> Option A

4. Quick Check:

   Head points to new first node after deletion [OK]

Hint: Head always points to the first node, update after deletion [OK]

Common Mistakes:

• Not updating head pointer after deletion
• Setting head to null even if list has more nodes
• Leaving head pointing to deleted node

2. Which of the following is the correct syntax to delete the first node in a doubly linked list in Python?

easy

A. head = None; head.next = None

B. head.prev = None; head = head.next

C. head = head.next; head.prev = None

D. head.next = None; head = head.prev

Solution

1. Step 1: Move head to next node

   Assign head = head.next to move head forward.

2. Step 2: Remove backward link

   Set head.prev = None to disconnect previous first node.

3. Final Answer:

   head = head.next; head.prev = None -> Option C

4. Quick Check:

   Update head then clear prev link [OK]

Hint: Update head first, then clear prev pointer [OK]

Common Mistakes:

• Setting prev before moving head
• Trying to set next of head to None incorrectly
• Setting head to None without updating

3. What will be the output linked list after deleting the first node from this doubly linked list?

Initial list: 10 <-> 20 <-> 30 <-> null

Code snippet:

head = head.next
head.prev = None

medium

A. 20 <-> 30 <-> null

B. 10 <-> 30 <-> null

C. 30 <-> null

D. null

Solution

1. Step 1: Move head to second node

   Head moves from 10 to 20.

2. Step 2: Remove backward link of new head

   Set 20.prev = None, disconnecting 10.

3. Final Answer:

   20 <-> 30 <-> null -> Option A

4. Quick Check:

   First node removed, list starts at 20 [OK]

Hint: After deletion, head points to second node [OK]

Common Mistakes:

• Forgetting to set prev to None
• Incorrectly skipping nodes
• Outputting original list without change

4. Identify the error in this code snippet for deleting the first node of a doubly linked list:

if head is not None:
    head = head.next
    head.prev = None

medium

A. No error, code is correct

B. head.prev = None causes error if head.next is None

C. head = head.next should be after setting prev to None

D. Missing deletion of the old head node

Solution

1. Step 1: Check head.next for None

   If head.next is None, head becomes None after assignment.

2. Step 2: Setting head.prev causes error

   Trying to set head.prev = None when head is None causes AttributeError.

3. Final Answer:

   head.prev = None causes error if head.next is None -> Option B

4. Quick Check:

   Check for None before setting prev [OK]

Hint: Check if head is None before setting head.prev [OK]

Common Mistakes:

• Not checking if head.next is None
• Assuming list has more than one node always
• Ignoring possible AttributeError

5. Given a doubly linked list with nodes: 5 <-> 15 <-> 25 <-> 35 <-> null, after deleting the first node twice, what will be the resulting list?

hard

A. null

B. 15 <-> 25 <-> 35 <-> null

C. 35 <-> null

D. 25 <-> 35 <-> null

Solution

1. Step 1: First deletion moves head from 5 to 15

   After first deletion, list is 15 <-> 25 <-> 35 <-> null.

2. Step 2: Second deletion moves head from 15 to 25

   After second deletion, list is 25 <-> 35 <-> null.

3. Final Answer:

   25 <-> 35 <-> null -> Option D

4. Quick Check:

   Two deletions remove first two nodes [OK]

Hint: Each deletion moves head to next node [OK]

Common Mistakes:

• Deleting only once instead of twice
• Not updating head correctly after each deletion
• Confusing node values or order