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

Time Complexity: Delete from Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

We want to understand how long it takes to remove the first item from a doubly linked list.

Specifically, how the time needed changes as the list grows larger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public void DeleteFromBeginning()
{
    if (head == null) return; // empty list
    head = head.Next;
    if (head != null)
        head.Prev = null;
}
    

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 only.
• How many times: Exactly once per call, no loops or recursion.

How Execution Grows With Input

Removing the first node always takes the same number of steps, no matter how big the list is.

Input Size (n)	Approx. Operations
10	3 steps
100	3 steps
1000	3 steps

Pattern observation: The time stays constant as the list grows.

Final Time Complexity

Time Complexity: O(1)

This means deleting from the beginning takes the same short time no matter how large the list is.

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 a few pointers at the start, no need to look at other nodes.

Interview Connect

Knowing this operation is quick helps you explain efficient list manipulations clearly and confidently.

Self-Check

"What if we changed to deleting 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 becomes null immediately

B. It remains unchanged

C. It points to the last node

D. It moves to the second node in the list

Solution

1. Step 1: Understand the role of head pointer

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

2. Step 2: Effect of deleting the first node

   When the first node is deleted, the head pointer 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 D

4. Quick Check:

   Head points to new first node after deletion [OK]

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

Common Mistakes:

• Assuming head becomes null even if list has more nodes
• Not updating head pointer after deletion
• Pointing head to last node mistakenly

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

easy

A. head = head.next; head.prev = null;

B. head = head.prev; head.next = null;

C. head.next = null; head.prev = null;

D. head = null; head.next = null;

Solution

1. Step 1: Move head to next node

   To delete the first node, assign head to head.next to point to the second node.

2. Step 2: Remove backward link

   Set head.prev to null to disconnect the previous first node.

3. Final Answer:

   head = head.next; head.prev = null; -> Option A

4. Quick Check:

   Correct syntax updates head and prev pointer [OK]

Hint: Set head to next and prev of new head to null [OK]

Common Mistakes:

• Setting head.prev instead of head.next
• Not nullifying prev pointer of new head
• Setting head to null prematurely

3. Given the doubly linked list: 10 <-> 20 <-> 30 <-> null, what will be the list after deleting the first node?

medium

A. 10 <-> 30 <-> null

B. 20 <-> 30 <-> null

C. 30 <-> null

D. null

Solution

1. Step 1: Identify the first node

   The first node has value 10, which will be removed.

2. Step 2: Update head to second node

   Head moves to node with value 20, and its prev pointer is set to null.

3. Final Answer:

   20 <-> 30 <-> null -> Option B

4. Quick Check:

   First node removed, list starts at 20 [OK]

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

Common Mistakes:

• Removing wrong node (like 20 or 30)
• Not updating prev pointer of new head
• Leaving old head in the list

4. Consider this code snippet to delete the first node from a doubly linked list:

if (head != null) {
    head = head.next;
    head.prev = null;
}

What error can occur here?

medium

A. Logical error: head should not be updated

B. Syntax error due to missing semicolon

C. NullReferenceException if list has only one node

D. No error, code is correct

Solution

1. Step 1: Analyze when list has one node

   If list has one node, head.next is null after assignment.

2. Step 2: Accessing head.prev causes error

   Setting head.prev = null when head is null causes NullReferenceException.

3. Final Answer:

   NullReferenceException if list has only one node -> Option C

4. Quick Check:

   Accessing property on null causes exception [OK]

Hint: Check if head is null before setting head.prev [OK]

Common Mistakes:

• Not checking if head is null after moving to next
• Assuming code always works for single-node list
• Ignoring runtime exceptions

5. You have a doubly linked list with nodes: 5 <-> 15 <-> 25 <-> 35 <-> null. After deleting the first node twice, what is the resulting list?

hard

A. 25 <-> 35 <-> null

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

C. 35 <-> null

D. null

Solution

1. Step 1: Delete first node once

   First deletion removes node with value 5; head moves to 15.

2. Step 2: Delete first node second time

   Second deletion removes node with value 15; head moves to 25.

3. Final Answer:

   25 <-> 35 <-> null -> Option A

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 second deletion
• Confusing node values order