Delete from Beginning of Doubly Linked List in DSA Javascript - 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.

How does the time needed change as the list grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Node {
  constructor(value) {
    this.value = value;
    this.next = null;
    this.prev = null;
  }
}

function deleteFromBeginning(head) {
  if (!head) return null;
  let newHead = head.next;
  if (newHead) newHead.prev = null;
  return newHead;
}
    

This code removes the first node from a doubly linked list and returns the new head.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Accessing and updating the first two nodes' pointers.
• How many times: This happens only once, no loops or recursion.

How Execution Grows With Input

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

Input Size (n)	Approx. Operations
10	3-4 steps
100	3-4 steps
1000	3-4 steps

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 constant amount of time regardless of list size.

Common Mistake

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

[OK] Correct: We only update the first two nodes' pointers, so the list size does not affect the time.

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 had to delete the last node instead? 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 remains unchanged

B. It moves to the second node in the list

C. It points to the last node

D. It becomes null immediately

Solution

1. Step 1: Understand the head pointer role

   The head pointer always points to the first node in the 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 B

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 without checking list length
• 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 from a doubly linked list in JavaScript?

easy

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

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

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

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

Solution

1. Step 1: Move head to next node

   Assign head to head.next to remove the first node reference.

2. Step 2: Update new head's prev pointer

   Set head.prev to null to disconnect backward link from old first node.

3. Final Answer:

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

4. Quick Check:

   Correct syntax updates head and prev pointer [OK]

Hint: Update head first, then set new head.prev to null [OK]

Common Mistakes:

• Setting head.prev before moving head
• Setting head.next to null incorrectly
• Nullifying head before updating pointers

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

medium

A. 30 <-> null

B. 10 <-> 30 <-> null

C. 20 <-> 30 <-> null

D. null

Solution

1. Step 1: Identify the first node

   The first node is 10, which will be removed.

2. Step 2: Update head to second node

   Head moves to 20, and 20.prev is set to null.

3. Final Answer:

   20 <-> 30 <-> null -> Option C

4. Quick Check:

   First node removed, list starts at 20 [OK]

Hint: After deletion, list starts from second node [OK]

Common Mistakes:

• Leaving old head in list
• Not updating prev pointer of new head
• Removing wrong node

4. Given this code snippet to delete the first node, what is the error?

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

medium

A. head.prev assignment causes error if list has one node

B. No error, code works fine

C. head.next should be assigned to null before head update

D. head should be set to null before updating prev

Solution

1. Step 1: Check list with one node

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

2. Step 2: Accessing head.prev causes error

   head is now null, so head.prev causes runtime error (cannot read property 'prev' of null).

3. Final Answer:

   head.prev assignment causes error if list has one node -> Option A

4. Quick Check:

   Null head causes error on prev access [OK]

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

Common Mistakes:

• Not handling single-node list case
• Accessing properties of null head
• Assuming list always has multiple nodes

5. You have a doubly linked list with nodes: 5 <-> 15 <-> 25 <-> 35 <-> null. Write a function to delete the first node and return the updated list head. What will be the list after deletion?

hard

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

B. 5 <-> 25 <-> 35 <-> null

C. 25 <-> 35 <-> null

D. null

Solution

1. Step 1: Move head to next node

   Head moves from 5 to 15, the second node.

2. Step 2: Set new head's prev to null

   Set 15.prev = null to disconnect from old first node.

3. Step 3: Return updated head

   Return the new head pointing to 15.

4. Final Answer:

   15 <-> 25 <-> 35 <-> null -> Option A

5. Quick Check:

   First node removed, list starts at 15 [OK]

Hint: Update head and set new head.prev to null [OK]

Common Mistakes:

• Not updating prev pointer of new head
• Returning old head instead of new head
• Deleting wrong node or skipping nodes