Delete from Beginning of Doubly Linked List in DSA Typescript - 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 {
  value: number;
  next: Node | null = null;
  prev: Node | null = null;
  constructor(value: number) { this.value = value; }
}

function deleteFromBeginning(head: Node | null): Node | null {
  if (!head) return null;
  const 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 a few pointers (head, head.next, head.next.prev).
• 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	2-3 pointer updates
100	2-3 pointer updates
1000	2-3 pointer updates

Pattern observation: The number of steps stays the same regardless of list size.

Final Time Complexity

Time Complexity: O(1)

This means deleting from the start takes a fixed amount of time no matter how long 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, so the list size does not affect the time.

Interview Connect

Knowing this helps you explain why some operations are quick even on big lists, showing you understand data structure efficiency.

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 moves to the previous node

B. It becomes null immediately

C. It stays pointing to the deleted node

D. It moves to the next 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 list.

2. Step 2: Effect of deleting the first node

   When the first node is deleted, head must point to the next node to keep the list accessible.

3. Final Answer:

   It moves to the next node in the list -> Option D

4. Quick Check:

   head points to next node after deletion [OK]

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

Common Mistakes:

• Setting head to null without checking if list is empty
• Not updating head after deletion
• Pointing head to deleted node

2. Which of the following is the correct TypeScript syntax to delete the first node from a doubly linked list assuming head is the pointer to the first node?

easy

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

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

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

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

Solution

1. Step 1: Move head to next node

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

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

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

3. Final Answer:

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

4. Quick Check:

   Correct syntax to update head and prev pointer [OK]

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

Common Mistakes:

• Setting head.prev before moving head
• Assigning head.prev to null before head changes
• Setting head.next to null incorrectly

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

medium

A. 20 <-> 30 <-> null

B. 10 <-> 30 <-> null

C. 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 next node

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

3. Final Answer:

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

4. Quick Check:

   First node removed, list starts at 20 [OK]

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

Common Mistakes:

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

4. Consider this TypeScript 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.prev should not be set to null

B. Syntax error due to missing semicolon

C. Runtime error if list has only one node

D. No error, code is correct

Solution

1. Step 1: Check condition when list has one node

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

2. Step 2: Accessing head.prev causes error

   head becomes null, so head.prev causes runtime error (cannot access property of null).

3. Final Answer:

   Runtime error if list has only one node -> Option C

4. Quick Check:

   Null pointer access error possible [OK]

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

Common Mistakes:

• Not checking if head is null after moving to next
• Assuming list always has multiple nodes
• Ignoring runtime null errors

5. You have a doubly linked list with nodes: 5 <-> 15 <-> 25 <-> 35 <-> null. Write the correct sequence of operations to delete the first node safely, considering the list might have only one node.

hard

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

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

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

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

Solution

1. Step 1: Check if list is empty

   First, verify head is not null to avoid errors on empty list.

2. Step 2: Move head to next node and check again

   After moving head, check if new head is not null before setting prev to null.

3. Final Answer:

   if (head !== null) { head = head.next; if (head !== null) head.prev = null; } -> Option B

4. Quick Check:

   Safe deletion with null checks [OK]

Hint: Always check for null before accessing pointers [OK]

Common Mistakes:

• Not checking if head is null after moving
• Setting prev pointer without null check
• Assuming list has multiple nodes always