Insert at Beginning of Doubly Linked List in DSA Typescript - Time & Space Complexity

Time Complexity: Insert at Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

We want to know how the time to add a new node at the start of a doubly linked list changes as the list grows.

How does the number of steps grow when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Node {
  data: number;
  prev: Node | null = null;
  next: Node | null = null;
  constructor(data: number) { this.data = data; }
}

function insertAtBeginning(head: Node | null, data: number): Node {
  const newNode = new Node(data);
  newNode.next = head;
  if (head !== null) head.prev = newNode;
  return newNode;
}
    

This code creates a new node and inserts it at the start of the doubly linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating and linking a single new node.
• How many times: Only once per insertion, no loops or recursion involved.

How Execution Grows With Input

Adding a node at the start always takes the same steps, no matter how big the list is.

Input Size (n)	Approx. Operations
10	4-5 steps
100	4-5 steps
1000	4-5 steps

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

Final Time Complexity

Time Complexity: O(1)

This means inserting at the beginning takes a constant amount of time no matter how large the list is.

Common Mistake

[X] Wrong: "Inserting at the start takes longer as the list grows because we have to move all nodes."

[OK] Correct: We only change a few pointers at the start; no need to move or visit other nodes.

Interview Connect

Knowing that insertion at the start is quick helps you explain efficient list operations clearly and confidently.

Self-Check

"What if we changed this to insert at the end of the doubly linked list without a tail pointer? How would the time complexity change?"

Practice

1. What is the main purpose of inserting a node at the beginning of a doubly linked list?

easy

A. To reverse the entire list

B. To add a new node after the tail node

C. To delete the first node in the list

D. To add a new node before the current head node

Solution

1. Step 1: Understand the head node position

   The head node is the first node in the doubly linked list.

2. Step 2: Insert new node before head

   Inserting at the beginning means placing the new node before the current head, making it the new head.

3. Final Answer:

   To add a new node before the current head node -> Option D

4. Quick Check:

   Insert at beginning = add before head [OK]

Hint: Beginning means before the head node [OK]

Common Mistakes:

• Confusing insertion at beginning with insertion at end
• Thinking insertion deletes nodes
• Mixing up head and tail nodes

2. Which of the following TypeScript code snippets correctly creates a new node and inserts it at the beginning of a doubly linked list?

easy

A. newNode.next = head; if(head) head.prev = newNode; head = newNode;

B. newNode.prev = head; if(head) head.next = newNode; head = newNode;

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

D. head = newNode; newNode.next = head; newNode.prev = head;

Solution

1. Step 1: Set newNode.next to current head

   The new node's next pointer should point to the current head node.

2. Step 2: Update current head's prev to newNode if head exists

   If the list is not empty, the current head's prev pointer must point back to the new node.

3. Step 3: Update head to newNode

   Finally, the head pointer is updated to the new node.

4. Final Answer:

   newNode.next = head; if(head) head.prev = newNode; head = newNode; -> Option A

5. Quick Check:

   Set newNode.next=head, head.prev=newNode, head=newNode [OK]

Hint: newNode.next = head; head.prev = newNode; head = newNode [OK]

Common Mistakes:

• Swapping next and prev pointers
• Not updating head pointer
• Setting newNode.prev incorrectly

3. Given the following TypeScript code for a doubly linked list insertion at beginning, what will be the printed list after insertion?

class Node {
  data: number;
  next: Node | null = null;
  prev: Node | null = null;
  constructor(data: number) { this.data = data; }
}

let head: Node | null = new Node(10);
head.next = new Node(20);
head.next.prev = head;

const newNode = new Node(5);
newNode.next = head;
head.prev = newNode;
head = newNode;

// Print list
let temp = head;
const result: number[] = [];
while(temp) {
  result.push(temp.data);
  temp = temp.next;
}
console.log(result);

medium

A. [5, 10, 20]

B. [10, 20, 5]

C. [20, 10, 5]

D. [5, 20, 10]

Solution

1. Step 1: Initial list before insertion

   List is 10 <-> 20, head points to 10.

2. Step 2: Insert newNode with data 5 at beginning

   newNode.next = head (10), head.prev = newNode, head = newNode (5).

3. Step 3: Traverse list from new head

   Traverse from 5: 5 -> 10 -> 20.

4. Final Answer:

   [5, 10, 20] -> Option A

5. Quick Check:

   New head 5 followed by 10 and 20 [OK]

Hint: New node becomes head, list order starts with new node [OK]

Common Mistakes:

• Not updating head to newNode
• Incorrectly linking prev pointers
• Printing list from old head

4. Identify the error in the following TypeScript code that attempts to insert a node at the beginning of a doubly linked list:

const newNode = new Node(15);
newNode.prev = null;
newNode.next = head;
head.prev = newNode;
head = newNode;

medium

A. newNode.prev should point to head

B. Missing check if head is null before accessing head.prev

C. head should be assigned before setting newNode.next

D. newNode.next should be null

Solution

1. Step 1: Check if head is null before accessing head.prev

   If the list is empty (head is null), accessing head.prev causes an error.

2. Step 2: Add condition to update head.prev only if head exists

   Use if(head) head.prev = newNode; to avoid runtime error.

3. Final Answer:

   Missing check if head is null before accessing head.prev -> Option B

4. Quick Check:

   Always check head before head.prev [OK]

Hint: Check if head exists before accessing its properties [OK]

Common Mistakes:

• Ignoring null head and causing runtime error
• Swapping next and prev pointers
• Assigning head too early

5. You have a doubly linked list with nodes containing values [30, 40, 50]. You want to insert a new node with value 20 at the beginning. After insertion, which of the following correctly represents the list and the pointers of the new head node?

hard

A. List: 20 <-> 30 <-> 40 <-> 50; new head prev points to 30, next = null

B. List: 30 <-> 40 <-> 50 <-> 20; new head prev = 50, next = null

C. List: 20 <-> 30 <-> 40 <-> 50; new head prev = null, next points to 30

D. List: 50 <-> 40 <-> 30 <-> 20; new head prev = null, next points to 40

Solution

1. Step 1: Insert new node with value 20 before current head 30

   New node becomes head, its prev is null, next points to old head (30).

2. Step 2: Update old head's prev to new node

   Old head (30) prev pointer updated to new node (20).

3. Step 3: Confirm list order and pointers

   List order is 20 <-> 30 <-> 40 <-> 50 with new head prev=null, next=30.

4. Final Answer:

   List: 20 <-> 30 <-> 40 <-> 50; new head prev = null, next points to 30 -> Option C

5. Quick Check:

   New head prev=null, next=old head [OK]

Hint: New head prev always null, next points to old head [OK]

Common Mistakes:

• Setting new head prev to old tail
• Reversing list order accidentally
• Not updating old head prev pointer