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

Time Complexity: Insert at End of Doubly Linked List

O(n)

Understanding Time Complexity

We want to understand how the time to insert a new item at the end of a doubly linked list changes as the list grows.

How does the number of steps needed grow when the list gets longer?

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 insertAtEnd(head: Node | null, value: number): Node {
  const newNode = new Node(value);
  if (!head) return newNode;
  let current = head;
  while (current.next) {
    current = current.next;
  }
  current.next = newNode;
  newNode.prev = current;
  return head;
}
    

This code adds a new node with the given value at the end of a doubly linked list by walking through the list from the start.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through each node until the last one.
• How many times: It runs once for each node in the list until the end is reached.

How Execution Grows With Input

As the list gets longer, the time to find the end grows roughly in direct proportion to the number of nodes.

Input Size (n)	Approx. Operations
10	About 10 steps to reach the end
100	About 100 steps to reach the end
1000	About 1000 steps to reach the end

Pattern observation: The steps increase linearly as the list size grows.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert at the end grows directly with the number of nodes in the list.

Common Mistake

[X] Wrong: "Inserting at the end is always fast and takes constant time."

[OK] Correct: Without a pointer to the last node, we must walk through the whole list, so time grows with list size.

Interview Connect

Understanding this helps you explain how linked lists work and why keeping track of the tail node can speed up insertions.

Self-Check

"What if we kept a direct reference to the last node? How would the time complexity change?"

Practice

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

easy

A. To add a new element after the last node

B. To remove the first node

C. To reverse the list

D. To find the middle node

Solution

1. Step 1: Understand the structure of a doubly linked list

   A doubly linked list has nodes connected forward and backward, allowing traversal in both directions.

2. Step 2: Purpose of insertion at the end

   Inserting at the end means adding a new node after the current last node, updating pointers accordingly.

3. Final Answer:

   To add a new element after the last node -> Option A

4. Quick Check:

   Insert at end = add after last node [OK]

Hint: Insert at end means add after last node [OK]

Common Mistakes:

• Confusing insertion at end with deletion
• Thinking insertion reverses the list
• Assuming insertion happens at the start

2. Which of the following TypeScript code snippets correctly initializes a new node for a doubly linked list?

easy

A. const newNode = { data: 5, next: undefined };

B. const newNode = { data: 5, next: null, prev: null };

C. const newNode = { value: 5, nextNode: null };

D. const newNode = { data: 5 };

Solution

1. Step 1: Identify required properties for a doubly linked list node

   A node must have data, next pointer, and prev pointer to link both directions.

2. Step 2: Check each option for correct properties

   const newNode = { data: 5, next: null, prev: null }; has data, next, and prev all properly set. Others miss prev or use wrong property names.

3. Final Answer:

   const newNode = { data: 5, next: null, prev: null }; -> Option B

4. Quick Check:

   Node needs data, next, prev [OK]

Hint: Node needs data, next, and prev properties [OK]

Common Mistakes:

• Omitting prev pointer
• Using wrong property names like value or nextNode
• Setting next or prev as undefined instead of null

3. Given the following TypeScript code for inserting at the end of a doubly linked list, 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; }
}

class DoublyLinkedList {
  head: Node | null = null;

  insertAtEnd(data: number) {
    const newNode = new Node(data);
    if (!this.head) {
      this.head = newNode;
      return;
    }
    let temp = this.head;
    while (temp.next) {
      temp = temp.next;
    }
    temp.next = newNode;
    newNode.prev = temp;
  }

  printList() {
    let temp = this.head;
    let result = '';
    while (temp) {
      result += temp.data + ' -> ';
      temp = temp.next;
    }
    result += 'null';
    console.log(result);
  }
}

const dll = new DoublyLinkedList();
dll.insertAtEnd(10);
dll.insertAtEnd(20);
dll.insertAtEnd(30);
dll.printList();

medium

A. 10 -> 20 -> 30 -> null

B. 30 -> 20 -> 10 -> null

C. 10 -> 20 -> null

D. null

Solution

1. Step 1: Trace insertAtEnd calls

   First insert adds 10 as head. Second adds 20 after 10. Third adds 30 after 20.

2. Step 2: Trace printList output

   Print starts at head (10), then 20, then 30, then null.

3. Final Answer:

   10 -> 20 -> 30 -> null -> Option A

4. Quick Check:

   Inserted nodes in order = 10 -> 20 -> 30 [OK]

Hint: Insertion at end appends nodes in order [OK]

Common Mistakes:

• Confusing order and printing reversed list
• Missing last inserted node
• Printing null instead of list

4. Identify the error in the following TypeScript method for inserting at the end of a doubly linked list:

insertAtEnd(data: number) {
  const newNode = new Node(data);
  if (!this.head) {
    this.head = newNode;
  }
  let temp = this.head;
  while (temp.next) {
    temp = temp.next;
  }
  temp.next = newNode;
  newNode.prev = temp;
}

medium

A. newNode should be created outside the method

B. Incorrect assignment of newNode.prev

C. Loop condition should be temp !== null

D. Missing return after setting head when list is empty

Solution

1. Step 1: Analyze empty list case

   If head is null, method sets head to newNode but continues to loop and assign next, causing error.

2. Step 2: Fix by adding return after setting head

   Adding return after setting head prevents further code execution and avoids null pointer errors.

3. Final Answer:

   Missing return after setting head when list is empty -> Option D

4. Quick Check:

   Return after head set avoids errors [OK]

Hint: Return immediately after setting head if list empty [OK]

Common Mistakes:

• Not returning after setting head
• Misunderstanding loop condition
• Incorrect pointer assignments

5. You want to insert a new node with data 40 at the end of a doubly linked list that currently has nodes 10 <-> 20 <-> 30. After insertion, what will be the correct state of the list including the prev and next pointers of the new node?

hard

A. 10 <-> 20 <-> 30, with 40.prev and 40.next both null (not linked)

B. 40 <-> 10 <-> 20 <-> 30, where 40.next points to 10 and 40.prev is null

C. 10 <-> 20 <-> 30 <-> 40, where 40.prev points to 30 and 40.next is null

D. 10 <-> 20 <-> 30 <-> 40, where 40.prev and 40.next both point to null

Solution

1. Step 1: Understand insertion at end

   The new node 40 should be linked after 30, so 30.next = 40 and 40.prev = 30.

2. Step 2: Confirm pointers of new node

   Since 40 is last, 40.next must be null to mark list end.

3. Final Answer:

   10 <-> 20 <-> 30 <-> 40, where 40.prev points to 30 and 40.next is null -> Option C

4. Quick Check:

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

Hint: New tail node prev = old tail, next = null [OK]

Common Mistakes:

• Setting new node's next pointer incorrectly
• Not linking new node's prev pointer
• Inserting new node at start instead of end