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

Time Complexity: Insert at End of Doubly Linked List

O(1)

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 {
  constructor(data) {
    this.data = data;
    this.next = null;
    this.prev = null;
  }
}

class DoublyLinkedList {
  constructor() {
    this.head = null;
    this.tail = null;
  }

  insertAtEnd(data) {
    const newNode = new Node(data);
    if (!this.tail) {
      this.head = newNode;
      this.tail = newNode;
      return;
    }
    this.tail.next = newNode;
    newNode.prev = this.tail;
    this.tail = newNode;
  }
}
    

This code adds a new node at the end of a doubly linked list by updating the tail pointer and linking nodes.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating a new node and updating pointers.
• How many times: Exactly once per insertion, no loops or traversals.

How Execution Grows With Input

Each insertion does a fixed number of steps regardless of list size.

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

Pattern observation: The number of steps stays the same no matter how long the list is.

Final Time Complexity

Time Complexity: O(1)

This means inserting at the end takes the same small amount of time no matter how big the list is.

Common Mistake

[X] Wrong: "Inserting at the end takes longer as the list grows because you have to walk through the list to find the end."

[OK] Correct: Because the list keeps a direct pointer to the tail, it does not need to walk through the list. It updates pointers directly in constant time.

Interview Connect

Understanding this helps you explain why doubly linked lists are useful for quick insertions at both ends, a common question in coding interviews.

Self-Check

"What if we did not keep a tail pointer and had to find the end each time? 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 reverse the order of the nodes in the list

B. To remove the first node from the list

C. To add a new element after the last node, updating both next and previous links

D. To find the middle node of the list

Solution

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

   A doubly linked list has nodes with pointers to both the next and previous nodes, 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 and updating the pointers accordingly.

3. Final Answer:

   To add a new element after the last node, updating both next and previous links -> Option C

4. Quick Check:

   Insert at end = Add after last node [OK]

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

Common Mistakes:

• Confusing insertion at end with deletion
• Not updating previous pointer of new node
• Trying to insert at beginning instead

2. Which of the following is the correct syntax to create a new node in JavaScript for a doubly linked list?

easy

A. const newNode = new Node(value);

B. const newNode = { value: data, nextNode: null };

C. const newNode = [value, null, null];

D. const newNode = { data: value, next: null, prev: null };

Solution

1. Step 1: Identify the node structure for doubly linked list

   A node should have data, next pointer, and previous pointer properties.

2. Step 2: Check each option for correct properties

   const newNode = { data: value, next: null, prev: null }; correctly uses data, next, and prev keys with null pointers initially.

3. Final Answer:

   const newNode = { data: value, next: null, prev: null }; -> Option D

4. Quick Check:

   Node = data + next + prev [OK]

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

Common Mistakes:

• Using wrong property names like value instead of data
• Missing prev pointer in node
• Using array instead of object for node

3. Consider the following code snippet that inserts nodes at the end of a doubly linked list. What will be the printed list after inserting 10, 20, and 30?

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

class DoublyLinkedList {
  constructor() {
    this.head = null;
  }

  insertAtEnd(data) {
    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. null

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

C. 10 -> 20 -> null

D. 30 -> 20 -> 10 -> null

Solution

1. Step 1: Insert nodes one by one at the end

   First insert 10 as head, then 20 after 10, then 30 after 20.

2. Step 2: Print the list from head to end

   Traverse from head: 10 -> 20 -> 30 -> null is printed.

3. Final Answer:

   10 -> 20 -> 30 -> null -> Option B

4. Quick Check:

   Insert order = print order [OK]

Hint: Insert at end keeps order; print from head shows insertion order [OK]

Common Mistakes:

• Confusing insertion order with reversed output
• Not updating prev pointer causing broken links
• Printing from tail instead of head

4. The following code tries to insert a node at the end of a doubly linked list but causes an error. What is the mistake?

insertAtEnd(data) {
  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. Missing return after setting head when list is empty

B. Incorrectly assigning newNode.prev instead of newNode.next

C. Not creating newNode with correct constructor

D. Using while loop instead of for loop

Solution

1. Step 1: Analyze the empty list case

   If head is null, newNode is assigned as head but code continues to traverse and assign next pointers.

2. Step 2: Identify missing return causing duplicate insertion

   Without return after setting head, code tries to add newNode again after head, causing a cycle or error.

3. Final Answer:

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

4. Quick Check:

   Return after empty insert prevents duplicate links [OK]

Hint: Return immediately after empty list insertion [OK]

Common Mistakes:

• Forgetting to stop function after empty list insert
• Mixing up prev and next pointers
• Assuming loop type causes error

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

hard

A. 10 -> 20 -> 30 -> 40 -> null, newNode.prev points to 30, newNode.next is null

B. 40 -> 10 -> 20 -> 30 -> null, newNode.prev is null, newNode.next points to 10

C. 10 -> 20 -> 30 -> null, newNode.prev and newNode.next both null

D. 10 -> 20 -> 30 -> 40 -> null, newNode.prev is null, newNode.next points to 30

Solution

1. Step 1: Insert new node at the end

   New node with value 40 is added after node 30, so 30's next points to new node.

2. Step 2: Set new node's pointers correctly

   New node's prev points to 30, and next is null because it's the last node.

3. Final Answer:

   10 -> 20 -> 30 -> 40 -> null, newNode.prev points to 30, newNode.next is null -> Option A

4. Quick Check:

   Last node's next = null, newNode.prev = previous last node [OK]

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

Common Mistakes:

• Setting newNode.prev to null incorrectly
• Placing new node at the beginning instead
• Not updating previous last node's next pointer