Create and Initialize Doubly Linked List in DSA Javascript - Time & Space Complexity

Time Complexity: Create and Initialize Doubly Linked List

O(n)

Understanding Time Complexity

When we create and initialize a doubly linked list, we want to know how the time needed grows as we add more items.

We ask: How long does it take to build the list as it gets 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 createDoublyLinkedList(arr) {
  let head = null;
  let tail = null;
  for (let val of arr) {
    const newNode = new Node(val);
    if (!head) {
      head = newNode;
      tail = newNode;
    } else {
      tail.next = newNode;
      newNode.prev = tail;
      tail = newNode;
    }
  }
  return head;
}
    

This code builds a doubly linked list from an array by adding nodes one by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each element of the input array once.
• How many times: Exactly once per element, so n times if the array has n items.

How Execution Grows With Input

Each new item in the array causes one new node to be created and linked.

Input Size (n)	Approx. Operations
10	About 10 node creations and linkings
100	About 100 node creations and linkings
1000	About 1000 node creations and linkings

Pattern observation: The work grows directly with the number of items; doubling items doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to create the list grows in a straight line with the number of items.

Common Mistake

[X] Wrong: "Creating a doubly linked list takes more than linear time because of the extra pointers."

[OK] Correct: Each node is created once and linked in constant time; the extra pointers do not add extra loops or repeated work.

Interview Connect

Understanding this helps you explain how data structures build up efficiently, a key skill in many coding challenges.

Self-Check

"What if we added a nested loop to link nodes in pairs? How would the time complexity change?"

Practice

1. What is the main difference between a doubly linked list and a singly linked list?

easy

A. A doubly linked list has nodes with pointers to both previous and next nodes.

B. A doubly linked list stores data in arrays instead of nodes.

C. A doubly linked list can only be traversed forward.

D. A doubly linked list does not use pointers at all.

Solution

1. Step 1: Understand node structure in doubly linked list

   Each node in a doubly linked list has two pointers: one to the next node and one to the previous node.

2. Step 2: Compare with singly linked list

   Singly linked list nodes have only one pointer to the next node, so they cannot go backward.

3. Final Answer:

   A doubly linked list has nodes with pointers to both previous and next nodes. -> Option A

4. Quick Check:

   Doubly linked list = two pointers per node [OK]

Hint: Remember: doubly linked means two directions [OK]

Common Mistakes:

• Thinking doubly linked lists use arrays
• Believing doubly linked lists only go forward
• Confusing pointers with data storage

2. Which of the following is the correct way to define a Node class for a doubly linked list in JavaScript?

easy

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

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

C. class Node { constructor(data) { this.data = data; this.left = null; this.right = null; } }

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

Solution

1. Step 1: Identify required pointers for doubly linked list node

   A doubly linked list node needs both 'prev' and 'next' pointers initialized to null.

2. Step 2: Check constructor parameters and properties

   class Node { constructor(data) { this.data = data; this.prev = null; this.next = null; } } correctly defines 'data', 'prev', and 'next' properties in the constructor.

3. Final Answer:

   class Node { constructor(data) { this.data = data; this.prev = null; this.next = null; } } -> Option B

4. Quick Check:

   Node needs prev and next pointers [OK]

Hint: Doubly linked nodes have both prev and next [OK]

Common Mistakes:

• Omitting the prev pointer
• Using wrong pointer names like left/right
• Using different property names for data

3. What will be the output of the following code snippet?

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

class DoublyLinkedList {
  constructor() {
    this.head = null;
    this.tail = null;
  }
  append(data) {
    const newNode = new Node(data);
    if (!this.head) {
      this.head = newNode;
      this.tail = newNode;
    } else {
      this.tail.next = newNode;
      newNode.prev = this.tail;
      this.tail = newNode;
    }
  }
}

const list = new DoublyLinkedList();
list.append(1);
list.append(2);
list.append(3);

let current = list.head;
const result = [];
while (current) {
  result.push(current.data);
  current = current.next;
}
console.log(result);

medium

A. []

B. [3, 2, 1]

C. [null, null, null]

D. [1, 2, 3]

Solution

1. Step 1: Append nodes 1, 2, 3 to the list

   Each append adds a new node at the tail, linking prev and next pointers correctly.

2. Step 2: Traverse from head to tail collecting data

   Starting at head (1), moving next collects 1, then 2, then 3, then stops at null.

3. Final Answer:

   [1, 2, 3] -> Option D

4. Quick Check:

   Traversal from head collects [1, 2, 3] [OK]

Hint: Traverse from head using next to get list order [OK]

Common Mistakes:

• Confusing traversal direction
• Not updating tail pointer on append
• Pushing null values instead of data

4. Identify the error in the following code that tries to append a node to a doubly linked list:

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

class DoublyLinkedList {
  constructor() {
    this.head = null;
    this.tail = null;
  }
  append(data) {
    const newNode = new Node(data);
    if (!this.head) {
      this.head = newNode;
      this.tail = newNode;
    } else {
      this.tail.next = newNode;
      this.tail.prev = newNode;
      this.tail = newNode;
    }
  }
}

medium

A. The constructor is missing initialization of head and tail.

B. The newNode should not have prev or next pointers.

C. The line 'this.tail.prev = newNode;' should be 'newNode.prev = this.tail;'.

D. The append method should not update the tail pointer.

Solution

1. Step 1: Analyze pointer updates in append method

   When adding newNode, the previous tail's next should point to newNode, and newNode's prev should point to old tail.

2. Step 2: Identify incorrect pointer assignment

   The code incorrectly sets 'this.tail.prev = newNode;' which wrongly changes the old tail's prev pointer instead of newNode's prev pointer.

3. Final Answer:

   The line 'this.tail.prev = newNode;' should be 'newNode.prev = this.tail;'. -> Option C

4. Quick Check:

   Correct prev pointer must link newNode to old tail [OK]

Hint: Prev pointer goes from new node back to old tail [OK]

Common Mistakes:

• Swapping prev and next pointers
• Not updating newNode.prev correctly
• Forgetting to update tail pointer

5. You want to create a doubly linked list from an array of values [10, 20, 30] and then traverse it backward from tail to head. Which code snippet correctly initializes the list and prints the values backward?

hard

A. const list = new DoublyLinkedList();
for (const val of [10, 20, 30]) list.append(val);
let current = list.tail;
while (current) { console.log(current.data); current = current.prev; }

B. const list = new DoublyLinkedList();
for (let i = 2; i >= 0; i--) list.append([10, 20, 30][i]);
let current = list.head;
while (current) { console.log(current.data); current = current.next; }

C. const list = new DoublyLinkedList();
for (const val of [10, 20, 30]) list.append(val);
let current = list.head;
while (current) { console.log(current.data); current = current.prev; }

D. const list = new DoublyLinkedList();
for (const val of [10, 20, 30]) list.append(val);
let current = list.tail;
while (current) { console.log(current.data); current = current.next; }

Solution

1. Step 1: Append values in order to the list

   Using a for-of loop appends 10, then 20, then 30, building the list head to tail.

2. Step 2: Traverse backward from tail using prev pointer

   Starting at tail (30), moving prev prints 30, 20, 10 in reverse order.

3. Final Answer:

   const list = new DoublyLinkedList(); for (const val of [10, 20, 30]) list.append(val); let current = list.tail; while (current) { console.log(current.data); current = current.prev; } -> Option A

4. Quick Check:

   Backward traversal uses tail and prev pointer [OK]

Hint: Traverse backward from tail using prev pointer [OK]

Common Mistakes:

• Traversing backward from head
• Using next pointer to go backward
• Appending values in reverse order but traversing forward