Enqueue Using Linked List in DSA Typescript - Time & Space Complexity

Time Complexity: Enqueue Using Linked List

O(1)

Understanding Time Complexity

We want to understand how the time needed to add an item to a queue changes as the queue grows.

Specifically, how long does it take to add one element at the end of a linked list?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

class Queue {
  tail: Node | null = null;
  head: Node | null = null;

  enqueue(value: number) {
    const newNode = new Node(value);
    if (this.tail) {
      this.tail.next = newNode;
      this.tail = newNode;
    } else {
      this.head = newNode;
      this.tail = newNode;
    }
  }
}
    

This code adds a new item to the end of a linked list representing a queue.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating a new node and updating the tail pointer.
• How many times: Exactly once per enqueue call, no loops or traversals.

How Execution Grows With Input

Adding one item always takes the same steps, no matter how big the queue is.

Input Size (n)	Approx. Operations
10	5-6 steps
100	5-6 steps
1000	5-6 steps

Pattern observation: The time to add does not grow with the queue size; it stays constant.

Final Time Complexity

Time Complexity: O(1)

This means adding an item takes the same short time no matter how many items are already in the queue.

Common Mistake

[X] Wrong: "Adding an item takes longer as the queue grows because we must find the end each time."

[OK] Correct: Because we keep a direct pointer to the end (tail), we do not search; we add instantly.

Interview Connect

Knowing this helps you explain why linked lists are good for queues and shows you understand efficient data structure design.

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 does the enqueue operation do in a linked list implementation of a queue?

easy

A. Removes the first element from the linked list

B. Adds a new element at the end (tail) of the linked list

C. Adds a new element at the beginning (head) of the linked list

D. Deletes the last element from the linked list

Solution

1. Step 1: Understand enqueue operation

   Enqueue means adding an element to the queue.

2. Step 2: Identify linked list position for enqueue

   In a linked list queue, new elements are added at the tail (end).

3. Final Answer:

   Adds a new element at the end (tail) of the linked list -> Option B

4. Quick Check:

   Enqueue = Add at tail [OK]

Hint: Enqueue always adds at the tail in linked list queue [OK]

Common Mistakes:

• Confusing enqueue with dequeue operation
• Adding new element at head instead of tail
• Thinking enqueue removes elements
• Mixing linked list positions

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

easy

A. newNode = new Node();

B. let newNode = Node(value);

C. const newNode = new Node(value);

D. const newNode = Node.new(value);

Solution

1. Step 1: Recall TypeScript class instantiation

   To create an object, use new ClassName(params).

2. Step 2: Check options for correct syntax

   Only const newNode = new Node(value); correctly creates a new Node instance.

3. Final Answer:

   const newNode = new Node(value); -> Option C

4. Quick Check:

   Use 'new' keyword to instantiate class [OK]

Hint: Use 'new' keyword to create class instances in TypeScript [OK]

Common Mistakes:

• Omitting 'new' keyword when creating objects
• Using function call syntax without 'new'
• Incorrect property access like Node.new
• Not declaring variable with let or const

3. What will be the state of the queue after executing the following enqueue operations on an empty linked list queue?

enqueue(10); enqueue(20); enqueue(30);

medium

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

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

C. null -> 10 -> 20 -> 30

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

Solution

1. Step 1: Understand enqueue order

   Enqueue adds elements at the tail, so order is preserved as inserted.

2. Step 2: Trace each enqueue

   After enqueue(10): 10 -> null
   After enqueue(20): 10 -> 20 -> null
   After enqueue(30): 10 -> 20 -> 30 -> null

3. Final Answer:

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

4. Quick Check:

   Enqueue order = insertion order [OK]

Hint: Enqueue adds at tail, so order stays same as insertion [OK]

Common Mistakes:

• Reversing order of elements after enqueue
• Confusing enqueue with push at head
• Misreading linked list direction
• Ignoring null at the end

4. Consider this enqueue function snippet for a linked list queue:

enqueue(value: number) {
  const newNode = new Node(value);
  if (!this.tail) {
    this.head = newNode;
    this.tail = newNode;
    return;
  }
  this.tail.next = newNode;
  this.tail = newNode;
}

What is the bug in this code?

medium

A. It does not update the previous tail's next pointer to newNode

B. It incorrectly sets head to null when queue is empty

C. It creates newNode without value

D. It sets tail to null after enqueue

Solution

1. Step 1: Analyze enqueue logic

   When queue is empty, head and tail should point to newNode.

2. Step 2: Check linking of nodes

   Code sets tail = newNode but does not link old tail's next to newNode, breaking chain.

3. Final Answer:

   It does not update the previous tail's next pointer to newNode -> Option A

4. Quick Check:

   Link old tail's next to newNode [OK]

Hint: Always link old tail's next to new node when enqueueing [OK]

Common Mistakes:

• Forgetting to update old tail's next pointer
• Not handling empty queue case properly
• Setting tail to null accidentally
• Creating node without value parameter

5. You have a linked list queue with elements: 5 -> 15 -> 25 -> null.
After enqueue(35), what will be the correct linked list representation and tail node value?

hard

A. 5 -> 15 -> 25 -> 35 -> null, tail value = 25

B. 35 -> 5 -> 15 -> 25 -> null, tail value = 25

C. 5 -> 15 -> 25 -> null, tail value = 25

D. 5 -> 15 -> 25 -> 35 -> null, tail value = 35

Solution

1. Step 1: Understand enqueue effect on queue

   Enqueue adds new element at tail, so 35 goes after 25.

2. Step 2: Update tail pointer

   Tail must point to the new last node, which holds 35.

3. Final Answer:

   5 -> 15 -> 25 -> 35 -> null, tail value = 35 -> Option D

4. Quick Check:

   Enqueue adds at tail, tail updates to new node [OK]

Hint: Tail always points to last enqueued node [OK]

Common Mistakes:

• Adding new node at head instead of tail
• Not updating tail pointer after enqueue
• Confusing tail value with head value
• Leaving tail pointing to old last node