Enqueue Operation in DSA Typescript - Time & Space Complexity

Time Complexity: Enqueue Operation

O(1)

Understanding Time Complexity

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

How does the enqueue operation's speed depend on the number of items already in the queue?

Scenario Under Consideration

Analyze the time complexity of the enqueue operation in a queue implemented with a linked list.

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

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

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

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

Identify Repeating Operations

Look for loops or repeated steps that grow with input size.

• Primary operation: Adding a new node and updating pointers.
• How many times: Exactly once per enqueue call, no loops involved.

How Execution Grows With Input

Each enqueue adds one node by updating a few pointers, no matter how big the queue is.

Input Size (n)	Approx. Operations
10	3-4 pointer updates
100	3-4 pointer updates
1000	3-4 pointer updates

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

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: "Enqueue takes longer as the queue grows because it has to find the end each time."

[OK] Correct: The queue keeps a direct pointer to the end (tail), so it does not search; it just updates pointers quickly.

Interview Connect

Understanding that enqueue is fast and constant time helps you explain efficient queue operations clearly in interviews.

Self-Check

What if the queue was implemented using an array without a tail pointer? How would the enqueue time complexity change?

Practice

1. What does the enqueue operation do in a queue data structure?

easy

A. Adds an element to the end of the queue

B. Removes an element from the front of the queue

C. Checks if the queue is empty

D. Returns the size of the queue

Solution

1. Step 1: Understand the queue structure

   A queue works like a line where elements are added at the back and removed from the front.

2. Step 2: Define the enqueue operation

   Enqueue means adding a new element to the end of the queue, so it waits its turn.

3. Final Answer:

   Adds an element to the end of the queue -> Option A

4. Quick Check:

   Enqueue = Add at end [OK]

Hint: Enqueue means add at the back of the queue [OK]

Common Mistakes:

• Confusing enqueue with dequeue (removal)
• Thinking enqueue checks queue size
• Assuming enqueue removes elements

2. Which of the following is the correct TypeScript syntax to add an element 5 to a queue represented by an array queue?

easy

A. queue.pop(5);

B. queue.push(5);

C. queue.shift(5);

D. queue.unshift(5);

Solution

1. Step 1: Identify array methods for queue operations

   In TypeScript, push adds an element at the end, which matches enqueue.

2. Step 2: Match enqueue with correct method

   pop removes from end, shift removes from front, unshift adds at front. So only push adds at the end.

3. Final Answer:

   queue.push(5); -> Option B

4. Quick Check:

   Enqueue uses push() to add at end [OK]

Hint: Use push() to add at end of array for enqueue [OK]

Common Mistakes:

• Using pop() which removes instead of adds
• Using shift() or unshift() which affect front of queue
• Confusing push() with unshift()

3. What will be the state of the queue after executing the following TypeScript code?

let queue: number[] = [10, 20, 30];
queue.push(40);
queue.push(50);

medium

A. [10, 20, 30, 40, 50]

B. [50, 40, 10, 20, 30]

C. [10, 20, 30]

D. [40, 50]

Solution

1. Step 1: Start with initial queue

   The queue starts as [10, 20, 30].

2. Step 2: Apply enqueue operations

   First, push(40) adds 40 at the end: [10, 20, 30, 40]. Then push(50) adds 50 at the end: [10, 20, 30, 40, 50].

3. Final Answer:

   [10, 20, 30, 40, 50] -> Option A

4. Quick Check:

   push adds at end, final queue = [10,20,30,40,50] [OK]

Hint: push() adds elements at the end in order [OK]

Common Mistakes:

• Thinking push adds at front
• Ignoring second push operation
• Confusing push with pop or shift

4. Identify the error in the following TypeScript code that tries to enqueue an element 25 to a queue represented by an array queue:

let queue: number[] = [5, 10, 15];
queue.pop(25);

medium

A. The element 25 should be added using shift

B. pop adds element at the front, so wrong method

C. The queue array is not initialized properly

D. pop does not take arguments and removes from the end

Solution

1. Step 1: Understand pop() method behavior

   pop() removes the last element from the array and does not accept any arguments.

2. Step 2: Identify misuse of pop()

   Calling pop(25) is incorrect because pop() cannot add elements; it only removes.

3. Final Answer:

   pop does not take arguments and removes from the end -> Option D

4. Quick Check:

   pop() removes, push() adds [OK]

Hint: pop() removes last element; push() adds at end [OK]

Common Mistakes:

• Using pop() to add elements
• Confusing shift() and pop()
• Passing arguments to pop()

5. You have a queue implemented as an array in TypeScript. You want to enqueue multiple elements [100, 200, 300] at once while preserving order. Which code snippet correctly enqueues all elements in order?

hard

A. queue.unshift(100, 200, 300);

B. queue.push([100, 200, 300]);

C. queue.push(100, 200, 300);

D. queue.pop(100); queue.pop(200); queue.pop(300);

Solution

1. Step 1: Understand push with multiple arguments

   push() can take multiple arguments and adds them in order at the end of the array.

2. Step 2: Analyze each option

   queue.push(100, 200, 300); adds 100, 200, 300 in order at the end. queue.push([100, 200, 300]); adds a single array element, nesting the array. queue.unshift(100, 200, 300); adds elements at the front, reversing order. queue.pop(100); queue.pop(200); queue.pop(300); uses pop which removes elements, not adds.

3. Final Answer:

   queue.push(100, 200, 300); -> Option C

4. Quick Check:

   push(...items) adds all at end in order [OK]

Hint: Use push with multiple args to enqueue many elements [OK]

Common Mistakes:

• Using push with array argument nests array
• Using unshift adds at front, reversing order
• Using pop to add elements