Dequeue Operation in DSA Javascript - Time & Space Complexity

Time Complexity: Dequeue Operation

O(n)

Understanding Time Complexity

We want to understand how long it takes to remove an item from a dequeue (double-ended queue).

Specifically, how the time changes as the number of items grows.

Scenario Under Consideration

Analyze the time complexity of the dequeue operation removing from the front.

class Dequeue {
  constructor() {
    this.items = [];
  }

  dequeueFront() {
    if (this.items.length === 0) return null;
    return this.items.shift();
  }
}
    

This code removes the first item from the dequeue using the array's shift method.

Identify Repeating Operations

Look at what happens when we remove from the front.

• Primary operation: Removing the first element with shift().
• How many times: Each removal shifts all remaining items one position left.

How Execution Grows With Input

When we remove one item, all other items move one step forward.

Input Size (n)	Approx. Operations
10	About 9 moves
100	About 99 moves
1000	About 999 moves

Pattern observation: The number of moves grows roughly the same as the number of items.

Final Time Complexity

Time Complexity: O(n)

This means removing from the front takes longer as the dequeue grows because all items must shift.

Common Mistake

[X] Wrong: "Removing from the front is always fast and constant time like popping from the end."

[OK] Correct: Because shifting all elements after removal takes time proportional to the number of items.

Interview Connect

Understanding this helps you explain why some dequeue implementations use linked lists to get faster removals from both ends.

Self-Check

"What if we used a linked list instead of an array for the dequeue? How would the time complexity of removing from the front change?"

Practice

1. What is a dequeue in data structures?

easy

A. A stack that allows only last-in, first-out operations

B. A queue where elements can only be added at the front

C. A list that only allows insertion at the middle

D. A double-ended queue where elements can be added or removed from both ends

Solution

1. Step 1: Understand the definition of dequeue

   A dequeue is a data structure that allows insertion and deletion from both front and rear ends.

2. Step 2: Compare options with definition

   A double-ended queue where elements can be added or removed from both ends correctly describes a dequeue. Options A, B, and D describe other structures or incorrect behaviors.

3. Final Answer:

   A double-ended queue where elements can be added or removed from both ends -> Option D

4. Quick Check:

   Dequeue = Double-ended queue [OK]

Hint: Dequeue means double-ended queue, both ends allowed [OK]

Common Mistakes:

• Confusing dequeue with stack or normal queue
• Thinking elements can only be added at one end
• Assuming dequeue is a type of list

2. Which of the following is the correct syntax to add an element 5 at the front of a dequeue named dq in JavaScript using an array?

easy

A. dq.pushFront(5);

B. dq.unshift(5);

C. dq.addFront(5);

D. dq.insertFront(5);

Solution

1. Step 1: Recall JavaScript array methods for front insertion

   JavaScript arrays use unshift() to add elements at the front.

2. Step 2: Match method with options

   Only dq.unshift(5); uses unshift(5), which is correct. Other options are invalid methods.

3. Final Answer:

   dq.unshift(5); -> Option B

4. Quick Check:

   Array front insert = unshift() [OK]

Hint: Use unshift() to add at front in JS arrays [OK]

Common Mistakes:

• Using pushFront which is not a JS array method
• Confusing push (adds at end) with front insertion
• Assuming addFront or insertFront exist in JS arrays

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

let dq = [];
dq.push(10);
dq.unshift(20);
dq.push(30);
dq.shift();
console.log(dq);

medium

A. [10, 30]

B. [20, 10, 30]

C. [20, 30]

D. [10, 20, 30]

Solution

1. Step 1: Trace each operation on the dequeue array

   Start with empty dq = []. push(10) adds 10 at end: [10]. unshift(20) adds 20 at front: [20, 10]. push(30) adds 30 at end: [20, 10, 30]. shift() removes front element (20): [10, 30].

2. Step 2: Determine final state of dq

   After all operations, dq is [10, 30].

3. Final Answer:

   [10, 30] -> Option A

4. Quick Check:

   After shift(), front removed, dq = [10, 30] [OK]

Hint: Remember shift() removes front, push() adds end [OK]

Common Mistakes:

• Confusing shift() with pop()
• Mixing order of unshift and push
• Forgetting shift() removes front element

4. Identify the error in the following dequeue operation code:

let dq = [];
dq.push(1);
dq.popFront();
console.log(dq);

medium

A. popFront() is not a valid JavaScript array method

B. push() cannot be used on empty arrays

C. popFront() should be pop() to remove last element

D. dq should be initialized as a Dequeue object, not array

Solution

1. Step 1: Check JavaScript array methods used

   JavaScript arrays do not have a method named popFront(). The correct method to remove front element is shift().

2. Step 2: Identify the error

   Using popFront() causes a runtime error as it is undefined.

3. Final Answer:

   popFront() is not a valid JavaScript array method -> Option A

4. Quick Check:

   popFront() invalid in JS arrays [OK]

Hint: Use shift() to remove front, pop() for end [OK]

Common Mistakes:

• Assuming popFront() exists like pop()
• Confusing pop() with front removal
• Not knowing shift() removes front element

5. You have a dequeue implemented as a JavaScript array dq with elements [5, 10, 15, 20]. You want to remove the element 5 from the front and add 25 at the rear, then remove the element 20 from the rear and add 30 at the front. What will be the final state of dq?

hard

A. [30, 5, 10, 15, 25]

B. [10, 15, 25, 30]

C. [30, 10, 15, 25]

D. [10, 15, 20, 25, 30]

Solution

1. Step 1: Remove front element

   Start dq = [5, 10, 15, 20]. Remove front element 5 using shift(): dq = [10, 15, 20]. Rear is now 20.

2. Step 2: Remove rear, add rear, add front

   Remove rear element 20 using pop(): dq = [10, 15]. Add 25 at rear using push(): dq = [10, 15, 25]. Add 30 at front using unshift(): dq = [30, 10, 15, 25].

3. Final Answer:

   [30, 10, 15, 25] -> Option C

4. Quick Check:

   Front removed 5, rear removed 20, added 30 front, 25 rear [OK]

Hint: Use shift/pop for removal, unshift/push for addition [OK]

Common Mistakes:

• Removing wrong elements from front or rear
• Mixing order of operations
• Using pop() instead of shift() for front removal