Double Ended Queue Deque in DSA Javascript - Time & Space Complexity

Time Complexity: Double Ended Queue Deque

O(n) for front operations, O(1) for back operations

Understanding Time Complexity

We want to understand how fast operations on a double ended queue (deque) run as the number of items grows.

How does adding or removing items from either end affect the time it takes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Deque {
  constructor() {
    this.items = [];
  }
  addFront(element) {
    this.items.unshift(element);
  }
  addBack(element) {
    this.items.push(element);
  }
  removeFront() {
    return this.items.shift();
  }
  removeBack() {
    return this.items.pop();
  }
}
    

This code shows basic operations to add or remove items from the front or back of a deque using an array.

Identify Repeating Operations

Look at the main actions that repeat when we use the deque.

• Primary operation: Adding or removing items at the front or back.
• How many times: Each operation runs once per call, but some (like unshift and shift) move many items internally.

How Execution Grows With Input

Adding or removing at the back uses push/pop which take about the same time no matter how many items there are.

Adding or removing at the front uses unshift/shift which move all other items, so time grows with the number of items.

Input Size (n)	Approx. Operations for addFront/removeFront
10	10 moves
100	100 moves
1000	1000 moves

Pattern observation: Operations at the front take longer as the deque grows, while back operations stay fast.

Final Time Complexity

Time Complexity: O(n) for front operations, O(1) for back operations.

This means adding or removing at the back is quick no matter the size, but at the front it takes longer as the deque grows.

Common Mistake

[X] Wrong: "All deque operations take the same constant time."

[OK] Correct: Using arrays, front operations move many items, so they take longer as the deque grows, unlike back operations.

Interview Connect

Understanding these time differences helps you choose the right data structure and explain your choices clearly in interviews.

Self-Check

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

Practice

1. What is a Double Ended Queue (Deque)?

easy

A. A stack where elements are added and removed only from the top.

B. A queue where elements can only be added at the rear and removed from the front.

C. A data structure where elements can be added or removed from both front and rear ends.

D. A list that allows random access to elements by index.

Solution

1. Step 1: Understand the definition of Deque

   A Deque allows insertion and deletion at both ends, unlike a queue or stack which restrict operations to one end.

2. Step 2: Compare with other data structures

   Queue allows operations only at front and rear separately; stack only at one end; list allows random access but not double-ended insertion/removal.

3. Final Answer:

   A data structure where elements can be added or removed from both front and rear ends. -> Option C

4. Quick Check:

   Deque = double-ended queue [OK]

Hint: Deque means double-ended queue, both ends usable [OK]

Common Mistakes:

• Confusing deque with stack or simple queue
• Thinking deque allows random access by index
• Assuming deque operations only at one end

2. Which of the following is the correct way to add an element to the front of a deque named dq in JavaScript using an array?

easy

A. dq.unshift(element);

B. dq.pop(element);

C. dq.push(element);

D. dq.shift(element);

Solution

1. Step 1: Identify array methods for front insertion

   In JavaScript, unshift() adds an element to the start (front) of an array.

2. Step 2: Check other methods

   push() adds to the end, pop() removes from end, shift() removes from front.

3. Final Answer:

   dq.unshift(element); -> Option A

4. Quick Check:

   unshift adds front element [OK]

Hint: Use unshift() to add front element in JS array [OK]

Common Mistakes:

• Using push() instead of unshift() for front insertion
• Confusing pop() and shift() as insertion methods
• Passing argument to pop() or shift() which don't take any

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

const 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 deque

   Start with empty array [].
   push(10) => [10]
   unshift(20) => [20, 10]
   push(30) => [20, 10, 30]
   shift() removes front element 20 => [10, 30]

2. Step 2: Final state of dq

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

3. Final Answer:

   [10, 30] -> Option A

4. Quick Check:

   After shift(), front 20 removed, left [10, 30] [OK]

Hint: Track each push/unshift/shift step carefully [OK]

Common Mistakes:

• Forgetting shift() removes front element
• Mixing order of push and unshift effects
• Assuming shift() removes last element

4. Identify the error in the following code snippet that tries to remove an element from the rear of a deque implemented as an array named dq:

dq.removeLast();

medium

A. dq.pop() should be used instead of removeLast().

B. removeLast() is not a valid JavaScript array method.

C. removeLast() requires an argument to specify the element.

D. dq should be a linked list to use removeLast().

Solution

1. Step 1: Check JavaScript array methods for removing last element

   JavaScript arrays do not have a method named removeLast(). The correct method to remove the last element is pop().

2. Step 2: Analyze other options

   Linked list is unrelated here; removeLast() does not take arguments; pop() is the correct method.

3. Final Answer:

   removeLast() is not a valid JavaScript array method. -> Option B

4. Quick Check:

   pop() removes last element, removeLast() invalid [OK]

Hint: Use pop() to remove last element in JS array [OK]

Common Mistakes:

• Assuming removeLast() exists in JS arrays
• Trying to pass arguments to pop() or removeLast()
• Confusing linked list methods with array methods

5. You want to implement a deque that supports the following operations efficiently: addFront, addRear, removeFront, removeRear. Which data structure is best suited for this and why?

hard

A. Array, because it allows fast insertion and deletion at both ends.

B. Stack, because it supports adding and removing elements efficiently.

C. Singly linked list, because it allows fast insertion and deletion at both ends.

D. Doubly linked list, because it allows fast insertion and deletion at both ends without shifting elements.

Solution

1. Step 1: Analyze operation requirements

   We need fast insertion and deletion at both front and rear ends.

2. Step 2: Compare data structures

   Array requires shifting elements for front operations, making it inefficient.
   Singly linked list allows fast insertion/removal only at one end efficiently.
   Doubly linked list allows fast insertion/removal at both ends without shifting.
   Stack supports operations only at one end.

3. Final Answer:

   Doubly linked list, because it allows fast insertion and deletion at both ends without shifting elements. -> Option D

4. Quick Check:

   Doubly linked list = best for deque operations [OK]

Hint: Use doubly linked list for efficient double-ended ops [OK]

Common Mistakes:

• Choosing array ignoring shifting cost
• Assuming singly linked list supports both ends efficiently
• Confusing stack with deque