Double Ended Queue Deque in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Double Ended Queue (Deque)?

A Double Ended Queue, or Deque, is a data structure where elements can be added or removed from both the front and the back ends.

beginner

Name two main operations that can be performed on a Deque.

Insertion and deletion can be done at both ends:
1. InsertFront and InsertRear
2. DeleteFront and DeleteRear

beginner

How does a Deque differ from a Queue?

A Queue allows insertion at the rear and deletion at the front only, while a Deque allows insertion and deletion at both front and rear ends.

intermediate

What is the time complexity of insertion and deletion operations in a Deque implemented using a doubly linked list?

Both insertion and deletion at either end take O(1) time because pointers can be updated directly without shifting elements.

beginner

Show the state of the Deque after these operations: InsertRear(10), InsertFront(20), InsertRear(30), DeleteFront(), InsertFront(40).

Step by step:
Start: empty
InsertRear(10): 10
InsertFront(20): 20 -> 10
InsertRear(30): 20 -> 10 -> 30
DeleteFront(): 10 -> 30
InsertFront(40): 40 -> 10 -> 30

Which operation is NOT possible in a Deque?

A Insert at front

B Insert in the middle

C Delete at rear

D Delete at front

Deques allow insertion and deletion only at the front or rear ends, not in the middle.

What is the best data structure to implement a Deque for O(1) insertion and deletion at both ends?

A Array

B Singly linked list

C Stack

D Doubly linked list

A doubly linked list allows direct access to both ends for O(1) insertion and deletion.

After InsertFront(5) and InsertRear(15) on an empty Deque, what is the order of elements?

A 5 -> 15

B 15 -> 5

C 5

D 15

InsertFront(5) adds 5 at front, then InsertRear(15) adds 15 at rear, so order is 5 -> 15.

Which of these is a valid use case for a Deque?

A Undo functionality in text editors

B Simple FIFO queue

C Stack only operations

D Sorting algorithms

Undo operations often require adding/removing from both ends, which a Deque supports.

What happens if you try to delete from an empty Deque?

A Deletes first element

B Deletes last element

C Returns error or null

D Deque automatically adds an element

Deleting from an empty Deque is invalid and should return an error or null.

Explain how insertion and deletion work in a Double Ended Queue (Deque).

Think about how you can add or remove items from both ends.

Describe a real-life example where a Deque would be useful and why.

Consider situations where you can go forward and backward.

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 are added only at the rear and removed from the front

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

D. A list where elements can be accessed randomly by index

Solution

1. Step 1: Understand the definition of Deque

   A Deque allows insertion and deletion at both front and rear ends, unlike a queue or stack.

2. Step 2: Compare with other data structures

   Queue allows operations at one end for insertion and the other for deletion; stack allows operations only at one end.

3. Final Answer:

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

4. Quick Check:

   Deque = double-ended queue allowing both ends operations [OK]

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

Common Mistakes:

• Confusing deque with stack or queue
• Thinking deque allows random access like arrays
• Assuming deque only works like a queue

2. Which of the following is the correct syntax to declare a deque of integers in C++?

easy

A. deque<int> d = new deque();

B. deque<int> d;

C. deque<int> d[];

D. deque d<int>;

Solution

1. Step 1: Recall C++ STL deque declaration syntax

   The correct syntax uses template syntax: deque<int> d; declares a deque of integers named d.

2. Step 2: Check other options for syntax errors

   'deque<int> d = new deque();' uses invalid 'new' syntax for STL containers, 'deque d<int>;' has wrong template placement, 'deque<int> d[];' declares an array of deques incorrectly.

3. Final Answer:

   deque<int> d; -> Option B

4. Quick Check:

   Correct C++ deque declaration = deque<int> d; [OK]

Hint: Use template syntax: deque<Type> name; [OK]

Common Mistakes:

• Placing template brackets incorrectly
• Using Java or other language syntax
• Declaring arrays of deques without proper syntax

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

#include <iostream>
#include <deque>
using namespace std;
int main() {
  deque<int> d;
  d.push_back(10);
  d.push_front(20);
  d.push_back(30);
  d.pop_front();
  for (auto x : d) cout << x << " ";
  return 0;
}

medium

A. 10 30

B. 30 10

C. 20 10 30

D. 10 20 30

Solution

1. Step 1: Trace deque operations step-by-step

   Initially empty deque. push_back(10) -> [10]. push_front(20) -> [20, 10]. push_back(30) -> [20, 10, 30]. pop_front() removes 20 -> [10, 30].

2. Step 2: Print elements in deque

   Loop prints elements in order: 10 30

3. Final Answer:

   10 30 -> Option A

4. Quick Check:

   After pop_front, deque = 10 30 [OK]

Hint: Track push_front/back and pop_front carefully [OK]

Common Mistakes:

• Forgetting pop_front removes front element
• Mixing order of push_front and push_back
• Assuming pop_front removes from back

4. Identify the error in the following C++ code using deque:

#include <deque>
using namespace std;
int main() {
  deque<int> d;
  d.push_front(5);
  d.pop_back();
  d.pop_back();
  return 0;
}

medium

A. deque<int> d; is invalid declaration

B. push_front() is not a valid deque method

C. Missing #include <iostream> for cout

D. Calling pop_back() on empty deque causes undefined behavior

Solution

1. Step 1: Analyze deque operations

   After push_front(5), deque has one element [5]. First pop_back() removes 5, deque becomes empty []. Second pop_back() is called on empty deque.

2. Step 2: Understand behavior of pop_back on empty deque

   Calling pop_back() on empty deque causes undefined behavior or runtime error.

3. Final Answer:

   Calling pop_back() on empty deque causes undefined behavior -> Option D

4. Quick Check:

   pop_back on empty deque = error [OK]

Hint: Never pop from empty deque to avoid errors [OK]

Common Mistakes:

• Assuming pop_back on empty deque is safe
• Confusing push_front with invalid method
• Ignoring missing iostream is irrelevant here

5. You want to implement a sliding window maximum using a deque in C++. Which deque operation is essential to maintain the window elements in decreasing order?

hard

A. Remove elements from the back while they are smaller than the new element

B. Remove elements from the front while they are smaller than the new element

C. Add new elements only at the front

D. Add new elements only at the back without removal

Solution

1. Step 1: Understand sliding window maximum logic

   To keep maximum at front, remove all smaller elements from back before adding new element at back.

2. Step 2: Identify correct deque operation

   Removing smaller elements from back maintains decreasing order, ensuring front is max.

3. Final Answer:

   Remove elements from the back while they are smaller than the new element -> Option A

4. Quick Check:

   Sliding window max uses back removals for order [OK]

Hint: Remove smaller from back to keep max at front [OK]

Common Mistakes:

• Removing from front instead of back
• Adding elements without removing smaller ones
• Adding only at front breaks order