Double Ended Queue Deque in DSA C++

Mental Model

A deque lets you add or remove items from both the front and the back easily.

Analogy: Think of a line of people where you can join or leave from either the front or the back, like a double-sided queue at a theme park.

front -> [ ] -> [ ] -> [ ] -> back
↑
head pointer

Dry Run Walkthrough

Input: Start with empty deque, then add 1 at front, add 2 at back, add 3 at front, remove from back

Goal: Show how elements are added and removed from both ends of the deque

Step 1: Add 1 at front

front -> [1] -> back
↑

Why: We add the first element at the front, so front and back both point to 1

Step 2: Add 2 at back

front -> [1] -> [2] -> back
↑

Why: Add 2 after 1 at the back, so back pointer moves to 2

Step 3: Add 3 at front

front -> [3] -> [1] -> [2] -> back
↑

Why: Add 3 before 1 at the front, so front pointer moves to 3

Step 4: Remove from back

front -> [3] -> [1] -> back
↑

Why: Remove last element 2 from back, back pointer moves to 1

Result:

front -> [3] -> [1] -> back

Annotated Code

DSA C++

#include <iostream>
#include <deque>

using namespace std;

int main() {
    deque<int> dq;

    // Add 1 at front
    dq.push_front(1); // front: 1

    // Add 2 at back
    dq.push_back(2);  // front: 1, back: 2

    // Add 3 at front
    dq.push_front(3); // front: 3, then 1, 2

    // Remove from back
    dq.pop_back();    // removes 2

    // Print deque
    for (int val : dq) {
        cout << val << " -> ";
    }
    cout << "null" << endl;

    return 0;
}

dq.push_front(1); // front: 1

Add element 1 at the front of deque

dq.push_back(2); // front: 1, back: 2

Add element 2 at the back of deque

dq.push_front(3); // front: 3, then 1, 2

Add element 3 at the front, shifting previous front

dq.pop_back(); // removes 2

Remove element from the back

Output

3 -> 1 -> null

Complexity Analysis

Time: O(1) for each add or remove operation because deque supports fast insertions and deletions at both ends

Space: O(n) where n is the number of elements stored, as deque stores all elements

vs Alternative: Compared to a normal queue or stack, deque allows operations at both ends efficiently instead of just one end

Edge Cases

Empty deque when removing

pop operations do nothing or cause error if not checked

DSA C++

No pop operation is called without checking size in this simple example

Adding to empty deque

front and back pointers both point to the new element

DSA C++

dq.push_front(1); // handles empty deque correctly

When to Use This Pattern

When a problem needs adding or removing items from both ends quickly, use a deque because it supports double-ended operations efficiently.

Common Mistakes

Mistake: Using push_back when push_front is needed or vice versa
Fix: Carefully choose push_front or push_back depending on which end you want to operate on

Mistake: Trying to pop from empty deque without checking
Fix: Check if deque is empty before popping to avoid errors

Summary

A deque lets you add or remove items from both front and back efficiently.

Use a deque when you need flexible double-ended access to elements.

Remember: push_front and pop_front work on the front; push_back and pop_back work on the back.

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