Dequeue Using Linked List in DSA C# - Time & Space Complexity

Time Complexity: Dequeue Using Linked List

O(1)

Understanding Time Complexity

We want to understand how the time to add or remove items in a dequeue using a linked list changes as the number of items grows.

How does the time needed grow when the dequeue gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public class Node {
    public int Value;
    public Node Next, Prev;
    public Node(int val) { Value = val; }
}

public class Dequeue {
    private Node head, tail;

    public void AddFront(int val) {
        Node newNode = new Node(val);
        if (head == null) { head = tail = newNode; return; }
        newNode.Next = head;
        head.Prev = newNode;
        head = newNode;
    }

    public void RemoveFront() {
        if (head == null) return;
        head = head.Next;
        if (head != null) head.Prev = null;
        else tail = null;
    }
}
    

This code adds and removes items at the front of a dequeue implemented with a linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding or removing a node at the front involves only a few pointer changes.
• How many times: Each add or remove runs once per call, no loops or recursion inside.

How Execution Grows With Input

Each add or remove operation takes the same small number of steps no matter how many items are in the dequeue.

Input Size (n)	Approx. Operations
10	5-6 steps
100	5-6 steps
1000	5-6 steps

Pattern observation: The time stays about the same no matter how big the dequeue is.

Final Time Complexity

Time Complexity: O(1)

This means adding or removing at the front takes a constant amount of time regardless of the dequeue size.

Common Mistake

[X] Wrong: "Removing from the front takes longer as the dequeue grows because we have to move through all nodes."

[OK] Correct: We keep a direct pointer to the front node, so removal only changes a few pointers without walking the list.

Interview Connect

Knowing that linked list dequeue operations run in constant time shows you understand efficient data structure design, a key skill in interviews.

Self-Check

"What if we had to find a node by value before removing it? How would the time complexity change?"

Practice

1. What is the main advantage of implementing a Dequeue using a linked list compared to an array?

easy

A. It automatically sorts the elements.

B. It uses less memory than an array.

C. It allows insertion and deletion from both ends in constant time.

D. It prevents duplicate elements.

Solution

1. Step 1: Understand Dequeue operations

   A dequeue allows adding and removing elements from both front and rear ends.

2. Step 2: Compare linked list vs array

   Linked list supports constant time insertion and deletion at both ends, unlike arrays which may require shifting elements.

3. Final Answer:

   It allows insertion and deletion from both ends in constant time. -> Option C

4. Quick Check:

   Linked list dequeue = O(1) insert/delete both ends [OK]

Hint: Linked list supports fast add/remove at both ends [OK]

Common Mistakes:

• Thinking arrays allow O(1) insertion at front
• Confusing memory usage advantage
• Assuming automatic sorting

2. Which of the following is the correct way to declare a node class for a doubly linked list in C# for implementing a dequeue?

easy

A. public class Node { int data; Node next; }

B. public class Node { public int data; public Node next; public Node prev; }

C. class Node { public int data; Node next; Node prev; }

D. public struct Node { int data; Node next; Node prev; }

Solution

1. Step 1: Check access modifiers and fields

   For linked list nodes, fields should be public to access from dequeue class.

2. Step 2: Verify presence of next and prev pointers

   Doubly linked list nodes need both next and prev references.

3. Final Answer:

   public class Node { public int data; public Node next; public Node prev; } -> Option B

4. Quick Check:

   Public fields + next + prev = correct node class [OK]

Hint: Node needs public data, next, and prev for dequeue [OK]

Common Mistakes:

• Missing public keyword for fields
• Using struct instead of class
• Omitting prev pointer

3. Consider the following C# code snippet implementing a dequeue using a linked list. What will be printed after these operations?

Dequeue dq = new Dequeue();
dq.InsertFront(10);
dq.InsertRear(20);
dq.InsertFront(5);
dq.DeleteRear();
dq.Display();

medium

A. 5 -> 10 -> 20 -> null

B. 10 -> 5 -> null

C. 10 -> 20 -> null

D. 5 -> 10 -> null

Solution

1. Step 1: Trace insertions

   InsertFront(10) adds 10 at front: 10 -> null InsertRear(20) adds 20 at rear: 10 -> 20 -> null InsertFront(5) adds 5 at front: 5 -> 10 -> 20 -> null

2. Step 2: Trace deletion and display

   DeleteRear() removes 20 from rear: 5 -> 10 -> null Display prints elements from front to rear.

3. Final Answer:

   5 -> 10 -> null -> Option D

4. Quick Check:

   After delete rear, list = 5 -> 10 [OK]

Hint: Track insert/delete order carefully [OK]

Common Mistakes:

• Forgetting delete rear removes last element
• Mixing front and rear insertions
• Incorrect display order

4. The following C# method is intended to delete the front node of a dequeue implemented using a doubly linked list. What is the error?

public void DeleteFront() {
    if (front == null) return;
    front = front.next;
    front.prev = null;
}

medium

A. It does not handle the case when the list becomes empty after deletion.

B. It should update rear pointer instead of front.

C. It should set front.next to null before updating.

D. It should not set front.prev to null.

Solution

1. Step 1: Analyze deletion steps

   After moving front to front.next, if front becomes null (list empty), front.prev = null causes NullReferenceException.

2. Step 2: Identify missing null check

   Code must check if front is null before setting front.prev = null to avoid error.

3. Final Answer:

   It does not handle the case when the list becomes empty after deletion. -> Option A

4. Quick Check:

   Null check needed after front update [OK]

Hint: Check for empty list after deletion [OK]

Common Mistakes:

• Ignoring null after front update
• Updating rear pointer incorrectly
• Setting pointers in wrong order

5. You want to implement a method ReverseDisplay() for a dequeue using a doubly linked list that prints elements from rear to front. Which approach is correct?

hard

A. Start from rear node and traverse using prev pointers until null, printing each node's data.

B. Start from front node and traverse using next pointers until null, printing each node's data.

C. Use recursion starting from front node to print in reverse order.

D. Swap front and rear pointers and then traverse from front using next pointers.

Solution

1. Step 1: Understand doubly linked list structure

   Each node has next and prev pointers; rear node's next is null, front node's prev is null.

2. Step 2: Reverse traversal logic

   To print from rear to front, start at rear and move backward using prev pointers until null.

3. Final Answer:

   Start from rear node and traverse using prev pointers until null, printing each node's data. -> Option A

4. Quick Check:

   Traverse backward from rear using prev [OK]

Hint: Traverse prev pointers from rear to front [OK]

Common Mistakes:

• Traversing next pointers from front for reverse
• Swapping pointers incorrectly
• Using recursion unnecessarily