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

Time Complexity: Queue Implementation Using Linked List

O(1)

Understanding Time Complexity

We want to understand how fast the main operations of a queue using a linked list run as the queue grows.

Specifically, how does adding or removing items change with more elements?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public class Node {
    public int Data;
    public Node Next;
    public Node(int data) { Data = data; Next = null; }
}

public class Queue {
    private Node front, rear;

    public void Enqueue(int data) {
        Node newNode = new Node(data);
        if (rear == null) {
            front = rear = newNode;
            return;
        }
        rear.Next = newNode;
        rear = newNode;
    }

    public int Dequeue() {
        if (front == null) throw new InvalidOperationException("Queue is empty");
        int value = front.Data;
        front = front.Next;
        if (front == null) rear = null;
        return value;
    }
}
    

This code adds items to the end and removes items from the front of a linked list to form a queue.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding or removing a single node by changing pointers.
• How many times: Each operation works on just one node at a time, no loops or recursion inside enqueue or dequeue.

How Execution Grows With Input

Each enqueue or dequeue does a fixed number of steps regardless of queue size.

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

Pattern observation: The number of steps stays about the same no matter how big the queue is.

Final Time Complexity

Time Complexity: O(1)

This means adding or removing an item takes the same short time no matter how many items are in the queue.

Common Mistake

[X] Wrong: "Enqueue or dequeue must check all nodes, so it takes longer as the queue grows."

[OK] Correct: The code keeps track of front and rear nodes, so it changes only a few pointers without scanning the whole list.

Interview Connect

Knowing that queue operations run in constant time shows you understand efficient data structure design, a key skill in many coding challenges.

Self-Check

"What if we did not keep a rear pointer and only had a front pointer? How would the time complexity of enqueue change?"

Practice

1. What is the main advantage of implementing a queue using a linked list instead of an array?

easy

A. Dynamic size without fixed capacity

B. Faster access to elements by index

C. Uses less memory for small queues

D. Simpler syntax for enqueue operation

Solution

1. Step 1: Understand array limitations

   Arrays have fixed size, so queues using arrays need resizing or have limited capacity.

2. Step 2: Linked list flexibility

   Linked lists grow dynamically by adding nodes, so queues can expand without size limits.

3. Final Answer:

   Dynamic size without fixed capacity -> Option A

4. Quick Check:

   Linked list queues grow dynamically = D [OK]

Hint: Linked lists grow dynamically, arrays do not [OK]

Common Mistakes:

• Thinking arrays allow dynamic resizing easily
• Confusing access speed with size flexibility
• Assuming linked lists use less memory always

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

easy

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

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

C. public struct Node { public int data; public Node next; }

D. public class Node { private int data; private Node next; }

Solution

1. Step 1: Check access modifiers

   For queue operations, node fields must be accessible; public allows this.

2. Step 2: Class vs struct

   Node should be a class to allow reference behavior; struct is value type and not suitable here.

3. Final Answer:

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

4. Quick Check:

   Public class with public fields = A [OK]

Hint: Use public class with public fields for linked list nodes [OK]

Common Mistakes:

• Using struct instead of class for nodes
• Omitting public keyword causing access errors
• Making fields private without accessors

3. What will be the output after executing the following C# code for a linked list queue?

Queue queue = new Queue();
queue.Enqueue(10);
queue.Enqueue(20);
queue.Enqueue(30);
int first = queue.Dequeue();
queue.Enqueue(40);
int second = queue.Dequeue();
Console.WriteLine(first + ", " + second);

medium

A. 10, 30

B. 20, 30

C. 10, 20

D. 20, 40

Solution

1. Step 1: Trace enqueue and dequeue operations

   Enqueue 10, 20, 30 adds these in order. Dequeue removes 10 (first). Enqueue 40 adds at end. Dequeue removes 20 (next).

2. Step 2: Identify values of first and second

   first = 10, second = 20. Output prints "10, 20".

3. Final Answer:

   10, 20 -> Option C

4. Quick Check:

   FIFO order = 10, 20 [OK]

Hint: Remember queue removes oldest element first (FIFO) [OK]

Common Mistakes:

• Confusing enqueue and dequeue order
• Assuming dequeue removes last element
• Mixing values after enqueue and dequeue

4. Identify the error in the following dequeue method of a linked list queue and select the fix:

public int Dequeue() {
  if (front == null) throw new InvalidOperationException("Queue is empty");
  int value = front.data;
  front = front.next;
  return value;
}

medium

A. Should set rear to null when queue becomes empty

B. Should throw NullReferenceException instead

C. No error; method is correct

D. Should update front.next to null before returning

Solution

1. Step 1: Analyze dequeue when one element remains

   If front moves to null after removing last node, rear still points to old node, causing inconsistency.

2. Step 2: Fix by setting rear to null when queue is empty

   When front is null, rear must also be set to null to indicate empty queue properly.

3. Final Answer:

   Should set rear to null when queue becomes empty -> Option A

4. Quick Check:

   Rear must be null if front is null [OK]

Hint: Set rear null when queue empties after dequeue [OK]

Common Mistakes:

• Ignoring rear pointer update on empty queue
• Throwing wrong exception type
• Unnecessary null assignment to front.next

5. You want to implement a method ReverseQueue() that reverses the order of elements in a linked list queue without using extra data structures. Which approach is best?

hard

A. Dequeue all elements and enqueue them back in reverse order using a stack

B. Swap data values between front and rear nodes repeatedly

C. Create a new queue and enqueue elements in reverse order by traversing original queue

D. Iteratively reverse the linked list nodes by changing next pointers

Solution

1. Step 1: Understand reversing linked list nodes

   Changing next pointers of nodes reverses the linked list in place without extra space.

2. Step 2: Compare with other options

   Using stack or new queue uses extra space; swapping data is inefficient and error-prone.

3. Final Answer:

   Iteratively reverse the linked list nodes by changing next pointers -> Option D

4. Quick Check:

   In-place reversal changes pointers = B [OK]

Hint: Reverse linked list by pointer changes, no extra space [OK]

Common Mistakes:

• Using extra data structures despite constraint
• Swapping data instead of pointers
• Creating new queues unnecessarily