Now that we understand the basics of queues and their implementations, let's dive into the operations that we can perform on a queue.

The two fundamental operations of a queue are: enqueue and dequeue.

1. Enqueue: This operation adds an element to the rear end of the queue. The enqueue operation is also known as insertion.

Here's the Java code for enqueue operation in a basic array implementation of a queue:

1void enqueue(int item) {
2    if (isFull()) {
3        throw new IllegalStateException("Queue is full");
4    }
5    
6    rear = (rear + 1) % maxSize;
7    queue[rear] = item;
8    currentSize++;
9}

2. Dequeue: This operation removes an element from the front end of the queue. The dequeue operation is also known as deletion.

Here's the Java code for dequeue operation in a basic array implementation of a queue:

1int dequeue() {
2    if (isEmpty()) {
3        throw new NoSuchElementException("Queue is empty");
4    }
5    
6    int item = queue[front];
7    front = (front + 1) % maxSize;
8    currentSize--;
9    return item;
10}

It's important to note that both enqueue and dequeue operations have a time complexity of O(1) in a basic array implementation of a queue.

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}

class QueueOperations {

    private int[] queue;

    private int front;

    private int rear;

    private int maxSize;

    private int currentSize;

    public QueueOperations(int size) {

        maxSize = size;

        queue = new int[maxSize];

        front = 0;

        rear = -1;

        currentSize = 0;

    }

    public void enqueue(int item) {

        if (isFull()) {

            throw new IllegalStateException("Queue is full");

        }

        rear = (rear + 1) % maxSize;

        queue[rear] = item;

        currentSize++;

    }

    public int dequeue() {

        if (isEmpty()) {

            throw new NoSuchElementException("Queue is empty");

        }