Implementing a Queue Using an Array - Feature ImageImplementing a Queue Using an Array - Feature Image
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Implementing a Queue Using an Array

Sven Woltmann
Sven Woltmann
May 16, 2022

The last part of the tutorial series was about implementing a queue with a linked list. In this part, we implement a queue with an array – first a bounded queue (i.e., one with a fixed capacity) – and then an unbounded queue (i.e., one whose capacity can change).

Let's start with the simple variant, the bounded queue.

Implementing a Bounded Queue with an Array

We create an empty array and fill it from left to right (i.e., ascending from index 0) with the elements inserted into the queue.

The following image shows a queue with an array called elements, which can hold eight elements. So far, six elements have been inserted into the queue. tailIndex always indicates the next insertion position:

Implementing a queue with an array
Implementing a queue with an array

When dequeuing the elements, we also read them from left to right and remove them from the array. headIndex always shows the next read position:

The following illustration shows the queue after we have retrieved the first four of the six elements:

Queue implemented with an array: Array filled in the middle
Queue implemented with an array: Array filled in the middle

Now that we are near the end of the array, we could (without additional logic) write only two more elements to the queue. To fill up the queue to eight elements again, there are two possible solutions:

  1. We move the remaining elements to the left, to the beginning of the array. This operation is costly, especially for large arrays.
  2. The better solution is a circular array. This means that when we reach the end of the array, we continue at its beginning. This applies to both the enqueue and dequeue operations.

Circular Array

To illustrate how a ring buffer works, I have rendered the array from the example as a circle:

Queue implemented with a circular array - 2 elements

We insert additional elements clockwise. In the following example, we add "mango", "fig", "pomelo", and "apricot" to positions 6, 7 – and then 0 and 1:

Queue implemented with a circular array - 6 elements

Back in the "flat" representation, the array now looks like this:

Queue with a "flat" representation of the circular array
Queue with a "flat" representation of the circular array

Both in the circle representation and this one, it is easy to see that the element "fig" at index 7 is followed by the element "pomelo" at index 0.

Dequeueing the elements works in the same way. With each dequeue operation, headIndex moves one position to the right, where 7 is not followed by 8 but by 0.

Full Queue vs. Empty Queue

tailIndex and headIndex are in the same position for both an empty and a full queue. To be able to recognize when the queue is full, we also store the number of elements.

This is what a full queue might look like:

Queue implementation: full circular array
Queue implementation: full circular array

And so an empty one (e.g., after all eight elements have been taken from the queue just shown):

Queue implementation: empty circular array
Queue implementation: empty circular array

Storing the number of elements is not the only – but a very simple – way to distinguish a full queue from an empty one. Alternatives are, for example:

  • Storing (besides the number of elements) only the tailIndex or the headIndex; then calculating the other from the number of elements (this, however, makes the code much more complex).
  • Not storing the number of elements and detecting a full queue by checking that tailIndex is equal to headIndex and that the array does not contain any element at the tailIndex position.
  • You do not fill the queue completely, but always leave at least one field empty.

Source Code for the Bounded Queue Using an Array

Implementing a bounded queue with an array is quite simple. You can also find the following code in the BoundedArrayQueue class in the GitHub repository.

public class BoundedArrayQueue<E> implements Queue<E> { private final Object[] elements; private int headIndex; private int tailIndex; private int numberOfElements; public BoundedArrayQueue(int capacity) { if (capacity < 1) { throw new IllegalArgumentException("Capacity must be 1 or higher"); } elements = new Object[capacity]; } @Override public void enqueue(E element) { if (numberOfElements == elements.length) { throw new IllegalStateException("The queue is full"); } elements[tailIndex] = element; tailIndex++; if (tailIndex == elements.length) { tailIndex = 0; } numberOfElements++; } @Override public E dequeue() { final E element = elementAtHead(); elements[headIndex] = null; headIndex++; if (headIndex == elements.length) { headIndex = 0; } numberOfElements--; return element; } @Override public E peek() { return elementAtHead(); } private E elementAtHead() { if (isEmpty()) { throw new NoSuchElementException(); } @SuppressWarnings("unchecked") E element = (E) elements[headIndex]; return element; } @Override public boolean isEmpty() { return numberOfElements == 0; } }
Code language: Java (java)

Note that BoundedArrayQueue does not implement the java.util.Queue interface, but a custom one that defines only the four methods enqueue(), dequeue(), peek(), and isEmpty() (see Queue in the GitHub repository):

public interface Queue<E> { void enqueue(E element); E dequeue(); E peek(); boolean isEmpty(); }
Code language: Java (java)

Find out how to use BoundedArrayQueue (and all other implementations of the Queue interface) in the QueueDemo program.

Implementing an Unbounded Queue with an Array

Implementing an unbounded queue, i.e., a queue with no size limit, is somewhat more complex. An array cannot grow. And even if it did – it could not grow at the end but would have to create free space at precisely the location where tailIndex and headIndex are pointing.

Let's look again at the full queue from the end of the previous example:

Queue implementation: full queue

To insert another element, we need to increase the queue's capacity by increasing the size of the array.

(For reasons of space in the graphical representation, we increase the capacity by only two elements. In reality, you usually find increases by a factor of 1.5 or 2.0).

However, we would have to create this free space between the tail and head of the queue, i.e., in the middle of the array:

Extending the array in the middle
Extending the array in the middle

This is not possible without further ado. An array cannot grow – and certainly not in the middle. Instead, we have to create a new array and copy the existing elements into it.

But if we have to recopy the elements anyway, we can copy them in the correct order to the beginning of the new array, like this:

Moving the elements to a new array and rearranging them
Moving the elements to a new array and rearranging them

The code for this is not that complicated, as you will see in the next section.

Source Code for the Unbounded Queue Using an Array

The following code shows the ArrayQueue class from the tutorial GitHub repository.

There are two constructors: one that lets you specify the initial size of the array and a default constructor that sets the initial capacity to ten.

Each time the enqueue() method is called, it checks whether the array is full. If it is, it invokes the grow() method.

The grow() method first calls calculateNewCapacity() to calculate the new size of the array. I have printed this method here in simplified form: it multiplies the current size by 1.5.

The calculateNewCapacity() method in the GitHub repository has a more sophisticated algorithm and ensures that a specific maximum size is not exceeded. However, the focus of this article should not be on determining the new size but on the actual expansion of the array.

Therefore, the growToNewCapacity() method creates the new array, copies the elements to the appropriate positions in the new array, and resets headIndex and tailIndex.

public class ArrayQueue<E> implements Queue<E> { private static final int DEFAULT_INITIAL_CAPACITY = 10; private Object[] elements; private int headIndex; private int tailIndex; private int numberOfElements; public ArrayQueue() { this(DEFAULT_INITIAL_CAPACITY); } public ArrayQueue(int capacity) { if (capacity < 1) { throw new IllegalArgumentException("Capacity must be 1 or higher"); } elements = new Object[capacity]; } @Override public void enqueue(E element) { if (numberOfElements == elements.length) { grow(); } elements[tailIndex] = element; tailIndex++; if (tailIndex == elements.length) { tailIndex = 0; } numberOfElements++; } private void grow() { int newCapacity = calculateNewCapacity(elements.length); growToNewCapacity(newCapacity); } private int calculateNewCapacity(int currentCapacity) { return currentCapacity + currentCapacity / 2; } private void growToNewCapacity(int newCapacity) { Object[] newArray = new Object[newCapacity]; // Copy to the beginning of the new array: tailIndex to end of the old array int oldArrayLength = elements.length; int numberOfElementsAfterTail = oldArrayLength - tailIndex; System.arraycopy(elements, tailIndex, newArray, 0, numberOfElementsAfterTail); // Append to the new array: beginning to tailIndex of the old array if (tailIndex > 0) { System.arraycopy(elements, 0, newArray, numberOfElementsAfterTail, tailIndex); } // Adjust head and tail headIndex = 0; tailIndex = oldArrayLength; elements = newArray; } // dequeue(), peek(), elementAtHead(), isEmpty() are the same as in BoundedArrayQueue }
Code language: Java (java)

The methods dequeue(), peek(), elementAtHead(), and isEmpty() are the same as in the BoundedArrayQueue from the section above. I have therefore not printed them again.

You may have noticed that the queue can grow but not shrink again. Perhaps our queue only needs to store a high number of elements during peak loads and would then occupy memory with a mostly empty array. We could extend the queue to copy its contents back to a smaller array after a certain grace period.

I leave this extension to you as a practice task.

Outlook

In the next and last part of this tutorial series, I will show you how to implement a PriorityQueue yourself, based on a min-heap.

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