Arrays are great for storing data. We have also seen that any element of an array can be read in O(1) time. But arrays are fixed in size. Changing the size of an array means creating a new array and copying all the elements to the original array. The simplest recourse to the resizing problem is to store each element in a different object and then hold a reference in each element to the next element. This way, the process of adding a new element will just involve creating the element and attaching it at the end of the last element of the original linked list. In another variation, the new element can be added to the beginning of the existing linked list:

Figure 3: An example of a linked list

Figure 3 shows an example of a linked list. The arrows represent a reference. Each element is stored in a wrapper object that also holds a reference to the next element wrapper. There are two additional references to the first and last elements, which are required for any operation to start...

Did you notice that there is no quick way to remove the element from the end of a linked list? This is because even if there is a quick way to find the last element, there is no quick way to find the element before it whose reference needs to be updated. We must walk all the way from the beginning to find the previous element. Well then, why not just have another reference to store the location of the last but one element? This is because after you remove the element, how would you update the reference otherwise? There would be no reference to the element right before that. What it looks like is that to achieve this, we have to store the reference of all the previous elements up to the beginning. The best way to do this would be to store the reference of the previous element in each of the elements or nodes along with the reference to the next element. Such a linked list is called a doubly linked list since the elements are linked both ways:

Figure 9: Doubly linked list...

A circular linked list is an ordinary linked list, except that the last element holds the reference to the first element as its next element. This, of course, justifies its name. It would be useful when, for example, you are holding a list of players in a list and they play in turn in a round robin fashion. The implementation is simplified if you use a circular linked list and just keep rotating as the players complete their turn:

Figure 14: A circular linked list

The basic structure of a circular linked list is the same as that of a simple linked list; no more fields or methods are required:

public class CircularLinkedList<E> extends LinkedList<E>{ 
}

    @Override 
    public Node<E> appendFirst(E value) { 
        Node<E> newNode = super.appendFirst(value); 
        last.next = first; 
        return newNode; 
  ...

We covered a few basic data structures and the algorithms for manipulating them. In addition to this, we also found out their running time complexities. To summarize this, an array provides you with the fastest random access there is with this time complexity: O(1). But arrays cannot change size; the only modification they allow is to change the value of an element. A linked list allows fast append at the end and insertion at the beginning at O(1) time. However, O(1) removal is only available for removing the first element. This is resolved by a doubly linked list that also allows O(1) removal from the end. A circular linked list holds a reference to the first element in the next reference of the last element. This makes the list a circular structure that allows one to loop indefinitely.

In the upcoming chapters, we will discuss the abstraction of data structures called abstract data types. We will use the data structures we have seen in this chapter to implement the abstract data...