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LINKED NODES The values of the index array k[] in Figure 3.6 are used as locators, addressing the actual data array a[]. We don t really need a separate array for them. Their relative positions in the index array match the positions of the corresponding data elements. So we can combine them into a single array of data-address pairs, as shown in Figure 3.7:
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Figure 3.7 Storing the indexes with their elements in the same array
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In this version, the array a[] would be defined as shown in Example 3.7.
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Node[] a = new Node[size];
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where Node would now be a separate class, defined like this:
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class Node { int data; int next; } This makes the array a[] a little more complex, but it eliminates the need for an auxiliary array
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altogether. Fortunately, Java allows an even better solution, one that allows us to eliminate both arrays! Taking an object-oriented point of view, we see in Figure 3.8 a sequence of Node objects. Each object contains a data element and the address of the next object in the sequence. In Java, objects are directly accessed by their addresses. That s what an object reference is: the address of where the object is stored in memory. So by reinterpreting the meaning of address, as a memory address (i.e., object reference) instead of an array index, we can simplify the structure to the one shown in Figure 3.8. Here, the arrows represent object references (i.e., memory addresses).
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Figure 3.8 Using objects for the elements and their references
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Now, instead of an array a[], we need only keep track of the single start reference. The Java runtime system does all the rest of the bookkeeping. The code is given in Example 3.3. EXAMPLE 3.3 A Node Class
1 2 3
class Node { int data; Node next;
Figure 3.9 A Node object
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4 5 6 7 8
Node(int data) { this.data = data; } }
Notice that the Node class is now self-referential: Its next field is declared to have type Node. Each Node object contains a field that is a reference to a Node object. The other field in the Node class is its data field, declared at line 2 here to be an int. Of course in general this field could be any type we want whatever type values we have to store in the list. The Node class in Example 3.3 also includes a one-argument constructor, at line 5. Note that, since we have explicitly defined a constructor that takes at least one argument, the compiler will not implicitly define a no-argument constructor. Therefore, since we have not explicitly defined a no-argument constructor, none will exist. That means that the only way a Node object can be created is with the one-argument constructor (at line 5); that is, we must provide a data value for each new Node object that we create. Figure 3.9 shows a typical Node object. Its data field contains the integer 22, and its next field contains a reference to another Node object (not shown). Although it is common to use an arrow like this to represent an object reference, it is good to keep in mind that the actual value of the reference is the memory address of the object to which it refers. In other programming languages, such variables are called pointers; hence their common depiction as arrows. Recall that in Java each reference variable either locates an object or is null. The value null means that the variable does not refer to any object. The memory address that is stored in a null reference variable is 0x0 (the hexadecimal value 0); no Figure 3.10 Another Node object object is ever stored at that address. Figure 3.10 shows a Node object whose next field is null. Example 3.4 shows how the five-element list could be built. EXAMPLE 3.4 Constructing a Linked List
Node start = new Node(22); Figure 3.11 Initializing start start.next = new Node(33); 3 start.next.next = new Node(44); 4 start.next.next.next = new Node(55); 5 start.next.next.next.next = new Node(66); At line 1, we create a node containing the data value 22 and initialize our start variable to it. The result is shown in Figure 3.11. Note that the start variable is merely a reference to the Node object. Also note that the next reference in the Node object is null, indicated by the black dot with no arrow emanating from it. The node s next field is null because the constructor (defined at line 5 in Example 3.3 on
page 50) does not initialize it. In Java, every class field that is an object reference (i.e., its type is either a class or an interface) is automatically initialized to null, unless it is initialized by its constructor to some existing object. In the figures that follow, each Node object is shown as a box with two parts: the left side contains the integer data, and the right side contains the next reference. This simply abbreviates the versions shown in Figure 3.9. Continuing the code in Example 3.4, at line 2, the start node s next field is assigned to a new Node object containing the data 33. Now the list has two nodes, as shown in Figure 3.12. Figure 3.12 Adding a node
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