Java programming fundamentals: Datastructures and algorithms in Java

Java 101: Datastructures and algorithms in Java, Part 4

Searching and sorting with singly linked lists and their algorithms in Java

Like arrays, linked lists are a fundamental datastructure category upon which more complex datastructures can be based. Unlike a sequence of elements, however, a linked list is a sequence of nodes, where each node is linked to the previous and next node in the sequence. Recall that a node is an object created from a self-referential class, and a self-referential class has at least one field whose reference type is the class name. Nodes in a linked list are linked via a node reference. Here's an example:


class Employee
{
   private int empno;
   private String name;
   private double salary;
   public Employee next;
   // Other members.
}

In this example, Employee is a self-referential class because its next field has type Employee. This field is an example of a link field because it can store a reference to another object of its class--in this case another Employee object.

This article introduces you to the ins and outs of singly linked lists in Java programming. You'll learn operations for creating a singly linked list, inserting nodes into a singly linked list, deleting nodes from a singly linked list, concatenating a singly linked list to another singly linked list, and inverting a singly linked list. We'll also explore algorithms most commonly used to sort singly linked lists, and conclude with an example demonstrating the Insertion Sort algorithm.

download
Download the three example applications for this article. Created by Jeff Friesen for JavaWorld.

What is a singly linked list?

A singly linked list is a linked list of nodes where each node has a single link field. In this datastructure, a reference variable contains a reference to the first (or top) node; each node (except for the last or bottom node) links to the next one; and the last node's link field contains the null reference to signify the list's end. Although the reference variable is commonly named top, you can choose any name you want.

Figure 1 presents a singly linked list with three nodes.

jw j101 datastructures 4 fig1 Jeff Friesen

Figure 1. A singly linked list where top references the A node, A connects to B, B connects to C, and C is the final node.

Below is pseudocode for a singly linked list.


DECLARE CLASS Node
  DECLARE STRING name
  DECLARE Node next
END DECLARE
DECLARE Node top = NULL

Node is a self-referential class with a name data field and a next link field. top is a reference variable of type Node that holds a reference to the first Node object in a singly linked list. Because the list doesn't yet exist, top's initial value is NULL.

Creating a singly linked list in Java

You create a singly linked list by attaching a single Node object. The following pseudocode creates a Node object, assigns its reference to top, initializes its data field, and assigns NULL to its link field:


top = NEW Node
top.name = "A"
top.next = NULL

Figure 2 shows the initial singly linked list that emerges from this pseudocode.

jw j101 datastructures 4 fig2 Jeff Friesen

Figure 2. The initial singly linked list consists of a single Node (A).

This operation has a time complexity of O(1)--constant. Recall that O(1) is pronounced "Big Oh of 1." (See Part 1 for a reminder of how time and space complexity measurements are used to evaluate datastructures.)

Inserting nodes into a singly linked list

Inserting a node into a singly linked list is somewhat more complicated than creating a singly linked list because there are three cases to consider:

  • Insertion before the first node.
  • Insertion after the last node.
  • Insertion between two nodes.

Insertion before the first node

A new node is inserted before the first node by assigning the top node's reference to the new node's link field and assigning the new node's reference to the top variable. This operation is demonstrated by the following pseudocode:


DECLARE Node temp
temp = NEW Node
temp.name = "B"
temp.next = top
top = temp

The resulting two-Node list appears in Figure 3.

jw j101 datastructures 4 fig3 Jeff Friesen

Figure 3. The expanded two-Node singly linked list places Node B ahead of Node A.

This operation has a time complexity of O(1).

Insertion after the last node

A new node is inserted after the last node by assigning null to the new node's link field, traversing the singly linked list to find the last node, and assigning the new node's reference to the last node's link field, as the following pseudocode demonstrates:


temp = NEW Node
temp.name = "C"
temp.next = NULL
DECLARE Node temp2
temp2 = top 
// We assume top (and temp2) are not NULL 
// because of the previous pseudocode.
WHILE temp2.next NE NULL
   temp2 = temp2.next
END WHILE
// temp2 now references the last node.
temp2.next = temp

Figure 4 reveals the list following the insertion of Node C after Node A.

jw j101 datastructures 4 fig4 Jeff Friesen

Figure 4. Node C comes last in the expanded three-node singly linked list.

This operation has a time complexity of O(n)--linear. Its time complexity could be improved to O(1) by maintaining a reference to the last node. In that case it wouldn't be necessary to search for the last node.

Insertion between two nodes

Inserting a node between two nodes is the most complex case. You insert a new node between two nodes by traversing the list to find the node that comes before the new node, assigning the reference in the found node's link field to the new node's link field, and assigning the new node's reference to the found node's link field. The following pseudocode demonstrates these tasks:


temp = NEW Node
temp.name = "D"
temp2 = top 
// We assume that the newly created Node inserts after Node 
// A and that Node A exists. In the real world, there is no 
// guarantee that any Node exists, so we would need to check 
// for temp2 containing NULL in both the WHILE loop's header 
// and after the WHILE loop completes.
WHILE temp2.name NE "A"
   temp2 = temp2.next
END WHILE
// temp2 now references Node A.
temp.next = temp2.next
temp2.next = temp

Figure 5 presents the list following the insertion of Node D between Nodes A and C.

jw j101 datastructures 4 fig5 Jeff Friesen

Figure 5. The ever-growing singly linked list places Node D between Nodes A and C.

This operation has a time complexity of O(n).

Deleting nodes from a singly linked list

Deleting a node from a singly linked list is also somewhat more complicated than creating a singly linked list. However, there are only two cases to consider:

  • Deletion of the first node.
  • Deletion of any node but the first node.

Deletion of the first node

Deleting the first node involves assigning the link in the first node's link field to the variable that references the first node, but only when there is a first node:


IF top NE NULL THEN
   top = top.next; // Reference the second Node (or NULL when there's only one Node).
END IF

Figure 6 presents before and after views of a list where the first Node has been deleted. Node B disappears and Node A becomes the first Node.

jw j101 datastructures 4 fig6 Jeff Friesen

Figure 6. Before and after views of a singly linked list where the first Node is deleted. The red X and dotted lines signify top's change of reference from Node B to Node A.

This operation has a time complexity of O(1).

Deletion of any node but the first node

Deleting any node but the first node involves locating the node that precedes the node to be deleted and assigning the reference in the node-to-be-deleted's link field to the preceding node's link field. Consider the following pseudocode:


IF top NE NULL THEN
   temp = top
   WHILE temp.name NE "A"
      temp = temp.next
   END WHILE
   // We assume that temp references Node A.
   temp.next = temp.next.next
   // Node D no longer exists.
END IF

Figure 7 presents before and after views of a list where an intermediate Node is deleted. Node D disappears.

jw j101 datastructures 4 fig7 Jeff Friesen

Figure 7. Before and after views of a singly linked list where an intermediate Node is deleted. The red X and dotted lines signify Node A's change of link from Node D to Node C.

This operation has a time complexity of O(n).

Example #1: Create, insert, and delete in a singly linked list

I've created a Java application named SLLDemo that demonstrates how to create, insert, and delete nodes in a singly linked list. Listing 1 presents this application's source code.

Listing 1. SSLDemo.java (version 1)


public final class SLLDemo
{
   private static class Node
   {
      String name;
      Node next;
   }

   public static void main(String[] args)
   {
      Node top = null;

      // 1. The singly linked list does not exist.

      top = new Node();
      top.name = "A";
      top.next = null;
      dump("Case 1", top);

      // 2. The singly linked list exists and the node must be inserted
      //    before the first node.

      Node temp;
      temp = new Node();
      temp.name = "B";
      temp.next = top;
      top = temp;
      dump("Case 2", top);

      // 3. The singly linked list exists and the node must be inserted
      //    after the last node.

      temp = new Node();
      temp.name = "C";
      temp.next = null;
      Node temp2;
      temp2 = top;
      while (temp2.next != null)
         temp2 = temp2.next;
      temp2.next = temp;
      dump("Case 3", top);

      // 4. The singly linked list exists and the node must be inserted
      //    between two nodes.

      temp = new Node();
      temp.name = "D";
      temp2 = top;
      while (temp2.name.equals("A") == false)
         temp2 = temp2.next;
      temp.next = temp2.next;
      temp2.next = temp;
      dump("Case 4", top);

      // 5. Delete the first node.

      top = top.next;
      dump("After first node deletion", top);

      // 5.1 Restore node B.

      temp = new Node();
      temp.name = "B";
      temp.next = top;
      top = temp;

      // 6. Delete any node but the first node.

      temp = top;
      while (temp.name.equals("A") == false)
         temp = temp.next;
      temp.next = temp.next.next;
      dump("After D node deletion", top);
   }

   private static void dump(String msg, Node topNode)
   {
      System.out.print(msg + " ");
      while (topNode != null)
      {
         System.out.print(topNode.name + " ");
         topNode = topNode.next;
      }
      System.out.println();
   }
}

Compile Listing 1 as follows:


javac SLLDemo.java

Run the resulting application as follows:


java SLLDemo

You should observe the following output:


Case 1 A 
Case 2 B A 
Case 3 B A C 
Case 4 B A D C 
After first node deletion A D C 
After D node deletion B A C

Concatenating singly linked lists

You might occasionally need to concatenate a singly linked list to another singly linked list. For example, suppose you have a list of words that start with letters A through M and another list of words starting with letters N through Z, and you want to combine these lists into a single list. The following pseudocode describes an algorithm for concatenating one singly linked list to another:


DECLARE Node top1 = NULL
DECLARE Node top2 = NULL
// Assume code that creates top1-referenced singly linked list.
// Assume code that creates top2-referenced singly linked list.
// Concatenate top2-referenced list to top1-referenced list.
IF top1 EQ NULL
   top1 = top2
   END
END IF
// Locate final Node in top1-referenced list.
DECLARE Node temp = top1
WHILE temp.next NE NULL
   temp = temp.next
END WHILE
// Concatenate top2 to top1.
temp.next = top2
END

In the trivial case, there is no top1-referenced list, and so top1 is assigned top2's value, which would be NULL if there was no top2-referenced list.

This operation has a time complexity of O(1) in the trivial case and a time complexity of O(n) otherwise. However, if you maintain a reference to the last node, there's no need to search the list for this node; the time complexity changes to O(1).

Inverting a singly linked list

Another useful operation on a singly linked list is inversion, which reverses the list's links to let you traverse its nodes in the opposite direction. The following pseudocode reverses the top1-referenced list's links:


DECLARE Node p = top1 // Top of original singly linked list.
DECLARE Node q = NULL // Top of reversed singly linked list.
DECLARE Node r        // Temporary Node reference variable.
WHILE p NE NULL       // For each Node in original singly linked list ...
   r = q              // Save future successor Node's reference.
   q = p              // Reference future predecessor Node.
   p = p.next         // Reference next Node in original singly linked list.
   q.next = r         // Link future predecessor Node to future successor Node.
END WHILE
top1 = q              // Make top1 reference first Node in reversed singly linked list.
END

This operation has a time complexity of O(n).

Example #2: Concatenating and inverting a singly linked list

I've created a second version of the SLLDemo Java application that demonstrates concatenation and inversion. Listing 2 presents this application's source code.

1 2 Page 1
Page 1 of 2