An Introduction to Data Structures

Chapter Goals

• To learn how to use the linked lists provided in the standard library
• To be able to use iterators to traverse linked lists
• To understand the implementation of linked lists
• To distinguish between abstract and concrete data types
• To know the efficiency of fundamental operations of lists and arrays
• To become familiar with the stack and queue types

Using Linked Lists

• A linked list consists of a number of nodes, each of which has a reference to the next node
• Adding and removing elements in the middle of a linked list is efficient
• Visiting the elements of a linked list in sequential order is efficient
• Random access is not efficient

Inserting an Element into a Linked List

Java's LinkedList class

• Generic class
  • Specify type of elements in angle brackets: LinkedList<Product>
• Package: java.util
• Easy access to first and last elements with methods
  

  void addFirst(E obj)
  void addLast(E obj)
  E getFirst()
  E getLast()
  E removeFirst()
  E removeLast()

List Iterator

• ListIterator type
• Gives access to elements inside a linked list
• Encapsulates a position anywhere inside the linked list
• Protects the linked list while giving access

A List Iterator

A Conceptual View of the List Iterator

List Iterator

• Think of an iterator as pointing between two elements
  • Analogy: like the cursor in a word processor points between two characters
• The listIterator method of the LinkedList class gets a list iterator

  LinkedList<String> employeeNames = . . .;
  ListIterator<String> iterator = employeeNames.listIterator();

List Iterator

• Initially, the iterator points before the first element
• The next method moves the iterator

  iterator.next();

• next throws a NoSuchElementException if you are already past the end of the list
• hasNext returns true if there is a next element

  if (iterator.hasNext())
      iterator.next();

List Iterator

• The next method returns the element that the iterator is passing

  while iterator.hasNext()
  {
     String name = iterator.next();
     Do something with name
  }

• Shorthand:

  for (String name : employeeNames)
  {
     Do something with name
  }

  Behind the scenes, the for loop uses an iterator to visit all list elements

List Iterator

• LinkedList is a doubly linked list
  • Class stores two links:
    • One to the next element, and
    • One to the previous element
• To move the list position backwards, use:
  • hasPrevious
  • previous

Adding and Removing from a LinkedList

• The add method:
  • Adds an object after the iterator
  • Moves the iterator position past the new element

  iterator.add("Juliet");

Adding and Removing from a LinkedList

• The remove method
  • Removes and
  • Returns the object that was returned by the last call to next or previous

  //Remove all names that fulfill a certain condition
  while (iterator.hasNext())
  {
     String name = iterator.next();
     if (name fulfills condition)
        iterator.remove();
  }

• Be careful when calling remove:
  • It can be called only once after calling next or previous
  • You cannot call it immediately after a call to add
  • If you call it improperly, it throws an IllegalStateException

Sample Program

• ListTester is a sample program that
  • Inserts strings into a list
  • Iterates through the list, adding and removing elements
  • Prints the list

File ListTester.java

Output

Dick
Harry
Juliet
Nina
Tom

Self Check

1. Do linked lists take more storage space than arrays of the same size?
2. Why don't we need iterators with arrays?

Answers

1. Yes, for two reasons. You need to store the node references, and each node is a separate object. (There is a fixed overhead to store each object in the virtual machine.)
2. An integer index can be used to access any array location.

Implementing Linked Lists

• Previous section: Java's LinkedList class
• Now, we will look at the implementation of a simplified version of this class
• It will show you how the list operations manipulate the links as the list is modified
• To keep it simple, we will implement a singly linked list
  • Class will supply direct access only to the first list element, not the last one
• Our list will not use a type parameter
  • Store raw Object values and insert casts when retrieving them

Implementing Linked Lists

• Node: stores an object and a reference to the next node
• Methods of linked list class and iterator class have frequent access to the Node instance variables
• To make it easier to use:
  • We do not make the instance variables private
  • We make Node a private inner class of LinkedList
  • It is safe to leave the instance variables public
    • None of the list methods returns a Node object

Implementing Linked Lists

public class LinkedList
{
   . . .
   private class Node
   {
      public Object data;
      public Node next;
   }
}

Implementing Linked Lists

• LinkedList class
  • Holds a reference first to the first node
  • Has a method to get the first element

Implementing Linked Lists

public class LinkedList
{
   public LinkedList()
   {
      first = null;
   }

   public Object getFirst()
   {
      if (first == null)
         throw new NoSuchElementException();
      return first.data;
   }

   . . .
   private Node first;
}

Adding a New First Element

• When a new node is added to the list
  • It becomes the head of the list
  • The old list head becomes its next node

Adding a New First Element

• The addFirst method

  public class LinkedList
  {
     . . .
     public void addFirst(Object obj)
     {
        Node newNode = new Node(); 
        newNode.data = obj;
        newNode.next = first; 
        first = newNode; 
     }
     . . .
  }

Adding a Node to the Head of a Linked List

Removing the First Element

• When the first element is removed
  • The data of the first node are saved and later returned as the method result
  • The successor of the first node becomes the first node of the shorter list
  • The old node will be garbage collected when there are no further references to it

Removing the First Element

• The removeFirst method

  public class LinkedList
  {
     . . .
     public Object removeFirst()
     {
        if (first == null)
           throw new NoSuchElementException();
        Object obj = first.data;
        first = first.next; 
        return obj;
     }
     . . .
  }

Removing the First Node from a Linked List

Linked List Iterator

• We define LinkedListIterator: private inner class of LinkedList
• Implements a simplified ListIterator interface
• Has access to the first field and private Node class
• Clients of LinkedList don't actually know the name of the iterator class
  • They only know it is a class that implements the ListIterator interface

LinkedListIterator

• The LinkListIterator class

  public class LinkedList
  {
     . . .
     public ListIterator listIterator()
     {
        return new LinkedListIterator();
     }
  
     private class LinkedListIterator implements ListIterator
     {
        public LinkedListIterator()
        {
           position = null;
           previous = null;
        }
  
        . . .
        private Node position;
        private Node previous;
     }
     . . .
  }

The Linked List Iterator's next Method

• position: reference to the last visited node
• Also, store a reference to the last reference before that
• next method: position reference is advanced to position.next
• Old position is remembered in previous
• If the iterator points before the first element of the list,
  then the old position is null and position must be set to first

The Linked List Iterator's next Method

public Object next()
{
   if (!hasNext())
      throw new NoSuchElementException();
   previous = position; // Remember for remove

   if (position == null)
      position = first;
   else
      position = position.next;

   return position.data;
}

The Linked List Iterator's hasNext Method

• The next method should only be called when the iterator is not at the end of the list
• The iterator is at the end
  • if the list is empty (first == null)
  • if there is no element after the current position (position.next == null)

The Linked List Iterator's hasNext Method

private class LinkedListIterator implements ListIterator
{
  . . .
   public boolean hasNext()
   {
      if (position == null)
         return first != null;
      else
         return position.next != null;
   }
   . . .
}

The Linked List Iterator's remove Method

• If the element to be removed is the first element, call removeFirst
• Otherwise, the node preceding the element to be removed needs to have its next reference updated to skip the removed element
• If the previous reference equals position:
  • this call does not immediately follow a call to next
  • throw an IllegalArgumentException
• It is illegal to call remove twice in a row
  • remove sets the previous reference to position

The Linked List Iterator's remove Method

public void remove()
{
   if (previous == position)
      throw new IllegalStateException();
   if (position == first)
   {
      removeFirst();
   }
   else
   {
      previous.next = position.next; 
   }
   position = previous; 
}

Removing a Node From the Middle of a Linked List

The Linked List Iterator's set Method

• Changes the data stored in the previously visited element
• The set method

  public void set(Object obj)
  {
     if (position == null)
        throw new NoSuchElementException();
     position.data = obj;
  }

The Linked List Iterator's add Method

• The most complex operation is the addition of a node
• add inserts the new node after the current position
• Sets the successor of the new node to the successor of the current position

The Linked List Iterator's add Method

public void add(Object obj)
{
   if (position == null)
   {
      addFirst(obj);
      position = first;
   }
   else
   {
      Node newNode = new Node();
      newNode.data = obj;
      newNode.next = position.next;  
      position.next = newNode;  
      position = newNode;  
   }
   previous = position; 
}

Adding a Node to the Middle of a Linked List

File LinkedList.java

File ListIterator.java

Self Check

3. Trace through the addFirst method when adding an element to an empty list.
4. Conceptually, an iterator points between elements (see Figure 3). Does the position reference point to the element to the left or to the element to the right?
5. Why does the add method have two separate cases?

Answers

3. When the list is empty, first is null. A new Node is allocated. It's data field is set to the newly inserted object. It's next field is set to null because first is null. The first field is set to the new node. The result is a linked list of length 1.
4. It points to the element to the left. You can see that by tracing out the first call to next. It leaves position to point to the first node.
5. If position is null, we must be at the head of the list, and inserting an element requires updating the first reference. If we are in the middle of the list, the first reference should not be changed.

Abstract and Concrete Data Types

• There are two ways of looking at a linked list
  • To think of the concrete implementation of such a list
    • Sequence of node objects with links between them
  • Think of the abstract concept of the linked list
    • Ordered sequence of data items that can be traversed with an iterator

Abstract and Concrete Data Types

Abstract Data Types

• Define the fundamental operations on the data
• Do not specify an implementation

Abstract and Concrete Array Type

• As with a linked list, there are two ways of looking at an array list
• Concrete implementation: a partially filled array of object references
• We don't usually think about the concrete implementation when using an array list
  • We take the abstract point of view
• Abstract view: ordered sequence of data items, each of which can be accessed by an integer index

Abstract and Concrete Data Types

Abstract and Concrete Data Types

• Concrete implementations of a linked list and an array list are quite different
• The abstractions seem to be similar at first glance
• To see the difference, consider the public interfaces stripped down to their minimal essentials

Fundamental Operations on Array List

public class ArrayList
{
   public Object get(int index) { . . . }
   public void set(int index, Object value) { . . . }
   . . .
}

Fundamental Operations on Linked List

public class LinkedList
{
   public ListIterator listIterator() { . . . }
   . . .
}

public interface ListIterator
{
   Object next();
   boolean hasNext();
   void add(Object value);
   void remove();
   void set(Object value);
   . . .
}

Abstract and Concrete Data Types

• ArrayList: combines the interfaces of an array and a list
• Both ArrayList and LinkedList implement an interface called List
  • List defines operations for random access and for sequential access
• Terminology is not in common use outside the Java library
• More traditional terminology: array and list
• Java library provides concrete implementations ArrayList and LinkedList for these abstract types
• Java arrays are another implementation of the abstract array type

Efficiency of Operations for Arrays and Lists

• Adding or removing an element
  • A fixed number of node references need to be modified
    to add or remove a node, regardless of the size of the list
  • In big-Oh notation:      O(1)
• Adding or removing an element
  • On average n/2 elements need to be moved
  • In big-Oh notation:     O(n)

Efficiency of Operations for Arrays and Lists

Abstract Data Types

• Abstract list
  • Ordered sequence of items that can be traversed sequentially
  • Allows for insertion and removal of elements at any position
• Abstract array
  • Ordered sequence of items with random access via an integer index

Self Check

6. What is the advantage of viewing a type abstractly?
7. How would you sketch an abstract view of a doubly linked list? A concrete view?
8. How much slower is the binary search algorithm for a linked list compared to the linear search algorithm?

Answers

6. You can focus on the essential characteristics of the data type without being distracted by implementation details.
7. The abstract view would be like Figure 9, but with arrows in both directions. The concrete view would be like Figure 8, but with references to the previous node added to each node.
8. To locate the middle element takes n / 2 steps. To locate the middle of the subinterval to the left or right takes another n / 4 steps. The next lookup takes n / 8 steps. Thus, we expect almost n steps to locate an element. At this point, you are better off just making a linear search that, on average, takes n / 2 steps.

Stacks and Queues

• Stack: collection of items with "last in first out" retrieval
• Queue: collection of items with "first in first out" retrieval

Stack

• Allows insertion and removal of elements only at one end
  • Traditionally called the top of the stack
• New items are added to the top of the stack
• Items are removed at the top of the stack
• Called last in, first out or LIFO order
• Traditionally, addition and removal operations are called push and pop
• Think of a stack of books

A Stack of Books

Queue

• Add items to one end of the queue (the tail)
• Remove items from the other end of the queue (the head)
• Queues store items in a first in, first out or FIFO fashion
• Items are removed in the same order in which they have been added
• Think of people lining up
  • People join the tail of the queue and wait until they have reached the head of the queue

A Queue

Stacks and Queues: Uses in Computer Science

• Queue
  • Event queue of all events, kept by the Java GUI system
  • Queue of print jobs
• Stack
  • Run-time stack that a processor or virtual machine keeps to organize the variables of nested methods

Abstract Data Type Stack

• Stack: concrete implementation of a stack in the Java library

  Stack<String> s = new Stack<String>();
  s.push("A");
  s.push("B");
  s.push("C");
  // The following loop prints C, B, and A
  while (s.size() > 0)
     System.out.println(s.pop());

• Uses an array to implement a stack

Abstract Data Type Queue

• Queue implementations in the standard library are designed for use with multithreaded programs
• However, it is simple to implement a basic queue yourself

A Queue Implementation

Self Check

9. Draw a sketch of the abstract queue type, similar to Figures 9 and 11.
10. Why wouldn't you want to use a stack to manage print jobs?

Answers

9. 
10. Stacks use a "last in, first out" discipline. If you are the first one to submit a print job and lots of people add print jobs before the printer has a chance to deal with your job, they get their printouts first, and you have to wait until all other jobs are completed.