Linked Lists

Introduction

A linked list is a linear data structure where each element is a separate object.

Each element (we will call it a node) of a list is comprising of two items - the data and a reference to the next node. The last node has a reference to null . The entry point into a linked list is called the head of the list. It should be noted that head is not a separate node, but the reference to the first node. If the list is empty then the head is a null reference.

A linked list is a dynamic data structure. The number of nodes in a list is not fixed and can grow and shrink on demand. Any application which has to deal with an unknown number of objects will need to use a linked list.

One disadvantage of a linked list against an array is that it does not allow direct access to the individual elements. If you want to access a particular item then you have to start at the head and follow the references until you get to that item.

Another disadvantage is that a linked list uses more memory compare with an array - we extra 4 bytes (on 32-bit CPU) to store a reference to the next node.

Types of Linked Lists

A singly linked list is described above

A doubly linked list is a list that has two references, one to the next node and another to previous node.

Another important type of a linked list is called a circular linked list where last node of the list points back to the first node (or the head) of the list.

The Node class

We implement the LinkedList class with two inner classes: static Node class and non-static LinkedListIterator class. See LinkedList.java for a complete implementation.

Let us assume the singly linked list above and trace down the effect of each fragment below. The list is restored to its initial state before each line executes

Linked List Operations

The method creates a node and prepends it at the beginning of the list.

Start with the head and access each node until you reach null. Do not change the head reference.

The method appends the node to the end of the list. This requires traversing, but make sure you stop at the last node

Find a node containing "key" and insert a new node after it. In the picture below, we insert a new node after "e":

Find a node containing "key" and insert a new node before that node. In the picture below, we insert a new node before "a":

For the sake of convenience, we maintain two references prev and cur . When we move along the list we shift these two references, keeping prev one step before cur . We continue until cur reaches the node before which we need to make an insertion. If cur reaches null, we don't insert, otherwise we insert a new node between prev and cur .

Examine this implementation

Find a node containing "key" and delete it. In the picture below we delete a node containing "A" The algorithm is similar to insert "before" algorithm. It is convinient to use two references prev and cur . When we move along the list we shift these two references, keeping prev one step before cur . We continue until cur reaches the node which we need to delete. There are three exceptional cases, we need to take care of:

1. list is empty


2. delete the head node


3. node is not in the list

The whole idea of the iterator is to provide an access to a private aggregated data and at the same moment hiding the underlying representation. An iterator is Java is an object, and therefore it's implementation requires creating a class that implements the Iterator interface. Usually such class is implemented as a private inner class. The Iterator interface contains the following methods:

• AnyType next() - returns the next element in the container


• boolean hasNext() - checks if there is a next element


• void remove() - (optional operation).removes the element returned by next()

In this section we implement the Iterator in the LinkedList class. First of all we add a new method to the LinkedList class:

Here LinkedListIterator is a private class inside the LinkedList class The LinkedListIterator class must provide implementations for next() and hasNext() methods. Here is the next() method:

Like for any other objects, we need to learn how to clone linked lists. If we simply use the clone() method from the Object class, we will get the following structure called a "shallow" copy:

The Object's clone() will create a copy of the first node, and share the rest. This is not exactly what we mean by "a copy of the object". What we actually want is a copy represented by the picture below

Since out data is immutable it's ok to have data shared between two linked lists. There are a few ideas to implement linked list copying. The simplest one is to traverse the original list and copy each node by using the addFirst() method. When this is finished, you will have a new list in the reverse order. Finally, we will have to reverse the list:

A better way involves using a tail reference for the new list, adding each new node after the last node.

Applications

Polynomial Algebra

The biggest integer that we can store in a variable of the type int is 2 31 - 1 on 32-but CPU. You can easily verify this by the following operations:

This code doesn't produce an error, it produces a result! The printed value is a negative integer -2147483648 = -2 31 . If the value becomes too large, Java saves only the low order 32 (or 64 for longs) bits and throws the rest away.

In real life applications we need to deal with integers that are larger than 64 bits (the size of a long). To manipulate with such big numbers, we will be using a linked list data structure. First we observe that each integer can be expressed in the decimal system of notation. 937 = 9*10 2 + 3*10 1 + 7*10 0 2011 = 2*10 3 + 0*10 2 + 1*10 1 + 1*10 0

Now, if we replace a decimal base 10 by a character, say 'x', we obtain a univariate polynomial, such as