.. This file is part of the OpenDSA eTextbook project. See .. http://opendsa.org for more details. .. Copyright (c) 2012-2020 by the OpenDSA Project Contributors, and .. distributed under an MIT open source license. .. avmetadata:: :title: Linked List Implementation :author: Cliff Shaffer :institution: Virginia Tech :requires: list ADT :satisfies: linked list :topic: Lists :keyword: Linked List :naturallanguage: en :programminglanguage: Java :description: Presents an implementation for a linked list. Linked Lists ============ Linked Lists ------------ In this module we present one of the two traditional implementations for lists, usually called a :term:`linked list`. The linked list uses :term:`dynamic memory allocation`, that is, it allocates memory for new list elements as needed. The following diagram illustrates the linked list concept. Here there are three :term:`nodes ` that are "linked" together. Each node has two boxes. The box on the right holds a link to the next node in the list. Notice that the rightmost node has a diagonal slash through its link box, signifying that there is no link coming out of this box. .. _LinkedListNodes: .. inlineav:: llistRepCON dgm :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistRepCON.js :align: center :keyword: Linked List Because a list node is a distinct object (as opposed to simply a cell in an array), it is good practice to make a separate list node class. (We can also re-use the list node class to implement linked implementations for the :ref:`stack ` and :ref:`queue ` data structures. Here is an implementation for list nodes, called the ``Link`` class. Objects in the ``Link`` class contain an ``element`` field to store the element value, and a ``next`` field to store a pointer to the next node on the list. The list built from such nodes is called a :term:`singly linked list`, or a :term:`one-way list`, because each list node has a single pointer to the next node on the list. .. codeinclude:: Lists/Link :tag: Link The ``Link`` class is quite simple. There are two forms for its constructor, one with an initial element value and one without. Member functions allow the link user to get or set the ``element`` and ``link`` fields. .. inlineav:: llistBadCON ss :long_name: Linked List Slideshow 1 :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistBadCON.js :output: show :keyword: Linked List Why This Has Problems ~~~~~~~~~~~~~~~~~~~~~ There are a number of problems with the representation just described. First, there are lots of special cases to code for. For example, when the list is empty we have no element for ``head``, ``tail``, and ``curr`` to point to. Implementing special cases for ``insert`` and ``remove`` increases code complexity, making it harder to understand, and thus increases the chance of introducing bugs. .. inlineav:: llistBadDelCON ss :long_name: Linked List Slideshow 2 :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistBadDelCON.js :output: show :keyword: Linked List A Better Solution ~~~~~~~~~~~~~~~~~ Fortunately, there is a fairly easy way to deal with all of the special cases, as well as the problem with deleting the last node. Many special cases can be eliminated by implementing linked lists with an additional :term:`header node` as the first node of the list. This header node is a link node like any other, but its value is ignored and it is not considered to be an actual element of the list. The header node saves coding effort because we no longer need to consider special cases for empty lists or when the current position is at one end of the list. The cost of this simplification is the space for the header node. However, there are space savings due to smaller code size, because statements to handle the special cases are omitted. We get rid of the remaining special cases related to being at the end of the list by adding a "trailer" node that also never stores a value. The following diagram shows initial conditions for a linked list with header and trailer nodes. .. _LinkedListInit: .. inlineav:: llistInitCON dgm :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistInitCON.js :align: center :keyword: Linked List Here is what a list with some elements looks like with the header and trailer nodes added. .. _LinkedListTailer: .. inlineav:: llistHeaderCON dgm :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistHeaderCON.js :align: center :keyword: Linked List Adding the trailer node also solves our problem with deleting the last node on the list, as we will see when we take a closer look at the remove method's implementation. Linked List Implementation ~~~~~~~~~~~~~~~~~~~~~~~~~~ Here is the implementation for the linked list class, named ``LList``. .. codeinclude:: Lists/LList :tag: LList | .. inlineav:: llistVarsCON ss :long_name: Linked List Variables Slideshow :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistVarsCON.js :output: show :keyword: Linked List | .. inlineav:: llistConsCON ss :long_name: Linked List Constructors Slideshow :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistConsCON.js :output: show :keyword: Linked List | .. inlineav:: llistInsertCON ss :long_name: Linked List Insert Slideshow :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistInsertCON.js :output: show :keyword: Linked List Here are some special cases for linked list insertion: Inserting at the end, and inserting to an empty list. .. inlineav:: llistSpecialCON ss :long_name: Linked List Special Insert Slideshow :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistSpecialCON.js :output: show :keyword: Linked List .. avembed:: Exercises/List/LlistInsertPRO.html ka :long_name: Linked List Insert Exercise :keyword: Linked List Linked List Remove ------------------ .. inlineav:: llistRemoveCON ss :long_name: Linked List Remove Slideshow :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistRemoveCON.js :output: show :keyword: Linked List .. avembed:: Exercises/List/LlistRemovePRO.html ka :long_name: Linked List Remove Exercise :keyword: Linked List .. inlineav:: llistOtherCON ss :long_name: Linked List Position Slideshow :links: AV/List/llistCON.css :scripts: AV/List/llist.js AV/List/llistOtherCON.js :output: show :keyword: Linked List Implementations for the remaining operations each require :math:`\Theta(1)` time.