.. 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: Implementing a Linked Stack
   :author: Cliff Shaffer
   :institution: Virginia Tech
   :requires: stack ADT
   :satisfies: linked stack
   :topic: Lists
   :keyword: Linked Stack
   :naturallanguage: en
   :programminglanguage: Java
   :description: Presents an implementation for linked stacks.

Linked Stacks
=============

Linked Stack Implementation
---------------------------

The linked stack implementation is quite simple.
Elements are inserted and removed only from the head of the list.
A header node is not used because no special-case code is required
for lists of zero or one elements.
Here is the complete linked stack implementation.

.. codeinclude:: Lists/LStack
   :tag: LStack1,LStack2

Here is a visual representation for the linked stack.

.. _LStackDiagram:

.. inlineav:: lstackDiagramCON dgm
   :links: AV/List/lstackCON.css
   :scripts: AV/List/llist.js AV/List/lstackDiagramCON.js
   :align: center   
   :keyword: Linked Stack Implementation


Linked Stack Push
~~~~~~~~~~~~~~~~~

.. inlineav:: lstackPushCON ss
   :long_name: Linked stack push
   :links: AV/List/lstackCON.css
   :scripts: AV/List/llist.js AV/List/lstackPushCON.js
   :output: show
   :keyword: Linked Stack Implementation
   
.. avembed:: Exercises/List/LstackPushPRO.html ka
   :long_name: Linked Stack Push Exercise
   :keyword: Linked Stack Implementation


Linked Stack Pop
----------------

.. inlineav:: lstackPopCON ss
   :long_name: Linked stack pop
   :links: AV/List/lstackCON.css
   :scripts: AV/List/llist.js AV/List/lstackPopCON.js
   :output: show
   :keyword: Linked Stack Implementation

.. avembed:: Exercises/List/LstackPopPRO.html ka
   :long_name: Linked Stack Pop Exercise
   :keyword: Linked Stack Implementation

   
Comparison of Array-Based and Linked Stacks
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

All operations for the array-based and linked stack implementations
take constant time, so from a time efficiency perspective,
neither has a significant advantage.
Another basis for comparison is the total space
required.
The analysis is similar to that done for list implementations.
The array-based stack must declare a fixed-size array initially, and
some of that space is wasted whenever the stack is not full.
The linked stack can shrink and grow but requires the overhead of a
link field for every element.

When implementing multiple stacks, sometimes you can take advantage of
the one-way growth of the array-based stack
by using a single array to store two stacks.
One stack grows inward from each end as illustrated by the figure
below, hopefully leading to less wasted space.
However, this only works well when the space requirements of the two
stacks are inversely correlated.
In other words, ideally when one stack grows, the other will shrink.
This is particularly effective when elements are taken from
one stack and given to the other.
If instead both stacks grow at the same time, then the free space
in the middle of the array will be exhausted quickly.

.. _TwoArrayStacks:

.. inlineav:: lstackTwostackCON dgm
   :links: AV/List/lstackCON.css
   :scripts: AV/List/llist.js AV/List/lstackTwostackCON.js
   :align: center
   :keyword: Linked Stack Implementation