ADT - Stacks & Queues

Data Structures: Abstract Data Type (ADT)

Stacks & Queues

Abstract Data Types Types

All processin processing g on a comput computer er involv involves es the manipula manipulatio tion n of data data This This data data can be organi!ed in the computer"s memory in different #ays according to ho# it is to be processed$ and the different methods of organi!ing data are kno#n as data structures %omputer languages such as ascal have built'in elementary data types (such as integer$ real$ oolean and char) and some built'in type structured or composite data types (data structures) such as record$ array and string These composite data types are made up of a number of elements of a specified type such as integer or real

Some data structures such as ueues$ stacks and binary trees are not built into the language and have to be constructed by the programmer These are kno#n as Abstract Data Types (ADT) An Abstract Data Type (ADT) is the combination of a data structure and a group of functions or procedures designed to manipulate the data #ithin the data structure

An ADT must possess the follo#ing characteristics: 

the facility to create a container to hold h old the data*

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the facility to add a ne# element to the container*

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the facility to remove+delete an element #hich satisfies some criterion from the container*

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the facility to find an element #hich satisfies some criterion criterion #ithin the container*

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the facility to destroy the container #hen it is no longer reuired

Stacks

A stack is a particular particular kind of seuence seuence that may only be accessed at one end$ kno#n as the top of the stack (like plates on a pile in a cafeteria) ,nly t#o operations can be carried out on a stack Adding a ne# item involves placing it on the top of the stack (pushing or stacking the item) -emoving an item involves the removal of the item that #as most recently added (popping the stack) The stack is a LIFO Structure . Last In$ First Out

repared by / /ones

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Stacks & Queues

2ote that items do not move up and do#n as the stack is pushed and popped* instead$ the position of the top of the stack changes A pointer called a stack pointer indicates the position of the top of the stack

Characteristics of a Stack 

The specific operation #hich defines a stack is the concept of 34ast'in'first'out5

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Data elements #hich have been added to the container are removed from the container in the reversed order to #hich they are inserted

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Typically$ this ADT is identified by a variable called 3the head5 #hich identifies the location of the most recent element added to the container

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The functions of 3push5 and 3pop5 are typically used to describe the process of inserting and deleting elements respectively$ from the stack

Implementation of a stack

A stack can be represented in memory by an array and t#o additional integer variables$ one holding the si!e of the array (ie the ma6imum si!e of the stack) and one holding the pointer to the top of the stack (Top) Top #ill initially be set to 7$ representing an empty stack

8 ; < = > 0

9a6StackSi!e  8

Anne 9illie %harles

Top  =

Diagram showing an array that can hold a maimum of ! elements with " items currently in the stock#


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The following pseudocode may be used to add $%push&' an element onto a stack(

rocedure ush ?f Top  9a6StackSi!e Then @rite 3Stack is full5 lse Add 0 to Top StackBTopC  2e#?tem nd?f ndrocedure

The following pseudocode may be used to remo)e $%pop&' an element from a stack(

rocedure op ?f Top  7 Then @rite 3Stack is empty5 lse opped?tem  StackBTopC Subtract 0 from Top nd?f ndrocedure

Applications of stacks

Stacks are very important data structures in computing They are used in many different situations in computing$ for e6ample: •

to store return addresses$ parameters and register contents #hen subroutines are called @hen the subroutine ends$ the address at the top of the stack is popped and the computers continues e6ecution from that address*

•

translating from one computer language to another$ and transferring control from one part of a program to another*

•

in evaluating mathematical e6pressions held in reverse olish notation$ ie a form of notation used by compilers as an intermediate step in translating e6pressions such as A: (%) E D+

Stacks can also be used to reverse the elements of a ueue This is done by pushing the elements of the ueue one by one on to a stack$ and then popping them one by one and replacing them in the ueue


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*ueue

A ueue is a First ?n First ,ut (F?F,) data structure 2e# elements may only be added to the end of a ueue$ and elements may only be retrieved from the front of a ueue The seuence of data items in a ueue is determined$ therefore$ by the order in #hich they are inserted The si!e of the ueue depends on the number of items in it$ Gust like a ueue at the cinema or supermarket checkout

Implementation of a +ueue

A ueue can be implemented as an array #ith a pointer to the front of the ueue and a pointer to the rear of the ueue An integer holding the si!e of the array (the ma6imum si!e of the ueue) is needed$ and it is useful to have an e6tra variable giving the number of items currently in the ueue

/ohn

%atherine

-ob

Front  0

-ear  =

9a6Si!e  8

2umber?nQueue  =

After > people have left the ueue and = more have Goined$ the ueue #ill look like this: -ob Front  = 9a6Si!e  8

9a6

4isa

Anna -ear  8

2umber?nQueue  <

2o# #hatH ,nly < people are in the ueue but the end of the array has been reached To overcome this problem$ the elements could be shuffled along$ so the front of the ueue is al#ays in location 0 This is kno#n as Linear *ueue  Io#ever$ busy ueues #ould spend rather a lot of time shuffling elements Another method to overcome the problem is to implement the ueue as a Circular *ueue $ so that #hen the ne6t person Goins they enter at the front of the array:

en


-ob

9a6

4isa

Anna

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Data Structures: Abstract Data Type (ADT) -ear  0

Stacks & Queues

Front  =

9a6Si!e  8

2umber?nQueue  ;

,rocedures to implement a circular +ueue

The abo)e +ueue may be implemented by declaring )ariables as follows(

QB8C as String Front$ -ear$ 2umber?nQueue as ?nteger

To initiali-e the +ueue(

rocedure ?nitiali!e Front  0 -ear  8

Jor -ear  7K

2umber?nQueue  7 ndrocedure

To add an element to the +ueue(

rocedure nQueue ?f 2umber?nQueue  8 Then @rite 3Queue overflo#5 lse ?f -ear  8 Then -ear  0 lse

or -ear  (-ear 9od 8) E 0 Add 0 to -ear

nd?f QB-earC  2e#?tem Add 0 to 2umber?nQueue nd?f ndrocedure To remo)e an element from the +ueue(


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rocedure DeQueue ?f 2umber?nQueue  7 Then @rite 3Queue empty5 lse 2e#?tem  QBFrontC Subtract 0 from 2umber?nQueue ?f Front  8 Then Front  0 lse

or Front  (Front 9od 8) E 0 Add 0 to Front

nd?f nd?f ndrocedure

Implementing a +ueue as a linked list

A ueue may be implemented as a special kind of linked list$ #ith each element in the ueue pointing to the ne6t item An e6ternal pointer points to the front of the ueue$ and items may only be removed from the front of the list and added to the end of the list

Data

Data

Data

Data

Front The front of the ueue is accessed through the pointer front To add an element to the ueue$ the pointers have to be follo#ed until the node containing a pointer of 7 is reached signifying the end of the ueue$ and this pointer is then changed to point to the ne# node (?n some implementations t#o pointers are kept* one to the front and one to the rear This saves having to traverse the #hole ueue #hen a ne# element is to be added)


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Stacks & Queues

Applications of a +ueue 

,utput #aiting to be printed is commonly stored in a ueue on disk ?n a room full of net#orked computers$ several people may send #ork to be printed at more or less the same time y putting the output into a ueue on disk$ the output is printed on a first come$ first served basis as soon as the printer is free

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%haracters typed at keyboard are held in a ueue in a keyboard buffer

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/obs #aiting to be run by the computer may be held in a ueue

Characteristics of a *ueue 

The specific operation #hich defines a ueue is a concept of 3First'in'first'out5

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Data elements #hich have been added to the container are removed from the container in e6actly the same order in #hich they #ere inserted

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Typically$ this ADT is identified by a variable called 3the head5 #hich identifies the location of the longest e6isting element in the container and another variable called 3tail5 #hich identifies the most recent element added to the container

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The functions of 3enueue5 and 3deueue5 are typically used to describe the process of inserting and deleting elements respectively from the ueue

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?n the ueue$ data elements are inserted through the tail and removed from the head


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ADT - Stacks & Queues

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