preparation data structures 03 abstract data_types

Data StructuresAbstract Data Types

Andres Mendez-Vazquez

May 6, 2015

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Images/cinvestav-1.jpg

Outline

1 IntroductionBasic IdeasAbstract Data Types

2 Linear List: An Example of ADTBasic DefinitionOperations

3 Generic Java InterfaceAbstract Classes Vs Interfaces

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Outline

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What is a data structure?

IntuitionA data object is a set or collection of instances!!!

Examplesinteger = {0, +1, -1, +2, -2, +3, -3, ...}daysOfWeek = {S,M,T,W,Th,F,Sa}

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Those instance may be related!!!

Something quite basicInstances may or may not be related.

ExamplemyDataObject = {apple, chair, 2, 5.2, red, green, Jack}

ThusData Structure ≈ Data object + relationships that exist among instancesand elements that comprise an instance.

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Examples

Among instances of integers369 < 370280 + 4 = 284

ThusThe relationships are usually specified by specifying operations on one ormore instances.

Examplesadd, subtract, predecessor, multiply

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Examples

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Examples

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Outline

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Abstract Data Type

Data TypeA data type such as int or double is a group of values and operations onthose values that is defined within a specific programming language.

Abstract Data TypeAn Abstract Data Type, or ADT, is a specification for a group of valuesand the operations on those values that is defined conceptually andindependently of any programming language.

ThusA data structure is an implementation of an ADT within a programminglanguage.

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Abstract Data Type

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Abstract Data Type

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Using Abstract Data Types

Something NotableAn abstract data type is defined indirectly, only by the operations that maybe performed on it and by mathematical constraints on the effects (andpossibly cost) of those operations.

Using Abstract Data Types1 An abstract object may be operated upon by the operations which

define its abstract type.2 An abstract object may be passed as a parameter to a procedure.3 An abstract object may be assigned to a variable.

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For More

We have the following“PROGRAMMING WITH ABSTRACT DATA TYPES” by Barbara Liskovand Stephen Zilles

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Abstract Data Types: An Example

We will start withAn example using Lists.

Actually in JavaAn interface in the Java programming language is an abstract type that isused to specify an interface (in the generic sense of the term) that classesmust implement.

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Abstract Data Types: An Example

We will start withAn example using Lists.

Actually in JavaAn interface in the Java programming language is an abstract type that isused to specify an interface (in the generic sense of the term) that classesmust implement.

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Outline

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Linear (or Ordered) Lists

DefinitionA linear list is a data structure that holds a sequential list of elements.

InstancesThey have the following structure, (e0, e1, e1, ..., en−1)

PropertiesWhere ei denotes a list elementn ≥ 0 is finiteList size is n

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What are the relations inside of a Liner List?

Having thisL = (e0, e1, e2, ..., en−1)

Relationshipse0 is the zero’th (or front) elementen−1 is the last elementei immediately precedes ei+1

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Examples

Simple onesStudents in COP3530 = (Jack, Jill, Abe, Henry, Mary, ..., Judy)Exams in COP3530 = (exam1, exam2, exam3)Days of Week = (S, M, T, W, Th, F, Sa)Months = (Jan, Feb, Mar, Apr, ..., Nov, Dec)

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Examples

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Examples

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Examples

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Outline

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Which operations must be supported?

We need the size of a linear listHey, we need to know how many elements the linear list has.

Determine list size forL = (a, b, c, d , e)

So, we need to have a operation that returns the sizesize(L)=5

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Linear List Operations: get(theIndex)

Get operationsGet element with given index.

For exampleL = (a, b, c, d , e)

Thusget(0) = aget(2) = cget(4) = eget(-1) = errorget(9) = error

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Linear List Operations: indexOf(theElement)

IndexOf operationsDetermine the index of an element.

ExampleL = (a, b, d , b, a)

ThusindexOf(d) = 2indexOf(a) = 0indexOf(z) = -1

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Linear List Operations: add(theIndex, theElement)

DefinitionAdd an element so that the new element has a specified index.

If we haveL = (a, b, c, d , e, f , g)

Thusadd(0,h) =⇒ L = (h, a, b, c, d , e, f , g)

I Thus, index of a, b, c, d , e, f , g increases by 1.

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Example

add(2,h) using the original L=⇒ L = (a, b, h, c, d , e, f , g)

I index of c, d , e, f , g increases by 1

What about out of the boundadd(10,h) =⇒ erroradd(-6,h) =⇒ error

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Example

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Example

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Linear List Operations: remove(theIndex)

DefinitionRemove and return element with given index.

For exampleL = (a, b, c, d , e, f , g)

ExampleRemove(2) returns c and L becomes (a, b, d , e, f , g)

I Index of d , e, f , g decreases by 1

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What about the Error

ForL = (a, b, c, d , e, f , g)

Thusremove(-1) =⇒ errorremove(20) =⇒ error

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What about the Error

ForL = (a, b, c, d , e, f , g)

Thusremove(-1) =⇒ errorremove(20) =⇒ error

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The Final Abstract Data Type for Linear List

Linear ListAbstractDataType LinearList{

instancesordered finite collections of zero or more elements

operationsisEmpty(): return true iff the list is empty, false otherwisesize(): return the list size (i.e., number of elements in the list)get(index): return the element with “index” indexindexOf(x): return the index of the first occurrence of x in the list, return -1

if x is not in the listremove(index): remove and return the indexth element, elements with higher

index have their index reduced by 1add(theIndex, x): insert x as the index of th element, elements with

theIndex ≥ index have their index increased by 1output(): output the list elements from left to right

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Java Interface

We can implement this idea of Abstract Data TypesUsing Java through the generic interface!!!An interface may include constants and abstract methods (i.e.,methods for which no implementation is provided).

Example for List

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Java InterfaceWe can implement this idea of Abstract Data Types

Using Java through the generic interface!!!An interface may include constants and abstract methods (i.e.,methods for which no implementation is provided).

Example for List

p u b l i c i n t e r f a c e L i n e a r L i s t <Item>{p u b l i c boo l ean isEmpty ( ) ;p u b l i c i n t s i z e ( ) ;p u b l i c I tem get ( i n t i nd ex ) ;p u b l i c i n t indexOf ( Item myobject ) ;p u b l i c vo i d add ( i n t index , I tem myobject ) ;p u b l i c I tem remove ( i n t i nd ex ) ;p u b l i c S t r i n g t o S t r i n g ( ) ;

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Implementing the Java Interface

Using a calss to implement the interface

c l a s s S imp l eA r r a y L i s t <Item> implementsL i n e a r L i s t <Item>{

// code f o r a l l methods must be p r o v i d ed

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Outline

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Abstract Classes Vs Interfaces

However, we have another way to implement ADTAbstract Classes

Abstract ClassesAn abstract class is a special kind of class that cannot be instantiated.It is a contract that is used to define hierarchies for all subclasses.

InterfaceAn interface is not a class.An interface has no implementation.It only has the definition of the methods without the body.

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Important

We haveA Java class may implement as many interfaces as it wants but can extendat most one class.

This is whyOnce you have chosen your design you can enforce the structure usingAbstract Classes!!!

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Important

We haveA Java class may implement as many interfaces as it wants but can extendat most one class.

This is whyOnce you have chosen your design you can enforce the structure usingAbstract Classes!!!

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Example of Abstract Class

p u b l i c a b s t r a c t c l a s s L i n e a r L i s t <Item>{p u b l i c boo l ean isEmpty ( ) ;p u b l i c i n t s i z e ( ) ;p u b l i c I tem get ( i n t i nd ex ) ;p u b l i c i n t indexOf ( Item myobject ) ;p u b l i c vo i d add ( i n t index , I tem myobject ) ;p u b l i c I tem remove ( i n t i nd ex ) ;p u b l i c S t r i n g t o S t r i n g ( ) ;

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preparation data structures 03 abstract data_types

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