Data Abstractions

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Data AbstractionsData Abstractions

Shyh-Kang JengShyh-Kang JengDepartment of Electrical Engineering/Department of Electrical Engineering/Graduate Institute of Communication Graduate Institute of Communication

EngineeringEngineeringNational Taiwan UniversityNational Taiwan University

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Data StructuresData Structures Conceptual organization of dataConceptual organization of data Basic data structuresBasic data structures

Homogeneous arrayHomogeneous array ListList

StackStack QueueQueue

TreeTree

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ListList A collection of entries that appear in a A collection of entries that appear in a

sequential ordersequential order ExamplesExamples

Class enrollment listsClass enrollment lists ““things-to-do” liststhings-to-do” lists DictionariesDictionaries SentencesSentences

Appear in both static and dynamic Appear in both static and dynamic formsforms

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StacksStacks A list in which all insertions and A list in which all insertions and

deletions are performed at the same deletions are performed at the same endend

A last-in, first-out (LIFO) structures A last-in, first-out (LIFO) structures Push and popPush and pop

C

A

B

Top

55

QueueQueue

A list in which all insertions are A list in which all insertions are performed at one end while all performed at one end while all deletions are made at the otherdeletions are made at the other

A first-in, first-out (FIFO) structureA first-in, first-out (FIFO) structure Head (front) and tail (rear)Head (front) and tail (rear)

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Organization ChartOrganization Chart

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File Structure of WindowsFile Structure of Windows

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TreesTrees

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TreesTrees NodesNodes

RootRoot Terminal (leaf)Terminal (leaf) Parent, children, siblingsParent, children, siblings

SubtreesSubtrees DepthDepth

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Data AbstractionData Abstraction Explores ways in which users can be Explores ways in which users can be

shielded from the details of actual data shielded from the details of actual data storage (memory cells and address) and storage (memory cells and address) and be allowed to access information as be allowed to access information as though it were stored in a more though it were stored in a more convenient form – Concept of convenient form – Concept of abstractionabstraction

The term user can be either human or a The term user can be either human or a software modulesoftware module

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Static vs. Dynamic Static vs. Dynamic StructuresStructures

Static structuresStatic structures Shape and size of the structure do not Shape and size of the structure do not

change over timechange over time Easier to manageEasier to manage

Dynamic structuresDynamic structures Either shape or size of the structure Either shape or size of the structure

changes over timechanges over time Must deal with adding and deleting data Must deal with adding and deleting data

entries as well as finding the memory entries as well as finding the memory space required by a growing data space required by a growing data structurestructure

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PointersPointers A memory cell (or perhaps a block of A memory cell (or perhaps a block of

memory cells) that contains the memory cells) that contains the address of another memory celladdress of another memory cell

ExamplesExamples Program counter as an instruction pointerProgram counter as an instruction pointer URLURL

Many programming languages include Many programming languages include pointers as a primitive data typepointers as a primitive data type Allow the declaration, allocation, and Allow the declaration, allocation, and

manipulation of pointersmanipulation of pointers Used to create dynamic data structuresUsed to create dynamic data structures

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Use of PointersUse of Pointers

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Stack and Heap SpaceStack and Heap Space

HeapStorage

StackStorage

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Homogeneous ArraysHomogeneous Arrays

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Two-Dimensional ArrayTwo-Dimensional Array

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Storage of a 2-D ArrayStorage of a 2-D Array Row major order vs. column major orRow major order vs. column major or

derder Finding an entry in the th row and tFinding an entry in the th row and t

h column of a h column of a -column 2-D array stor -column 2-D array stored in row major ordered in row major order

)1()1( jicx

i jc

Address polynomial

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Mini ReviewMini Review

Show how the array below would be Show how the array below would be arranged in main memory when arranged in main memory when stored in row major orderstored in row major order

55 33 77

44 22 88

11 99 66

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AnswerAnswer

5 3 7 4 2 8 1 9 65 3 7 4 2 8 1 9 6

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Mini ReviewMini Review Give a formula for finding the entrGive a formula for finding the entr

y in the th row and th column of y in the th row and th column of a 2-D array stored in column majoa 2-D array stored in column major orderr order

In C, C++, and Java, indices of arrays stIn C, C++, and Java, indices of arrays start at 0 rather than 1. In this case whaart at 0 rather than 1. In this case what address polynomial is used by the trat address polynomial is used by the translator to convert references of the fornslator to convert references of the form m Array[i][j]Array[i][j] into memory address? into memory address?

i j

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AnswersAnswers

)1()1( ijrx

jic

2222

Storing listsStoring lists

Contiguous listContiguous list = list stored in a homog = list stored in a homogeneous arrayeneous array

Linked listLinked list = list in which each node poi = list in which each node points to the next onents to the next one Head pointerHead pointer = pointer to first entry in list = pointer to first entry in list NIL pointerNIL pointer = non-pointer value used to indi = non-pointer value used to indi

cate end of listcate end of list

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Contiguous ListsContiguous Lists

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Contiguous ListContiguous List Convenient storage structure when Convenient storage structure when

implementing static listsimplementing static lists Inconvenient in dynamic casesInconvenient in dynamic cases

Delete a nameDelete a name Move entries to keep the list in the same Move entries to keep the list in the same

orderorder Add a name Add a name

Move the entire list to obtain an available Move the entire list to obtain an available block of contiguous cells large enough for the block of contiguous cells large enough for the expanded listexpanded list

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Linked ListLinked List

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Deleting an EntryDeleting an Entry

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Inserting an EntryInserting an Entry

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A Stack in MemoryA Stack in Memory

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Operations on QueuesOperations on Queues

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Circular Queues (1)Circular Queues (1)

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Circular Queues (2)Circular Queues (2)

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Mini ReviewMini Review Using paper and pencil, keep a record Using paper and pencil, keep a record

of the circular queue during the of the circular queue during the following scenario. Assume that the following scenario. Assume that the block reserved for the queue can block reserved for the queue can contain only four entries.contain only four entries. Insert entries A, B, CInsert entries A, B, C Remove two entriesRemove two entries Insert entries D, EInsert entries D, E Remove an entryRemove an entry Insert entry FInsert entry F Remove an entry Remove an entry

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AnswerAnswer

A B C

H T

B C

H T

C

H T

DC

HT

E DC

HT

E D

T H

E F D

T H

E F

H T

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Storing a binary treeStoring a binary tree Linked structureLinked structure

Each node = data cell + two child pointersEach node = data cell + two child pointers Accessed through a pointer to root nodeAccessed through a pointer to root node

Mapped to a contiguous arrayMapped to a contiguous array A[1] = root nodeA[1] = root node A[2],A[3] = children of A[1]A[2],A[3] = children of A[1] A[4],A[5],A[6],A[7] = children of A[2] and A[3]A[4],A[5],A[6],A[7] = children of A[2] and A[3] ……

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Binary Tree NodeBinary Tree Node

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Linked Storage System Linked Storage System

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Storage without PointersStorage without Pointers

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Inefficient StorageInefficient Storage

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Mini ReviewMini Review Draw a diagram representing how Draw a diagram representing how

the tree below appears in memory the tree below appears in memory when stored using the left and right when stored using the left and right child pointers.child pointers.

Draw another diagram showing how Draw another diagram showing how the tree would appear in contiguous the tree would appear in contiguous storage.storage.

y

x z

w

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AnswerAnswer

Y Z NILNIL

X NIL W NILNIL

Y X Z W

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Manipulating data structuresManipulating data structures

Ideally, a data structure should be Ideally, a data structure should be manipulated solely by pre-defined manipulated solely by pre-defined procedures.procedures. Example: A stack typically needs at Example: A stack typically needs at

least push and pop procedures.least push and pop procedures. The data structure along with these The data structure along with these

procedures constitutes a complete procedures constitutes a complete abstract tool.abstract tool.

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Printing a Linked ListPrinting a Linked List

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Binary Tree PackageBinary Tree Package

Search for the presence of an entrySearch for the presence of an entry Use the binary search algorithmUse the binary search algorithm

Print the list in orderPrint the list in order Insert a new entryInsert a new entry

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Ordered TreeOrdered Tree

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Search the Binary TreeSearch the Binary Tree

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Search Binary TreeSearch Binary Tree

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Printing a Binary TreePrinting a Binary Tree

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Mini ReviewMini Review

Draw a binary tree to store the list R, S, T,Draw a binary tree to store the list R, S, T, U, V, W, X, Y, and Z for future searching U, V, W, X, Y, and Z for future searching

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AnswerAnswer

V

T Y

S U

R

X Z

W

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Printing a Tree in OrderPrinting a Tree in Order

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Traversing a Binary TreeTraversing a Binary Tree

Inorder traversalInorder traversal Left – Root – Right Left – Root – Right

Preorder traversalPreorder traversal Root – Left – Right Root – Left – Right

Postorder traversalPostorder traversal Left – Right – Root Left – Right – Root

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Inserting an Entry (1)Inserting an Entry (1)

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Inserting an Entry (2)Inserting an Entry (2)

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Inserting an EntryInserting an Entry

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User-Defined TypesUser-Defined Types Expressing an algorithm is often more Expressing an algorithm is often more

convenient if types other than those convenient if types other than those provided as primitives in the provided as primitives in the programming languageprogramming language

Many modern programming languages Many modern programming languages allow programmers to define additional allow programmers to define additional data types, using the primitive types data types, using the primitive types and structures as building blocksand structures as building blocks

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Customized data typesCustomized data types User-defined data typeUser-defined data type = template for a = template for a

heterogeneous structureheterogeneous structure Abstract data typeAbstract data type = user-defined data type = user-defined data type

with methods for access and manipulationwith methods for access and manipulation ClassClass = abstract data type with extra features = abstract data type with extra features

Characteristics can be inheritedCharacteristics can be inherited Contents can be encapsulatedContents can be encapsulated Constructor methods to initialize new objectsConstructor methods to initialize new objects

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Customized Data TypesCustomized Data Typesstruct {struct {

char Name[8];char Name[8];int Age;int Age;float SkillRating;float SkillRating;

} Employee;} Employee;typedef struct {typedef struct {

char Name[8];char Name[8];int Age;int Age;float SkillRating;float SkillRating;

} EmployeeType;} EmployeeType;EmployeeType DistManager, SalesRep1, SalesRep2;EmployeeType DistManager, SalesRep1, SalesRep2;

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Declaration of Nodes of a Declaration of Nodes of a Binary TreeBinary Tree

typedef struct {typedef struct { char data;char data; Node* left;Node* left; Node* right;Node* right;} Node;} Node;

Node* root;Node* root;

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C++ ClassC++ Class

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Using ClassesUsing Classes

StackOfIntegers StackOne(50);StackOfIntegers StackOne(50); StackOne.push(106);StackOne.push(106); int OldValue = StackOne.pop();int OldValue = StackOne.pop();

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Standard Template LibraryStandard Template Library

A collection of predefined classes in A collection of predefined classes in C++ that describe popular data C++ that describe popular data structuresstructures

The programmer is thus relieved The programmer is thus relieved from the task of describing these from the task of describing these structures in detailstructures in detail

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Pointers in Machine Pointers in Machine LanguageLanguage

Machine language defined in Appendix CMachine language defined in Appendix C Load data (immediate addressing)Load data (immediate addressing)

2RXY2RXY Load address (direct addressing)Load address (direct addressing)

1RXY1RXY Load through pointer (indirect addressing)Load through pointer (indirect addressing)

DRXYDRXY DR0SDR0S

Save through pointerSave through pointer ER0SER0S

XY

R

S

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Expanding the Machine Expanding the Machine Language to Take Advantage Language to Take Advantage

of Pointersof Pointers

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Loading a Register from a Loading a Register from a Memory Cell Located by a Memory Cell Located by a

Pointer in a RegisterPointer in a Register

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Mini ReviewMini Review Suppose the machine language has been Suppose the machine language has been

extended to include pointer operations. extended to include pointer operations. Moreover, suppose register 8 contains the Moreover, suppose register 8 contains the pattern DB, the memory cell at address DB pattern DB, the memory cell at address DB contains the pattern CA, and the cell at contains the pattern CA, and the cell at address A5 contains the pattern CA. What address A5 contains the pattern CA. What bit pattern will be in register 5 bit pattern will be in register 5 immediately after executing the following immediately after executing the following instructions:instructions: 15A515A5 25CA25CA D508D508

6666

AnswersAnswers

CACA CACA CACA

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ExerciseExercise

Review problems Review problems

2, 5, 8, 14, 16, 19, 24, 26, 30, 2, 5, 8, 14, 16, 19, 24, 26, 30, 4444