cs2468: data structures and data management lecturer: lusheng wang office: b6422 phone: 3442 9820...

CS2468: Data Structures and Data Management • Lecturer: Lusheng Wang • Office: B6422• Phone: 3442 9820 • E-mail [email protected]• TA (Assignment Marking)

– Chao SHEN [email protected] , Phone: 3442 2546 – Dan WANG [email protected] , Phone: 3442 2546

Welcome to ask questions at ANY time.• The course Website: http://www.cs.cityu.edu.hk/~lwang/ccs2468.html• Some Java Source code:http://net3.datastructures.net/download.html• The course Website:Text Book: Michael T. Goodrich and Roberto Tamassia, Data Structure and

Algorithms in Java, John Wiley & Sons, Inc. 5th Edition

Stacks 1

Topics to be covered• Analysis of Algorithms

– worst case time and space complexity• Data Structures

– stack, queue, linked list, tree, priority queue, heap, hash, and graph,

• Searching algorithms– binary and AVL search trees;

• Sorting algorithms– merge sort, quick sort, bucket sort and radix sort; (Reduce some

contents)• Graph

– data structure, depth first search and breadth first search. (add some interesting contents).

• shortest path.

Stacks 2

Why This Course?

• You will be able to evaluate the quality of a program (Analysis of Algorithms: Running time and memory space )

• You will be able to write fast programs• You will be able to solve new problems• You will be able to give non-trivial methods to solve

problems. (Your algorithm (program) will be faster than others.)

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Course Evaluations • Course work: 30%• Final Exam: 70%• Course Work: – Three assignments, 15%– One quiz 3% – One mid term exam 9%– Lab quiz 3%

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5

OBTL: Course Intended Learning Outcomes 1.Describe the functionality of a data structure as an abstract data type; 2.Implement an abstract data type in a programming language; 3.Implement and test data structures for common structures; 4.Select an appropriate data structure from a given set of structures to

solve a given problem; 5.Design and implement data storage management with simple file

structures.

Will be tested in quiz or assignment or midterm.For each item, you have to get 40% to pass.

Pre-requisites:

• CS2360 Java Programming /orCS2362 Computer Programming for Engineers & Scientists /orCS2363 Computer Programming /orCS2372 Fundamentals of Programming /or equivalent

• Not known java?– Spend the rest of 8-10 days to study Java.– Read textbook p1-p53 – Design a class with two integers C1 and C2 and a method f() to

calculate the average value of c1 and c2.– If you cannot do that, you should worry…

Stacks 6

• Data Structures– A systematic way of organizing and accessing data.

--No single data structure works well for ALL purposes.– Data stored– operation on data

• Algorithms– an effective method expressed as a finite list of well-defined

instructions for calculating a function. – Algorithms are used for calculation, data processing, and automated

reasoning. – In simple words an algorithm is a step-by-step procedure for

calculations.

Stacks 7

How to describe algorithm?

• Nature languages – Chinese, English, etc.– Not accurate.

• Pseudo-code– Codes close to computer languages

• Omits details that are not essential for human understanding– Intended for human reading rather than machine reading

• Programs – C /C++ programs, Java programs.

• Pseudo-code is preferred – Allow a well-trained programmer to be able to implement. – Allow an expert to be able to analyze the running time.

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An Example of an Algorithm

Algorithm sorting(X, n)Input array X of n integersOutput array X sorted in a non-decreasing order for i 0 to n 1 do

for j i+1 to n-1 do

if (X[i]>X[j]) then { s=X[i]; X[i]=X[j]; X[j]=s; }

return X

// after i-th round, the i-th smallest number is at i-th position.

Stacks 9

Algorithm sorting(X, n)Input array X of n integersOutput array X sorted in a non-decreasing order for i from 0 to n 1 do

for j from i+1 to n-1 do

if X[i] is larger than X[j] swap(X[i], X[j])

return X

// after i-th round, the i-th smallest number is at i-th position.

Variables, Primitives

• A variable has its value – A type is associated,

• E.g., int, boolean, float, long, etc.

– A value is assigned to the variable• The value is stored in the memory • The size of the value is determined umbigously; 64 bit machine, int 8 bytes,

double 8 bytes, etc

– Examples• int x;• int y=50;• char c, z=‘A’;

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11

Objects (extension of variables)

• An object has both a state and behavior. • State defines the object,

• Behavior defines what the object does.

• What is the size of an object in the memory?

Class Name: Circle Data Fields:

radius is _______ Methods:

getArea

Circle Object 1 Data Fields:

radius is 10


radius is 25


radius is 125

A class template

Three objects of the Circle class

12

Class

• Class defines

• the type of an object

• the kinds of operations that it performs.

• A Java class uses variables to define data fields and methods to define behaviors.

• A class provides a special type of methods,

• known as constructors, which are invoked to construct objects from the class.

13

Classes class Circle {

/** The radius of this circle */ double radius = 1.0; /** Construct a circle object */ Circle() { } /** Construct a circle object */ Circle(double newRadius) { radius = newRadius; } /** Return the area of this circle */ double getArea() { return radius * radius * 3.14159; }

}

Data field

Method

Constructors

14

Class Diagram

Circle

radius: double Circle()

Circle(newRadius: double)

getArea(): double

circle1: Circle radius: 10

Class name

Data fields

Constructors and Methods



UML Class Diagram

UML notation for objects

15

© 2003 Brooks/Cole Publishing / Thomson Learning™

Figure 2.3: Classspecification of Person

State/attributes—variablesOperation/action – methods

16


Figure 2.7: Providingmethods to access the attributes of Person

17© 2003 Brooks/Cole Publishing / Thomson Learning™

Figure 2.8: An Instance fred of the Person class

18


Figure 2.9: Using the access methods to set fred’s attributes

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Constructors

Circle() {}

Circle(double newRadius) { radius = newRadius;}

Constructors are a special kind of methods that are invoked to construct objects.

20

Constructors, cont.A constructor with no parameters is referred to as a no-arg constructor.

Constructors must have the same name as the class itself.

Constructors do not have a return type—not even void.

Constructors are invoked using the new operator when an object is created. Constructors play the role of initializing objects.

21

Creating Objects Using Constructors

new ClassName();

Example:new Circle();

new Circle(5.0);

22

Declaring/Creating Objectsin a Single Step

ClassName objectRefVar = new ClassName();

Example:Circle myCircle = new Circle();

Create an objectAssign object reference

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Accessing Objects• Referencing the object’s data: objectRefVar.data e.g., myCircle.radius

• Invoking the object’s method: objectRefVar.methodName(arguments) e.g., myCircle.getArea()

Show a complete program C7-TestCircle1.html

Part-B1 Stacks (p198-p213)

Abstract Data Types (ADTs)

• Abstract data type– an abstraction of a

data structure• An ADT specifies:– Data stored– Operations on the

data– Error conditions

associated with operations

• e.g. : ADT modeling a students record– The data stored are

• Student name, id, as1, as2,as3, exam

– The operations supported are• int averageAs(as1,as2,as3)• Int finalMark(as1, as2,as3, exam) )

– Error conditions:• Calculate the final mark for absent

student

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The Stack ADT (§5.1)

• The Stack ADT stores arbitrary objects

• Insertions and deletions follow the last-in first-out (LIFO) scheme

• Main stack operations:– push(object)

• inserts an element

– object pop()• removes and returns the last

inserted element

• Auxiliary stack operations:– object top()

• returns the last inserted element without removing it

– integer size()• returns the number of

elements stored

– boolean isEmpty()• indicates whether no

elements are stored

Stacks 26

Applications of Stacks

• Direct applications– Undo sequence in a text editor– Chain of method calls in the Java Virtual Machine

• Indirect applications– Auxiliary data structure for algorithms– Component of other data structures

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Parentheses Matching

• An expression, i.e.,[(2+3)*x+5]*2. • Each “(”, “{”, or “[” must be paired with a

matching “)”, “}”, or “[”– correct: • ( )(( )){([( )])}• ((( )(( )){([( )])}))

– incorrect• )(( )){([( )])}(• ({[ ])}• ([)])• (

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Examples

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Picture is from http://www.davesquared.net/2008/07/brackets-braces-parenthesis-and-other.html

Examples

( ) ( ( ) ) { ( [ ( ) ] ) }

( (

(

( ( {

(

{

[

(

{

(

[

(

{

[

(

{

(

{ {

Examples

( ) ( ( ] ) { ( [ ( ) ] ) }

( (

(

( (

Mismatch!!!

Examples

( ) ( ( ) ) { ( [ ) ] ) }

( (

(

( ( {

(

{

[

(

{

(

{

Mismatch!!!

Examples

( ) ( ( ) ) { ( [

( (

(

( ( {

(

{

[

(

{

Mismatch!!!(stack is non-empty)

Examples

( ) ( ( ) ) )

( (

(

( (

Mismatch!!!(pop empty stack)

Parentheses Matching AlgorithmAlgorithm ParenMatch(X,n):Input: An array X of n tokens, each of which is either a grouping symbol, avariable, an arithmetic operator, or a numberOutput: true if and only if all the grouping symbols in X matchLet S be an empty stackfor i=0 to n-1 do

if X[i] is an opening grouping symbol thenS.push(X[i])

else if X[i] is a closing grouping symbol thenif S.isEmpty() then

return false {nothing to match with} if S.pop() does not match the type of X[i] then

return false {wrong type} if S.isEmpty() then

return true {every symbol matched} else

return false {some symbols were never matched}

Stacks 35

Parentheses Matching Example 1

• Input: () (() [()])

i X[i]

Operation Stack Output

0 ( Push ( (

1 ) Pop ( Test if ( and X[i] match? YES

2 ( Push ( (

3 ( Push ( ((

4 ) Pop (Test if ( and X[i] match? YES

(

5 [ Push [ ([

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• Input: () (() [()])

i X[i]

Operation Stack

Output

6 ( Push ( ([(


([

8 ] Pop [Test if [ and X[i] match? YES

(


Test if stack is Empty? YES TRUE

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• Input: ( () [] ]()

i X[i]

Operation Stack Output

0 ( Push ( (

1 ( Push ( ((


(

3 [ Push [ ([

4 ] Pop [Test if [ and X[i] match? YES

(

5 ] Pop (Test if ( and X[i] match ? NO FASLE

Stacks 38

Stack Interface in Java

• Java interface corresponding to our Stack ADT

• Requires the definition of class EmptyStackException

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public interface Stack {

public int size();

public boolean isEmpty();

public Object top()throws EmptyStackException;

public void push(Object o);

public Object pop() throws EmptyStackException;

}

Exceptions

• Attempting the execution of an operation of ADT may sometimes cause an error condition, called an exception

• Exceptions are said to be “thrown” by an operation that cannot be executed

• In the Stack ADT, operations pop and top cannot be performed if the stack is empty

• Attempting the execution of pop or top on an empty stack throws an EmptyStackException

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Array-based Stack (Implementation)

• A simple way of implementing the Stack ADT uses an array

• We add elements from left to right

• A variable t keeps track of the index of the top element

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S0 1 2 t

…

Algorithm size()return t + 1

Algorithm pop()if isEmpty() then

throw EmptyStackException else

t t 1return S[t + 1]

Array-based Stack (cont.)

• The array storing the stack elements may become full

• A push operation will then throw a FullStackException– Limitation of the array-

based implementation– Not intrinsic to the Stack

ADT

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S0 1 2 t

…

Algorithm push(o)if t = S.length 1 then

throw FullStackException else

t t + 1S[t] o

Array-based Stack (Cont.)

• A Stack might be empty

• top returns the element at the top of the Stack, but does not remove the top element. When the Stack is empty, an error occurs.

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S0 1 2 t

…

Algorithm isEmpty() if t<0 then return true else return false

Algorithm top()if isEmpty() then

throw EmptyStackException return S[t ]

cs2468: data structures and data management lecturer: lusheng wang office: b6422 phone: 3442 9820...

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