Data Structure and Algorithm: CIT231 Lecture 3: Arrays and ADT DeSiaMore DeSiaMore .

Data Structure and Algorithm: CIT231

Lecture 3: Arrays and ADT

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Function for Deleting Array

void array::del (int pos){

//skip to the desired positionfor (int i=pos; i<MAX; i++)arr[i-1] = arr[i];arr[i-1]=0;

}


Displaying the array

void array::display (){

cout<<endl;//Traverse the entire arrayfor (int i = 0; I < MAX; i++)

cout<<“ “<<arr[i];}


A first look an ADTs Solving a problem involves processing data, and an

important part of the solution is the careful organization of the data

In order to do that, we need to identify:1. The collection of data items 2. Basic operation that must be performed on them

Abstract Data Type (ADT): a collection of data items together with the operations on the data


Abstract Data Type (ADT)

The word “abstract” refers to the fact that the data and the basic operations defined on it are being studied independently of how they are implemented.

We think about what can be done with the data, not how it is done


Types A type (data type) is a set of values that an object can have.

An abstract data type (ADT) is a: data type Set of functions (operations) that operates on data of that type

Each function is defined by its signature. Can also specify operations formally (see section 4.2.5) (Algebraic data types): f(g(A,S)) = A


Example ADT ADT student: Operations: SetName: name x student student GetName: student name SetCourse: course x student student GetCourse: student course * GetCredits: student integer

In this example, Name and Course are undefined ADTs. They are defined by some other abstraction.


Real world ADT example


Implementation of ADT

An implementation of ADT consists of storage structures to store the data items and algorithms for basic operation


Data Structures, Abstract Data Types, and Implementations in Real World

Consider example of an airplane flight with 10 seats to be assigned

TasksList available seatsReserve a seat

How to store, access data?


Data Structures, Abstract Data Types, and Implementations Consider example of an airplane flight with

10 seats to be assigned Tasks

List available seatsReserve a seat

How to store, access data?10 individual variables


Use 10 individual variables Algorithm to List available seats

1. If seat1 == ‘ ’:display 1

2. If seat2 == ‘ ’: display 2

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.10. If seat10 == ‘ ’:

display 10

Algorithm to Reserve a seat

1. Set DONE to false2. If seat1 ==‘ ’:

print “do you want seat #1??”Get answerif answer==‘Y’:set seat1 to ‘X’set Done to True

3. If seat2 ==‘ ’:print “do you want seat #2??”Get answerif answer==‘Y’:set seat2 to ‘X’set Done to True

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Data Structures, Abstract Data Types, and Implementations Consider example of an airplane flight with 10

seats to be assigned Tasks

List available seatsReserve a seat

How to store, access data?10 individual variablesAn array of variables


Use Array Algorithm to List available seatsFor number ranging from 0 to max_seats-1, do:

If seat[number] == ‘ ’:Display number

Algorithm to Reserve a seat

Readin number of seat to be reservedIf seat[number] is equal to ‘ ’:

set seat[number] to ‘X’Else

Display a message that the seat having this number is occupied


ADTs In this simple example, it does illustrate the concept of

an Abstract Data Type

ADT consists of1. The collection of data items 2. Basic operation that must be performed on them

In the example, a collection of data is a list of seats The basic operations are (1) Scan the list to determine

which seats are occupied (2) change seat’s status


Data Structure and Abstract Data Type The term of Data Structure and Abstract Data Type

are often used interchangeably

However, we use ADT when data is studied at a logical level

The term data structure refers to a construct in programming language that can be used to store data


Array ADT

Collection of data elementsA fixed-size sequence of elements, all of the

same type

Basic OperationsDirect access to each element in the array by

specifying its position so that values can be retrieved from or stored in that position


Different types of Array

One-dimensional array: only one index is used Multi-dimensional array: array involving more

than one index

Static array: the compiler determines how memory will be allocated for the array

Dynamic array: memory allocation takes place during execution


Array and ADT Collection of data elements

A fixed-size sequence of elements, all of the same type

Basic Operations Direct access to each element in the array by specifying its position so

that values can be retrieved from or stored in that position

An Array as an ADT C++ Array

Fixed size ----------------------specify the capacity of the arrayOrdered-------------------------indices are numbered 0,1,2,…,capacity-1 Same type of elements-------specify the element type Direct access-------------------subscript operator[]


Multidimensional Arrays… 2D-Arrays A two dimensional array is a collection of

elements placed in m rows and n columns. The syntax of 2-D array includes two

subscripts, of which one represents number of rows and the other specifies the number of columns of an array

These two subscripts are used to reference an element in an array. For example arr[3][4] is a 2-D array containing 3 rows and 4 columns.


Multidimensional Arrays… 2D-Arrays Arr[0][2] is an element placed at 0th row

and 2nd column in the array. The two dimensional array is also called a matrix.

Representation of a 2-D array.

0 1 2 3

0 12 1 -6 25

1 30 73 156 34

2 4 29 42 56


Multidimensional Arrays … 2D-Arrays Consider a table of test scores for

several different students


Row Major and Column Major Arrangement Rows and columns of matrix are imaginary. Matrix are get stored in memory linearly as

computer memory can be viewed as consecutive units of memory.

This lead to two major arrangements in memory:Row Major arrangementColumn major arrangement

Consider an example below


Row Major and Column Major Arrangement int a[3][4] = { { 12,1,-9,23}

{ 14,7,11,121} { 6,78,15,34}

}


Row Major and Column Major Arrangement Since the array elements are stored in

adjacent memory locations we can access any elements of the array one we know the base address (starting address) of the array and number of rows and columns present in the array.

Example if the base address of the array above is 502 and we wish to refer the element 121, then the calculation involved would be as follows:


Row Major and Column Major Arrangement Row Major arrangement:Element 121 is present at a[1][3]. Hence location of

121 would be = 502 + 1*4+3 = 502 + 7 = 516 In general for an array a[m][n] the address of

element a[i][j] would be: Base address + i*n+j


Row Major and Column Major Arrangement Column Major arrangement:Element 121 is present at a[1][3]. Hence

location of 121 would be:= 502 + 3*3 + 1= 502 + 10= 522

Generally for an address of an array a[m][n] the address of element a[i][j] would be


Row Major and Column Major ArrangementBase address + j*m+i. Note the C++

permits only a Row Major arrangement, whereas, Pascal uses a Column Major Arrangement.


Data Structure and Algorithm: CIT231 Lecture 3: Arrays and ADT DeSiaMore DeSiaMore .

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