Lec-5 Arrays ADT

8/3/2019 Lec-5 Arrays ADT

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Arrays


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C++ Style Data Structures: Arrays(1)

An ordered set (sequence) with a fixed

number of elements, all of the same

type,where the basic operation is

direct access to each element in the

array so values can be retrieved from

or stored in this element.


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C++ Style Data Structures: Arrays(2)

Properties:

Ordered so thereisa first element,asecond one,etc.

Fixed numberofelements fixed capacity

Elementsmust be thesame type(andsize);@ usearrays only forhomogeneous datasets.

Direct access: Accessan element by giving itslocation

The time to accesseachelement is thesame forall

elements,regardless of position. in contrast to sequentialaccess(where to accessan

element, onemust first accessall those that precedeit.)


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Declaring arrays in C++

whereelement_type is any type

array_name is the name of the array any valid identifier

CAPACITY (a positive integerconstant) is the numberofelementsin the array

score[0]

score[1]

score[2]score[3]

score[99]

.

.

.

.

.

.

element_type array_name[CAPACITY];

e.g., double score[100];

Theelements (orpositions) of the array are indexed 0, 1, 2,..

.,CAPACITY- 1.

Can't input thecapacity,

Why?

The compilerreserves a block of consecutive memorylocations,enough to hold CAPACITYvalues of type

element_type.


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indices numbered 0, 1, 2,...,CAPACITY - 1

Howwell does C/C++ implement an array ADT?

As an ADT In C++

ordered

fixed size

same typeelements

direct access

element_type is the type ofelements

CAPACITY specifies the capacity of the array

subscript operator[]


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an arrayliteral

Array Initialization

Example:

double rate[5] = {0.11, 0.13, 0.16, 0.18, 0.21};

Note 1: If fewervalues supplied than array's capacity,remainingelements

assigned 0.

double rate[5] = {0.11, 0.13, 0.16};

Note 2: It is an errorif more values are supplied than the declared size of the array.

How this erroris handled,however,will vary from one compilerto another.

rate

0

1

2

3

4

0.11 0.13 0.16 0 0

rate

0 1

2

3

40.11 0.13 0.16 0.18 0.21

In C++, arrays can be initialized when they are declared.Numeric arrays:

element_type num_array[CAPACITY] = {list_of_initial_values};


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Note 1: If fewervalues are supplied than the declared size of the array,

the zeroes used to fill un-initialized elements are interpreted asthe null character'\0' whose ASCII code is 0.

const int NAME_LENGTH = 10;char collegeName[NAME_LENGTH]={'C', 'a', 'l', 'v', 'i', 'n'};

vowel

0 1 2 3 4

A E I O U

char vowel[5] = {'A', 'E', 'I', 'O', 'U'};

Character Arrays:

Character arrays may be initialized in the same manneras numeric arrays.

declares vowel to be an array of 5 characters and initializes it as follows:

collegeName

0 1 2 3 4 5 6 7 8 9

C a l v i n \0 \0 \0 \0


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AddressesWhen an array is declared, the address of the first byte(orword) in the block of

memory associated with the array is called thebase address of the array.

Each array reference must be translated into an offsetfrom this base address.

Forexample, ifeachelement of array score will be stored in 8 bytes and the baseaddress ofscore is 0x1396. A statement such as

cout


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The value of array_name is actually thebase address ofarray_name

array_name + index is the address ofarray_name[index].

An array reference array_name[index]

is equivalent to

Forexample, the following statements of pseudocode areequivalent:

print score[3]print *(score + 3)

Note: No bounds checking of indices is done!

* is thedereferencingoperator

*refreturns thecontents of the memory location with address ref

*(array_name + index)

What will happen incase

ofgoing overboard


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Problems with Arrays

1.The capacity of Array can NOT change during program execution.

What is the problem?

Memory wastage

Out ofrangeerrors

2. Arrays are NOT self contained objects

What is the problem?

No way to find the last value stored.

Not a self contained object as perOOP principles.


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C++ Style MultidimensionalArrays

Most high level languages support arrays with more than one dimension.

2D arrays are useful when data has to be arranged in tabularform.

Higherdimensional arrays appropriatewhen several characteristics associated

with data.

Test 1 Test 2 Test 3 Test 4Student 1 99.0 93.5 89.0 91.0

Student 2 66.0 68.0 84.5 82.0

Student 3 88.5 78.5 70.0 65.0: : : : :: : : : :

Student-n 100.0 99.5 100.0 99.0

Forstorage and processing, use a two-dimensional array.

Example: A table of test scores forseveral different students on

several different tests.


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Declaring Two-Dimensional Arrays

Standard form of declaration:

element_type array_name[NUM_ROWS][NUM_COLUMNS];

Example:const int NUM_ROWS = 30,

NUM_COLUMNS = 4;

double scoresTable[NUM_ROWS][NUM_COLUMNS];

Initializationj List the initial values in braces,row by row;

j May use internal braces foreachrow to improvereadability.

Example:double rates[][] = {{0.50, 0.55, 0.53}, // first row

{0.63, 0.58, 0.55}}; // second row

..

.

[0][1][2][3]

[29]

[0] [[1] [2] [3]


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Processing Two-Dimensional ArraysjRemember: Rows (and) columns are numbered from zero!!

jUsedoubly-indexed variables:

scoresT

able[2][3] is theentry in row 2 and column 3oorow index column index

jUsenested loops to vary the two indices, most often in a rowwise manner.

Counting

from 0


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Higher-Dimensional Arrays

The methods for2D arrays extend in the obvious way to 3D arrays.

Example: To store and process a table of test scores forseveral different

students on several different tests for several different semesters

const int SEMS = 10, STUDENTS = 30, TESTS = 4;

typedef double ThreeDimArray[SEMS][STUDENTS][TESTS];

ThreeDimArray gradeBook;

gradeBook[4][2][3] is the score of 4th

semesterforstudent 2 on test 3

// numberof semesters, students and tests all counted from zero!!


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Arrays of Arrays

double scoresTable[30][4];

Declares scoresTable to be a one-dimensional array containing

30 elements,each ofwhich is a one-dimensional array of 4 real numbers; that is,

scoresTable is a one-dimensional array ofrows ,each ofwhichhas 4real values. We could declare it as

typedef double RowOfTable[4];

RowOfTable scoresTable[30];

...

[0][1][2][3]

[29]

[0] [[1] [2] [3]

.

..

[0] [[1] [2] [3][0]

[1]

[2]

[3]

[29]


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scoresTable[i] is the i-th row of the table

Address Translation:Address Translation:

The array-of-arrays structure of multidimensional arrays explains

address translation.

Suppose the base address ofscoresTable is 0x12348:

scoresTable[10] 0x12348 + 10*(sizeof RowOfTable)

In general, ann-dimensional array canbe viewed (recursively) as a

one-dimensional array whose elements are (n - 1)-dimensional arrays.

In any case:

scoresTable[i][j] should be thought of as (scoresTable[i])[j]that is, as finding the j-thelement ofscoresTable[i].

p

scoresTable[10][3]p base(scoresTable[10]) + 3*(sizeof double)

scoresTable[10][4]

...

...

[3]

[0][1]

[9]

[10]

...

= 0x12348 + 10 * (4 * 8) + 3 * 8

= 0x124a0

= 0x12348 + 10 * (4 * 8)


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Implementing Multidimensional ArraysMore complicated than one dimensional arrays.

Memory is organized as a sequence of memory locations, and is thus 1D

How to use a 1D structure to store a MD structure?

A B C D

E F G H

I J K L

A characterrequires a single byte

Compilerinstructed to reserve 12 consecutive bytes

Two ways to store consecutively i.e.rowwise and columnwise.


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Implementing Multidimensional Arrays

A B C D

E F G HI J K L

RowWise

A

B

C

D

E

F

G

HI

J

K

L

ColumnWise

A

E

I

B

F

J

C

GK

D

H

L

A B C D

E F G H

I J K L

A B C D

E F G H

I J K L

Lec-5 Arrays ADT

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