array one two

8/9/2019 Array One Two

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Array


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Objective

Understand what is an array

Learn about types of array

Declaration Initialization

Ways to access individual elements

Other possible operations


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Need for an Array

ach variable can only be used to store asin!le value at a time"

"!" int a#

$oat b#

%he avera!e of two inte!er numbers !ivenby the user can easily be computed"

&ut printin! the numbers that are !reaterthan the avera!e' re(uires) *eadin! the numbers +alculatin! the avera!e

+hec,in! the each number with avera!e"


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+ont-

.o there is a need to store lar!enumber of variables of same typeunder a sin!le variable"

asy understandin! of the pro!ram"

"!"

%o store /ar,s of 01 students"

*ecord of sales of 211 salesman"


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De3nition

An array is a collection of individualdata elements that is

Ordered ) one can count o4 the elements

1'2'5'-

6i7ed in size

8omo!enous ) all elements have to be of

the same data type""!" int' $oat' double' char etc"

It is considered as derived data type"


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Array Applications

9iven a list of test scores' determine thema7imum and minimum scores"

*ead in a list of student names andrearran!e them in alphabetical order:sortin!;"

9iven the hei!ht measurements ofstudents in a class' output the names ofthose students who are taller than

avera!e"


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%ypes of Array

One Dimensional Array

%wo Dimensional Array

/ulti


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One Dimensional Array

Array is One Dimensional, there will be asingle subscript or index whose value

refers to the individual array elements

which ranges from 0 to (n!", where n isthe total number of elements in the array#

Also called as single dimensional array


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Declaration One DimensionalArray

%hree thin!s need to be speci3ed) %he type of data it can hold' i"e" int' $oat' double etc"

%he number of values it can hold or size' i"e" ma7imumnumber of elements it can hold

A name of array" .ynta7)

[]

E.g. intA[10];

must be an constant or a constante7pression" "


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+ont-

// array of 10 uninitialized ints

intA[10];

-- -- ----A -- -- ---- -- --

4 5 630 2 8 971


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+ont-

Declare an array of 21 inte!ers)intA[10]; // array of 10 ints

%o access an individual element we must apply a

subscript to array namedA. A subscript is a brac,eted e7pression"

%he e7pression in the brac,ets is ,nown as the inde7"

6irst element of array has inde7 1"

A[0]

.econd element of array has inde7 2' and so on"A[1] A[!] A["]#

Last element has an inde7 one less than the size of thearray"

A[$]

Incorrect inde7in! is a common error"


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+ont-

Invalid Declaration

double 7=>

no value assi!ned to the size"

int N#

double 7=N>

?ariable of inte!er data type speci3ed assize of the array


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+ont-

?alid Declaration @de3ne N 211

void main:;

double 7=N>#

B 8ere array size is de3ned usin! symbolic

constant' rather than 37ed inte!er"

Number of array elements can also be!iven by an e7pression"

@de3ne N 21 int A=NC2>


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Initializin! One DimensionalArray

// array of 10 uninitialized ints

intA[10];

A["] % 1;

int& % A["];

-- -- 1--A -- -- ---- -- --

4 5 630 2 8 971

A[4] A[5] A[6]A[3]A[0] A[2] A[8] A[9]A[7]A[1]


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+ont-

Array has multiple elements' bracesare used to denote the entire array ofvalues and commas are used to

separate the individual valuesassi!ned to the elements in the arrayinitialization statement as)intA[10] % '111!()"!1*$+,;

12 5 611A 2 1 83 9 7

4 5 630 2 8 971

A[4] A[5] A[6]A[3]A[0] A[2] A[8] A[9]A[7]A[1]


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+ont-

While initializin!' the size of a one' i#

GGInput .e!mentprintf:Jnter the elements of the arrayJ;#for:i1# iH21# iCC;

scanf:JKdJ'Ea=i>;#

GGOutput .e!mentprintf:Jn %he elements of the array arenJ;#for:i1# iH21# iCC;

printf:JtKdJ'a=i>;#B


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Other Way


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@includeHstdio"hvoid main:;

int a=50>' i' n#printf:Jnter the value of n) J;#scanf:JKdJ'En;#

GGInput .e!mentprintf:Jnter the elements of the arrayJ;#for:i1# iHn# iCC;

scanf:JKdJ'Ea=i>;#

GGOutput .e!mentprintf:Jn %he elements of the array arenJ;#for:i1# iHn# iCC;

printf:JtKdJ'a=i>;#B


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7ample

&i!!est amon! !iven Mn inte!ernumber" As Mn numbers are to be considered' all these elements are

read into an array :say a; and thenthe biggest/maximumamon! all these is found"

%o start with the very 3rst element a= 1 > is assumed to be the

ma7imum :max;"

%hen this maxis comparedwith the elements startin! from

the 5ndlocation i"e" startin! from the elements at thelocations a=2>' a= 5 >' a= P >'-' a=nQ 2>' one by one"

If at any comparison sta!e the max is found to be smallerthan a=i> then the contents of a=i> is copied into maxand thecomparison process is continued till the end"

At the end the value of the biggestelement will be availablein max"


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Program:

@includeHstdio"h@includeHconio"h

void main:;

int a=50>'i'n'ma7#

clrscr:;#

printf:JInput the value of n) J;#

scanf:JKdJ'En;#

GGInput .e!mentprintf:JInput the array elementsnJ;#

for:i1#iHn#iCC;

scanf:JKdJ'Ea=i>;#


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GGinitially a=1> is assumed as ma7imum

ma7 a=1>#

GG+omparison starts with 5nd element of the array

for:i2#iHn#iCC;

if:ma7Ha=i>;

ma7 a=i>#

B

printf:Jn%he ma7imum is Kd amon! the !iven elements

of the arrayJ' ma7;#!etch:;#

B


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Output

Input the value of n) 0

Input the array elements25 R 2S T P

%he ma7imum is 2S amon! the !iven elements of the array


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7ample

%o 3nd the avera!e of a !iven set ofn numbers" All the !iven numbers are stored in an array'

say a"Averageis found out by 3rst summingall the

elements and then dividin! the sumby totalnumber of elements Mn"

%his process can be mathematicallyrepresented as


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Program:


void main:;

int a=50>'i'n'sum1#

$oat avera!e#

clrscr:;#


scanf:JKdJ'En;#

GGInput .e!ment

printf:JInput the array elementsnJ;#

for:i1#iHn#iCC;

scanf:JKdJ'Ea=i>;#


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GGG3ndin! the sum of all elements

for:i1#iHn#iCC;sum sum C a=i>#

avera!e :$oat;sumGn#

printf:JnAvera!e K"5fJ' avera!e;#

!etch:;#

B

Output

Input the value of n) 0

Input the array elements25 R 2S T P

Avera!e R"T


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7ample

.earchin! As a set of inte!er elements are to be handled' it is

ta,en as an array' say a"

8ere the problem is to searchfor a re(uired

element in the !iven array" %he re(uired element is!enerally ,nown as the search key" Let this search,ey be represented by a variable called key"

%he searchin! process for the ,eys presence in thearray starts from the be!innin! of the array andcontinue till either the key is availableor tillthe end of the arrayis reached" %herefore' thismethod is ,nown as linear searchor sequentialsearch method"


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+ont-

Search key = 36

Search key = 30


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Program:

@includeHstdio"h

@includeHconio"h

void main:;

int a=51>',ey'i'n'$a! 1' pos 1#

clrscr:;#


scanf:JKdJ'En;#

GGInput .e!ment

printf:JInput the array elementsnJ;#

for:i1#iHn#iCC;

scanf:JKdJ'Ea=i>;#

printf:Jnnter ,ey number) J;# GG*eadin! the ,eyelement

scanf:JKdJ'E,ey;#


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for:i1#iHn#iCC;

GGWhether element is e(ual to ,ey number or not

if:a=i> ,ey;

$a! 2#

pos i#

brea,#

B

B

if:$a! 2;

printf:JKd is found in position number KdJ',ey'posC2;#else

printf:JKd is not found in the arrayJ',ey;#

!etch:;#

B


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7ercise

%o 3nd the ma7imum and minimumamon! the !iven elements in anarray"

%o read n inte!ers:zero' Cve'


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7ample

Write an al!orithm to sort set ofnumbers in ascendin! order"

Sortingis any process of arran!in!

elements accordin! to a certain se(uence" &ubble .ort

lements in consecutive locations are comparedfrom the be!innin! to the end of the array"

If they are in the re(uired order' nothin! is doneand the comparison of ne7t set of consecutiveelements is made"


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7ample

One pass has put the lar!est elementin its place"


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Program:


void main:;

int a=50>' i' n' j' temp#clrscr:;#

printf:Jnter the value of n) J;#scanf:JKdJ'En;#

GGInput .e!mentprintf:Jnter the elements of the arraynJ;#for:i1# iHn# iCC;

scanf:JKdJ'Ea=i>;#


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Program:

GG%his loop performs re(uired no" of passesfor:i1#iHn#a=j> a=jC2>#a=jC2> temp#

BB

B


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Program:

GGOutput .e!mentprintf:Jnn .orted elements arenJ;#

for:i1# iHn# iCC;printf:JKdtJ'a=i>;#

!etch:;#B

Output:nter the value of n) 0

nter the elements of the array

5 X T 0

.orted elements are

5 0 T X


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7ample

Write a pro!ram in c to cyclicallyrotate the elements in array" Fro!ramshould accept a choice in which

direction to rotate i"e" left to ri!ht"Dependin! on choice it shouldperform cyclic rotation"

.uppose array A contains elements

A[4]

430 21

2 41A 5

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

$


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+ont-

If choice is rotate left then outputshould be

If choice is rotate ri!ht then outputshould be

A[4]

430 21

3 52A 1

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

%

A[4]

430 211 35A 4

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

&

Program:


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Program:@includeHstdio"h@includeHconio"hvoid main:;

int a=50>' i' n' r' temp#printf:Jnter the value of n) J;#scanf:JKdJ'En;#

GGInput .e!ment

printf:Jnter the elements of the arraynJ;#for:i1# iHn# iCC;scanf:JKdJ'Ea=i>;#

GG+hoice inputprintf:Jn2" Left J;#

printf:Jn5" *i!ht J;#printf:Jnnter rotation choice from above) J;#scanf:JKdJ'Er;#

Program:


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gswitch:r;

case 2)

temp a=1># GG+opyin! 2stelement of array to variable"

GGLoop for copyin! other element to proper position

for:i2#iHn#iCC;a=i a=i>#

a=n temp

brea,#case 5)temp a=n# GG+opyin! :n


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Program:

GGOutput .e!ment

printf:Jnn .orted elements arenJ;#

for:i1# iHn# iCC;

printf:JKdtJ'a=i>;#

!etch:;#

B

Output:

nter the value of n) 0nter the elements of the array) 2 5 P S 0

2" Left to *i!ht

5" *i!ht to Left

nter rotation choice from above) 2

%he elements of after *otations are)

5 P S 0 2


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7ercise

Write a pro!ram to sort list elementsin descendin! order"


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Array with more than one dimensionsare called multidimensional arrays"

An array of two dimensions calledtwo dimensional array"

"!" +hess board"


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It is a collection of data elements ofsame data type arran!ed in rows andcolumns :that is' in two dimensions;"

"!"

int sales=P>=0>#


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Declaration of 5D Array

.ynta7) [][]

E.g. intA[*][*];

-must bean constant"

- are

the sizes of the arrays first andsecond dimension.


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Initializin! 5D Array

%he no" of subscript determines thedimensionality of an array"

%wo dimension can be named asrow:2stdimension; and column:5nddimension;"

"!"int a=P>=5> 2'2' 5'S'

P'XB#

int a=P>=5> 2'2B' 5'SB' P'XBB#

int a=P>=5> 2'2' 5'S' P'XB#

int a= >=5> 2'2' 5'S' P'X'0'TB#


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Accessin! 5D Array

%wo dimensional array is nothin! but matri7"

Let Abe a !iven matri7' havin! mrows andncolumns i"e" a m7 nmatri7

2stelement of matri7 is accessed as A=1>=1>"

Last element of matri7 is accessed as A=m=n"

*eadin! and Frintin! 5D


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*eadin! and Frintin! 5DArray

The general element of this matrix is aij"

8ere the 3rst subscript irepresents a row and

the second subscriptjrepresents a column" %his matri7 could be read in row-wise' i"e" in

the order a11' a12' a15' a21' a22and so on' or

could be read in column-wise' i"e" in the

order a11' a21' a12' a22and so on" &ut a matri7 is always printed row


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int a=21>=21>' i' j' m' n#printf:Jnter the value of m E n) J;#scanf:JKdKdJ'Em'En;#

GGInput .e!mentprintf:Jnter the elements of the matri7J;#for:i1# iHm# iCC;for:j1# jHn#jCC;scanf:JKdJ'Ea=i>=j>;#

GGOutput .e!mentprintf:Jn %he elements of the array arenJ;#for:i1# iHm# iCC;for:j1#jHn#jCC;printf:JKdtJ'a=i>=j>;#printf:YnZ;#B

B


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Output)

nter the value of m E n) 5 5nter the elements of the array 2 5 P S

%he elements of the array are

2 5

P S


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%ranspose

%ranspose of !iven matri7

LetAbe the !iven matri7 ofsize mby n"

Also let Bis the transpose of the !ivenmatri7" %he transpose of a matri7 isobtained by interchanging its rowelements and column elements"

"!"

][1A =

0 5 P 0 S RA S 2 & 5 X

R X T P 2 T


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&y comparin! the two representations

of B!iven above we see that any elementof Bi"e" bijis e(ual to aji"

%herefore' the relation bij= ajiis

used repeatedlyto !enerate all the elements

of the transposed matrix" Note if the size of matri7 is :m[ n; then the

size of its transpose will be :n[ m;"


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Fro!ram)


int a=21>=21>' b=21>=21>'i'j'm' n#

printf:Jnter the value of m E n) J;#scanf:JKdKdJ'Em'En;#

GGInput .e!mentprintf:Jnter the elements of the arrayJ;#

for:i1# iHm# iCC;for:j1#jHn#jCC;scanf:JKdJ'Ea=i>=j>;#


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GG%ransposin!for:i1#iHn#iCC;

for:j1#jHm#jCC;b=i>=j> a=j>=i>#GGOutput .e!mentprintf:Jn %ranspose of /atri7 AnJ;#

for:i1# iHn# iCC;for:j1#jHm#jCC;

printf:JtKdJ'b=i>=j>;#

printf:JnJ;#B

B


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Output)

nter the value of m E n) 5 P

nter the elements of the array 2 5 P S 0 T

%ranspose of /atri7 A

2 S

5 0

P T


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Norm

Norm

&y de3nition normof a matri7 isthe square root of the sum of the

squares of all its individual elements"


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+ont-

.ince all the elementsare to be considered' onehas to consider the !eneral element aij' where ais

a !iven matri7 of m rowsand n columns"%he square of every elementis obtained by simply

multiplying it by itself once' i"e" by usin! :aij\ aij;"%he sum of all :aij;5is obtained by the relation)

After 3ndin! the sumthe norm is obtained by3ndin! the s(uare root of the sum" usin! therelation


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Fro!ram)@includeHstdio"hvoid main:;

int a=21>=21>' i'j'm' n'sum#$oat norm#

printf:Jnter the value of m E n) J;#scanf:JKdKdJ'Em'En;#

GGInput .e!mentprintf:Jnter the elements of the arrayJ;#

for:i1# iHm# iCC;for:j1#jHn#jCC;scanf:JKdJ'Ea=i>=j>;#


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sum 1#for:i1#iHm#iCC;

for:j1#jHn#jCC;

sum sum C a=i>=j> \a=i>=j>#

norm s(rt:sum;#

GGOutput .e!mentprintf:Jn Norm of the !iven matri7 is

K"5fJ'norm;#

B


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Output)

nter the value of m E n) 5 5

nter the elements of the array 2 5 P S

Norm of the !iven matri7 is 5"11

/atri7 addition and


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/atri7 addition andsubtraction

In order to obtain the sum or di4erence oftwo !iven matrices' the sie of the givenmatrices must be same"

%he sum of two matrices is obtained bysummin! the correspondin! elements of the!iven matrices"

%he di4erence of two matrices is obtained

by 3ndin! out the di4erence between thecorrespondin! elements of the !ivenmatrices"

If


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If

sum

%hus every element of the sum matri7 + isobtained usin! the relation cij aijC bijfor all

values of iandj!

"i#erence

%hus every element of the di4erencematri7 "is obtained usin! therelation dij aij< bijfor all values of iandj"


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Fro!ram)@includeHstdio"h

void main:;

int a=21>=21>' b=21>=21>'c=21>=21>' i'j'm' n#

printf:Jnter the value of m E n) J;#

scanf:JKdKdJ'Em'En;#

GG*eadin! the matri7 A

printf:Jnter the elements of the matri7 AnJ;#

for:i1# iHm# iCC;

for:j1#jHn#jCC;

scanf:JKdJ'Ea=i>=j>;#

GG*eadin! the matri7 &printf:Jnter the elements of the matri7 &nJ;#


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printf: nter the elements of the matri7 &n ;#for:i1# iHm# iCC;for:j1#jHn#jCC;scanf:JKdJ'Eb=i>=j>;#

GG6indin! the sumfor:i1#iHm#iCC;for:j1#jHn#jCC;c=i>=j> a=i>=j> C b=i>=j>#

GGOutput .e!mentprintf:Jn *esultant /atri7 +nJ;#for:i1# iHm# iCC;for:j1#jHn#jCC;

printf:JtKdJ'c=i>=j>;#printf:JnJ;#B

B

O t t


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Output)

nter the value of m E n) 5 5

nter the elements of the matri7 A

2 5 P S

nter the elements of the matri7 &

0 T R

*esultant /atri7 +

T R

21 25

/atri7 /ultiplicationGFroduct


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/atri7 /ultiplicationGFroductof 9iven %wo /atri7

LetAand Bare two !iven matrices ofdimensions :m[ n; and :p[ q;respectively"

Also let $be theproduct matrix" 6or the multiplication of !iven two

matrices' number of columns of the %rstmatrix must bee(ual to number of rows of

the second matrix' i"e" nmust be e(ualtop" %he product matri7 $will be of size:m[ q;"


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Let

Obviously' Ais a :5 \ P; matri7' i"e" m 5

and n P Bis a :P [ P; matri7' i"e"p P and q P

.ince n & p' multiplication is possible" %he

resultantproduct matrix $will be a m[ q'i"e" 5 [ P matri7"

%he row elements of + are obtained asfollows)

+11) A11\ &11C A12\&21C A15\ &51

+12) A11\ &12C A12\&22C A15\ &52

+ ) A \ & C A \& C A \ &


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%he 3rst subscript of Awill be the 3rstsubscript of Cand the second subscript of B

will be the second subscript of C" Observe that second subscript of Aand the

3rst subscript of Bare same and vary from 1upto n


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Fro!ram)@includeHstdio"hvoid main:;

int a=21>=21>' b=21>=21>'c=21>=21>' i'j','m' n'p'(#printf:Jnter the order of matri7 A : m E n;) J;#scanf:JKdKdJ'Em'En;#

printf:Jnter the order of matri7 & : p E (;) J;#scanf:JKdKdJ'Ep'E(;#

if:n ] p;printf:Jn /atrices are not multipliableJ;#e7it:2;#B

GG*eadin! the matri7 A


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GG*eadin! the matri7 Aprintf:Jnter the elements of the matri7 AnJ;#for:i1# iHm# iCC;

for:j1#jHn#jCC;scanf:JKdJ'Ea=i>=j>;#

GG*eadin! the matri7 &printf:Jnter the elements of the matri7 &nJ;#for:i1# iHp# iCC;

for:j1#jH(#jCC;scanf:JKdJ'Eb=i>=j>;#

GG6indin! the productfor:i1#iHm#iCC; GG6or each row


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for:j1#jHn#jCC; GG6or each column

c=i>=j> 1#for:,1#,Hn#,CC; GGfor each matri7 elementc=i>=j> c=i>=j> C a=i>=,> \ b=,>=j>#B

BGGOutput .e!mentprintf:Jn *esultant /atri7 +nJ;#

for:i1# iHm# iCC;for:j1#jH(#jCC;printf:JtKdJ'c=i>=j>;#

printf:JnJ;#B

B

Output)


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Output)

nter the order of matri7 A : m E n;) 5 5

nter the order of matri7 & : p E (;) 5 5

nter the elements of the matri7 A

2 5 P S

nter the elements of the matri7 &

0 T R

*esultant /atri7 +

2X 55

SP 01

i


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7ercise

Write a pro!ram which will accept 5dimensional s(uare matri7 and 3nd outtranspose of it" Fro!ram should not ma,euse of another matri7"

Write a pro!ram which will accept 5dimensional s(uare matri7 and 3nd outthe trace of it" : traceof a matri7 is !iven

by the sum of all the elements on itsprinciple diagonal" ;

array one two

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