CZ1102 Computing & Problem Solving Lecture 4

8/8/2019 CZ1102 Computing & Problem Solving Lecture 4

1/26

Arraysand

Loops

Week

5

ByJi Hui


2/26

Array Whyweneedarray

Batch

inputting

data

for

processing

Vector Alsocalledlist,arraysinotherlanguage

Rowvector

Columnvector


3/26

(Cont)

Matrix

Multidimensional

array

Vectorsarespecialcasesofmatriceswithone

singlecolumnoronesinglerow

Matrixand

column

vector

will

be

discussed

in

futurelecturesonnumericallinearalgebra

1,2,3,4

5, 6, 7,8


4/26

Vectorinitialization

Initializeavector

>>x=[130

15]

x=

1 3 0 1 5

>>whos

Name Size Bytes Class Attributes

x

1x5

40

double


5/26

Moreways

of

initialization

Morewaystoinitializevector

Canuse

comma

to

separate

items

as

you

like

>>x=[1,3,0,1,3]

Dontforgetthecommas(orspaces)betweenelements,otherwise somethingunexpectedwill

happen>>x=[130,13]

Canuseonevectorinalistforanotherone

>>a=[130];

>>b=[1,3];

>>c=[a,b]


6/26

Initializingvectorsusingthecolon

operator

Avectorcanalsobegenerated(initialized)

withthe

colonoperator

Integer

j:kavector

with

elements

j,

j+1,j+2,...,k

J:m:k

whenm>0,avectorwithelementsj,j+m,j+2m,...,

suchthat

the

last

item


7/26

Example Someexamples

>>

x=1:3:6x=

1 4

>>x=0.1:0.3:1.0

x=

0.1000 0.2000 0.5000 0.8000

Whathappenwhenk>x=1:3:1

x=

Emptymatrix:1by0


8/26

Transposing

vectors

Sofarallvectorsarerowvectors,howtoget

columnvectors

Usingdash

>>x=[1,2,3]

x=

1

23

orusingsemicolon;

>>x=[1;2;3]

x=

1

23


9/26

Howto

access

items

in

vector

Subscript

x(k):

kth element

of

vector

x

>>x=[1,3,1,0,2];

>>x(4)

ans =

0

Asubscriptisindicatedinsideroundbrackets(alsocalledparentheses).

Asubscript

may

be

ascalar

or

avector.

InMATLABsubscriptsalwaysstartat1.


10/26

(cont)

x(j:k):thevectorofjth,(j+1)th,,kth elements

ofvector

x

>>x(2:4)

ans =

3 1 0

Whataboutr(1:2:5)?

Whatabout

r([1

25])?


11/26

Repetition Whyweneedrepetition?

Batchprocessingtheinputteddata

Example

(a)findthesquareofi=1,2,3,4,5,10? Withoutrepetition

>>

sqrt(1)>>sqrt(2)

>>sqrt(3)

.

.>>sqrt(10)

Toomanyrepetitivestatementsneeded


12/26

(cont)

(b)findthefactorialof5!

Withoutrepetition

>>1*2*3*4*5

Whattodowith1000!?

A struct fordoingsuchrepetitiveworksis

needed

Answer:for


13/26

for struct Theforstruct

for index=j:kstatements

End

or

for index=j:m:kstatementsend


14/26

Importantpoints

for

struct

indexmustbeavariable.Eachtimethroughtheloopitwillcontain

the

next

element

of

the

vector

j:kor

j:m:k,

and

for

each

ofthesevalues,statements(whichmaybeoneormorestatement)arecarriedout.

Oncompletionofthelooptheindexcontainsthelastvalue

used. Ifthevectorj:korj:m:kisempty,statementsarenotexecuted,

andcontrolpassestothestatementfollowingtheend

statement.

Theindex

does

not

have

to

appear

explicitly

in

statements.

It

is

basicallyacounter.


15/26

Example>>fori=1:5

x(i)=sqrt(i);end

>>x

x=

1.0000 1.4142 1.7321 2.0000 2.2361

>>i

i =

5


16/26

Samplecodes

Calculating10!

>>

x

=

1;>>for i=2:10,

x=x*i;

end

Calculating

>>x=0;

>>for k=1:50,

x=x+k^2;end


17/26

Acommon

mistake:

for

less

loops!

Averycommonmistakeistoomitthewordfor

fromafor

loop.

Insteadofreportinganerror,MATLABobliginglycreatesavector,andexecutesthestatementsin

theloop

only

once.

>>x=0

>>i=1:6,

x=x+i;end


18/26

Moreon

repetition

foronlyworkswhenyouknowwhentostoptheloops Deterministic

Whattodowhenyoudontknowwhentostop.

Forexample,

Problem:givenapositivefractionalnumberx,findthesmallestintegernthat>=x.i.e.ceil(x)providedinmatlab.

Onesolution:

count

1,2,3,,

stop

until

the

integer

>=x.


19/26

Indeterministic

repetition

with

while

whilestructwhile

condition

statements

end

The

while

construct

repeats

statementsWHILEitsconditionremainstrue

TheconditionistestedeachtimeBEFOREstatementsarerepeated.

conditionmustdependonstatementsinsomeway,otherwisetheloopwillneverend.


20/26

Programmingceil(x)

for

x>=0

Samplecode

>>x=5.4;

>>n=0;

>>while(n>n

n=

6


21/26

Whattodowhenyouwanttofinish

loopsearlier

before

its

end

breakstructwhile

condition fori=j:k,

statementsA statementsA

if(condionB),break;end; if(conditionB),break;end;

statementsB statementsBend end

Duringeachrepetition,afterstatemensA is

executed,if

conditionB holds

true,

the

while

loopswillendimmediatelyandgotothenextlineaftertheloop.


22/26

Example

Sampleproblem:givenapositiveintegerN>2

checkwhether

it

is

prime

or

not?

Solution:fori=3,N,checkwhetherthe

divison N/iisintegerornot?

Theinefficiency

Noneedtocheckeveryinteger,aslongasthere

existone

integer

such

that

the

division

is

integer,

itisnotaprime


23/26

Codeusing

forstruct

>>x=935

>>isprime=0;

>>fori=3:xr=x/i;

if(round(r)==r),

isprime=0;

endend

>> isprime

Isprime =

0>>i

i =

935


24/26

Bettercode

using

break

>>x=935

>>isprime=1;

>>fori=3:x

r=x/i;

if(round(r)==r),

isprime=0;

break;end

end

>> isprime

Isprime =0

>>i

i =

5


25/26

Whattodowhenyouwantexecute

partof

statements

during

the

loops

continuestructwhile

condition fori=j:k,

statementsA statementsA

if(condionB),continue;end; if(conditionB)continue;end

statementsB statementsB

end end

Ateachrepetition,afterstatementsA isexecuted,ifconditionB holdstrue,statementsB willnotbe

executedand

the

program

will

start

the

next

repetition.


26/26

Thedifferencebetweenbreak and

continue

OnceconditionB holdes true

break willfinish

the

whole

loop

and

execute

the

lineafterend

Continue willfinishonlythecurrentrepetitionof

theloop

and

execute

the

next

repetition

of

the

loop.

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CZ1102 Computing & Problem Solving Lecture 4