chapter 4: loops - ucsbkoclab.cs.ucsb.edu/teaching/cs8/docx/ch04.pdf · common error: infinite...

Chapter4:Loops

ChapterGoals• Toimplementwhileandforloops

• Tohand-tracetheexecutionofaprogram

• Tobecomefamiliarwithcommonloopalgorithms

• Tounderstandnestedloops

• Toimplementprogramsthatreadandprocessdatasets

• Touseacomputerforsimulations

Inthischapter,youwilllearnaboutloopstatementsinPython,aswellastechniquesforwritingprogramsthatsimulateactivitiesinthereal

world.

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Contents• Thewhile loop

• ProblemSolving:Hand-Tracing

• Application:ProcessingSentinels

• ProblemSolving:Storyboards

• CommonLoopAlgorithms

• Thefor loop

• Nestedloops

• ProcessingStrings

• Application:RandomNumbersandSimulation

• Graphics:DigitalImageProcessing

• ProblemSolving:SolveaSimplerProblemFirst

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Thewhile Loop

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Thewhile Loop• Examplesofloopapplications

• Calculatingcompoundinterest• Simulations,eventdrivenprograms• Drawingtiles…

• Compoundinterestalgorithm(Chapter1)

Steps

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Planningthewhile Loopbalance=10.0target=100.0year=0rate=0.025whilebalance<TARGET:year=year+1interest=balance*RATE/100balance=balance+interest

AloopexecutesinstructionsrepeatedlywhileaconditionisTrue.

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Syntax:while Statement

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Count-ControlledLoops• Awhile loopthatiscontrolledbyacounter

counter = 1 # Initialize the counter

while counter <= 10 : # Check the counterprint(counter)counter = counter + 1 # Update the loop variable

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Event-ControlledLoops• Awhile loopthatiscontrolledbyacounter

balance = INITIAL_BALANCE # Initialize the loop variable

while balance <= TARGET: # Check the loop variableyear – year + 1balance = balance * 2 # Update the loop variable

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ExecutionoftheLoop

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ExecutionoftheLoop(2)

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Doubleinv.py

Declare andinitialize avariableoutsideofthe looptocountyear

Increment theyear variableeach timethrough

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Investment Example• Openthefile:

• Doubleinv.py

• Runtheprogramwithseveraltestcases• Theprogramwillpromptyouforarate• Enteramixofvalidandinvalidrates

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while LoopExamples

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while LoopExamples (2)

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CommonError: IncorrectTestCondition• TheloopbodywillonlyexecuteifthetestconditionisTrue.

• IfbalisinitializedaslessthantheTARGETandshouldgrowuntilitreachesTARGET• Whichversionwillexecute the loopbody?

while bal < TARGET :year = year + 1interest = bal * RATEbal = bal + interest

while bal >= TARGET :year = year + 1interest = bal * RATEbal = bal + interest

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CommonError:InfiniteLoops• TheloopbodywillexecuteuntilthetestconditionbecomesFalse.

• Whatifyouforgettoupdatethetestvariable?• bal isthetestvariable (TARGET doesn’t change)• Youwill loopforever!(oruntilyoustoptheprogram)

while bal < TARGET :year = year + 1interest = bal * RATEbal = bal + interest

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CommonError:Off-by-OneErrors• A‘counter’variableisoftenusedinthetestcondition

• Yourcountercanstartat0or1,butprogrammersoftenstartacounterat0

• IfIwanttopaintall5fingersononehand,whenIamdone?• Ifyoustartat0,use“<“ Ifyoustartat1,use“<=“• 0,1,2,3,4 1,2,3,4,5

finger = 0FINGERS = 5while finger < FINGERS :

# paint fingerfinger = finger + 1

finger = 1FINGERS = 5while finger <= FINGERS :

# paint fingerfinger = finger + 1

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HandTracingLoops

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Hand-Tracing Loops• Example:Calculatethesumofdigits(1+7+2+9)

• Makecolumnsforkeyvariables(n,total,digit)• Examinethecodeandnumberthesteps• Setvariablestostatebeforeloopbegins

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TracingSumofDigits

• Startexecutingloopbodystatementschangingvariablevaluesonanewline• Crossoutvaluesinpreviousline

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TracingSumofDigits

• Continueexecutingloopstatementschangingvariables• 1729/10leaves172(noremainder)

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TracingSumofDigits• Testcondition.IfTrue,executeloopagain

• Variablenis172,Is172>0?,True!

• Makeanewlineforthesecondtimethroughandupdatevariables

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TracingSumofDigits• Thirdtimethrough

• Variablenis17whichisstillgreaterthan0

• Executeloopstatementsandupdatevariables

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TracingSumofDigits• Fourthloopiteration:

• Variablenis1atstartofloop.1>0?True• Executesloopandchangesvariablento0(1/10=0)

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TracingSumofDigits• Becausenis0,theexpression(n>0)isFalse

• Loopbodyisnotexecuted• Jumpstonextstatementaftertheloopbody

• Finallyprintsthesum!

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Summaryofthewhile Loop• while loopsareverycommon

• Initializevariablesbeforeyoutest• TheconditionistestedBEFOREtheloopbody

• Thisiscalledpre-test• Theconditionoftenusesacountervariable

• Somethinginsidetheloopshouldchangeoneofthevariablesusedinthetest

• Watchoutforinfiniteloops!

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SentinelValues

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ProcessingSentinelValues• Sentinelvaluesareoftenused:

• Whenyoudon’tknowhowmanyitems are inalist,usea‘special’characterorvaluetosignalthe “last” item

• Fornumeric inputofpositive numbers, it iscommon tousethevalue-1

Asentinelvaluedenotestheendofadataset,butitisnotpartofthedata.

salary = 0.0while salary >= 0 :

salary = float(input())if salary >= 0.0 :

total = total + salarycount = count + 1

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AveragingaSetofValues• Declareandinitializea‘total’variableto0

• Declareandinitializea‘count’variableto0

• Declareandinitializea‘salary’variableto0

• Promptuserwithinstructions

• Loopuntilsentinelvalueisentered• Saveenteredvaluetoinputvariable(‘salary’)• Ifsalaryisnot-1orless(sentinelvalue)

• Addsalaryvariabletototalvariable• Add1tocountvariable

• Makesureyouhaveatleastoneentrybeforeyoudivide!• Dividetotalbycountandoutput.• Done!

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Sentinel.py (1)

Outside the while loop: declare and initialize variables to use

Input new salary and compare to sentinel

Update running total and count (to calculate the average later)

Since salary is initialized to 0, the while loop statements will execute at least once

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Sentinel.py (2)

Prevent divide by 0

Calculate and output the average salary using the total and countvariables

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SentinelExample• Openthefile:

• Sentinal.py

• NoticetheuseoftheIF() testinsidethewhile loop• TheIF()checkstomakesurewearenotprocessingthesentinelvalue

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PrimingRead• Someprogrammersdon’tlikethe“trick”ofinitializingtheinputvariablewithavalueotherthanasentinel.

# Set salary to a value to ensure that the loop # executes at least once.salary = 0.0while salary >= 0 :

salary = float(input("Enter a salary or -1 to finish: "))while salary >= 0 :

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• Analternativeistochangethevariablewithareadbeforetheloop.

ModificationRead• Theinputoperationatthebottomoftheloopisusedtoobtainthenextinput.

# Priming readsalary = float(input("Enter a salary or -1 to finish: "))while salary >= 0.0 :

total = total + salarycount = count + 1# Modification readsalary = float(input("Enter a salary or -1 to finish: "))

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BooleanVariablesandSentinels• Abooleanvariablecanbeusedtocontrolaloop

• Sometimescalleda‘flag’variable

done = Falsewhile not done :

value = float(input("Enter a salary or -1 to finish: "))if value < 0.0:

done = Trueelse :

# Process value

Initialize done so that the loop will execute

Set done ‘flag’ to True if sentinel value is found

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Storyboards

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Storyboards• Oneusefulproblemsolvingtechniqueistheuseofstoryboardstomodeluserinteraction.Itcanhelpanswer:• Whatinformationdoestheuserprovide,andinwhichorder?• Whatinformationwillyourprogramdisplay,andinwhichformat?• Whatshouldhappenwhenthereisanerror?• Whendoestheprogramquit?

• Astoryboardconsistsofannotatedsketchesforeachstepinanactionsequence.

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StoryboardExample• Goal:Convertingasequenceofvalues

• Willrequirealoopandsomevariables• Handleoneconversioneachtimethroughtheloop

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WhatCanGoWrong?Unknownunittypes

• Whatistheusermisspellscentimetersandinches?• Whatotherconversionsareavailable?• Solution:

• Showalistoftheacceptableunittypes

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WhatElseCanGoWrong?• Howdoestheuserquittheprogram?

• Storyboardshelpyouplanaprogram• Knowingtheflowhelps youstructure yourcode

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CommonLoopAlgorithms

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CommonLoopAlgorithms1. SumandAverageValue

2. CountingMatches

3. PromptinguntilaMatchIsFound

4. MaximumandMinimum

5. ComparingAdjacentValues

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AverageExampletotal = 0.0count = 0inputStr = input("Enter value: ")while inputStr != "" :

value = float(inputStr)total = total + valuecount = count + 1inputStr = input("Enter value: ")

if count > 0 : average = total / count

else :average = 0.0

AverageofValues• Firsttotalthevalues• Initializecount to0

• Incrementperinput• Checkforcount 0

• Beforedivide!

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SumExample• SumofValues

• Initializetotalto0• Usewhileloopwithsentinel

total = 0.0inputStr = input("Enter value: ")while inputStr != "" :

value = float(inputStr)total = total + valueinputStr = input("Enter value: ")

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CountingMatches(e.g.,NegativeNumbers)

negatives = 0inputStr = input("Enter value: ")while inputStr != "“ :

value = int(inputStr)if value < 0 :

negatives = negatives + 1inputStr = input("Enter value: ")

print("There were", negatives, "negative values.")

• CountingMatches• Initializenegatives to0• Useawhile loop• Addtonegatives permatch

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PromptUntilaMatchisFound• InitializebooleanflagtoFalse

• Testsentinelinwhileloop• Getinput,andcomparetorange

• Ifinputisinrange,changeflagtoTrue• Loopwillstopexecuting

valid = Falsewhile not valid :

value = int(input("Please enter a positive value < 100: "))if value > 0 and value < 100 :

valid = Trueelse :

print("Invalid input.")

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Thisisanexcellentwaytovalidateuseprovidedinputs

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Maximum• Getfirstinputvalue

• Bydefinition,thisisthelargestthatyouhaveseensofar

• Loopwhileyouhaveavalidnumber(non-sentinel)• Getanotherinputvalue• Comparenewinputtolargest(orsmallest)• Updatelargestifnecessary

largest = int(input("Enter a value: "))inputStr = input("Enter a value: ")while inputStr != "“ :

value = int(inputStr)if value > largest :

largest = valueinputStr = input("Enter a value: ")

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Minimum• Getfirstinputvalue

• Thisisthesmallestthatyouhaveseensofar!

• Loopwhileyouhaveavalidnumber(non-sentinel)• Getanotherinputvalue• Comparenewinputtolargest(orsmallest)• Updatesmallestifnecessary

smallest = int(input("Enter a value: "))inputStr = input("Enter a value: ")while inputStr != "“ :

value = int(inputStr)if value < smallest :

smallest = valueinputStr = input("Enter a value: ")

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ComparingAdjacentValues• Getfirstinputvalue

• Usewhile todetermineiftherearemoretocheck• Copyinputtopreviousvariable• Getnextvalueintoinputvariable• Compareinputtoprevious,andoutputifsame

value = int(input("Enter a value: "))inputStr = input("Enter a value: ")while inputStr != "“ :

previous = valuevalue = int(inputStr)if value == previous :

print("Duplicate input")inputStr = input("Enter a value: ")

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GradesExample• Openthefile:

• Grades.py

• Lookcarefullyatthesourcecode.

• Themaximumpossiblescoreisreadasuserinput• Thereisalooptovalidatetheinput

• Thepassinggradeiscomputedas60%oftheavailablepoints

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Thefor Loop

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Thefor Loop• Usesofafor loop:

• Thefor loopcanbeusedtoiterateoverthecontentsofanycontainer.

• Acontainer isisanobject(Likeastring)thatcontainsorstoresacollectionofelements

• Astring isacontainerthatstoresthecollectionofcharactersinthestring

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AnExampleofafor Loop

stateName = "Virginia"i = 0while i < len(stateName) :

letter = stateName[i]print(letter)i = i + 1

whileversion

stateName = "Virginia"for letter in stateName :

print(letter) forversion

• Noteanimportantdifferencebetweenthewhileloopandtheforloop.• Inthewhileloop,theindexvariablei isassigned0,1,andsoon.• Intheforloop,theelementvariableisassignedstateName[0],stateName[1],andsoon.

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TheforLoop(2)• Usesofaforloop:

• Aforloopcanalsobeusedasacount-controlledloopthatiteratesoverarangeofintegervalues.

i = 1while i < 10 :

print(i)i = i + 1

for i in range(1, 10) : print(i)

while version

for version

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Syntaxofafor Statement (Container)• Usingaforlooptoiterateoverthecontentsofacontainer,anelementatatime.

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Syntaxofafor Statement (Range)• Youcanuseaforloopasacount-controlledlooptoiterateoverarangeofintegervalues

• Weusetherangefunctionforgeneratingasequenceofintegersthatlessthantheargumentthatcanbeusedwiththeforloop

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Planningafor Loop• Printthebalanceattheendofeachyearforanumberofyears

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GoodExamplesoffor Loops• Keeptheloopssimple!

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Investment Example

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ProgrammingTip• Findingthecorrectlowerandupperboundsforaloopcanbeconfusing.• Shouldyoustartat0orat1?• Shouldyouuse<=bor<basaterminationcondition?

• Countingiseasierforloopswithasymmetricbounds.• Thefollowingloopsareexecutedb- atimes.

int i = awhile i < b :

. . .i = i + 1

for i in range(a, b) :. . .

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ProgrammingTip• Theloopwithsymmetricbounds(“<=”,isexecutedb- a+1times.

• That“+1”isthesourceofmanyprogrammingerrors.

i = awhile i <= b :

. . .i = i + 1

# For this version of the loop the ‘+1’ is very noticeable!for year in range(1, numYears + 1) :

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Summaryofthefor Loop• for loopsareverypowerful

• Thefor loopcanbeusedtoiterateoverthecontentsofanycontainer,whichisanobjectthatcontainsorstoresacollectionofelements• astring isacontainer thatstoresthecollection ofcharacters inthestring.

• Afor loopcanalsobeusedasacount-controlledloopthatiteratesoverarangeofintegervalues.

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StepstoWriting aLoop• Planning:

• Decidewhatworktodoinsidetheloop• Specifytheloopcondition• Determinelooptype• Setupvariablesbeforethefirstloop• Processresultswhentheloopisfinished• Tracetheloopwithtypicalexamples

• Coding:• ImplementtheloopinPython

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ASpecialFormoftheprint Function• Pythonprovidesaspecialformoftheprintfunctionthatdoesnotstartanewlineaftertheargumentsaredisplayed

• Thisisusedwhenwewanttoprintitemsonthesamelineusingmultipleprintstatements

• Forexamplethetwostatements:

print(“00”, end=””)print(3 + 4)

• Producetheoutput:

007

• Includingend=“” asthelastargumenttotheprintfunctionprintsanemptystringafterthearguments,insteadonanewline

• Theoutputofthenextprint functionstartsonthesameline

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NestedLoops

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LoopsInsideofLoops• InChapterThreewelearnedhowtonestif statementstoallowustomakecomplexdecisions• Rememberthattonesttheif statementsweneedtoindentthecodeblock

• Complexproblemssometimesrequireanestedloop,oneloopnestedinsideanotherloop• Thenestedloopwillbeindentedinsidethecodeblockofthefirstloop

• Agoodexampleofusingnestedloopsiswhenyouareprocessingcellsinatable• Theouterloopiteratesoveralloftherowsinthetable• Theinnerloopprocessesthecolumnsinthecurrentrow

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OurExampleProblemStatement• PrintaTableHeaderthatcontainsx1,x2,x3,andx4

• PrintaTablewithfourcolumnsandtenrowsthatcontainthepowersofx1,x2,x3,andx4 forx=1to10

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ApplyingNestedLoops• Howwouldyouprintatablewithrowsandcolumns?

• Printtopline(header)• Useaforloop

• Printtablebody…• Howmanyrowsareinthetable?• Howmanycolumnsinthetable?

• Loopperrow• Looppercolumn

• Inourexamplethereare:• Fourcolumnsinthetable• Tenrowsinthetable

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PseudocodetoPrinttheTablePrintthetableheader

for x from 1 to 10print a new table rowprint a new line

• Howdoweprintatablerow?

For n from 1 to 4print xn

• Wehavetoplacethisloopinsidetheprecedingloop• Theinnerloopis“nested”insidetheouterloop

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PseudocodetoPrinttheTablePrintthetableheader:

for x from 1 to 10for n from 1 to 4print Xn

print a new line

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n è

xê

InnerLoop

FlowchartofaNestedLoopx=1

x<=10?

n=1

n<=4?

Printxn

n=n+1

Printnewline

x=x+1

True

False True

Done

False

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Powertable.py

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Bodyofouterloop,x=1è 10

Bodyofinnerloop,n=1è 4

The end=“” suppresses the new line, so the numbers are all printed on the same line

TheResults

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FirstExercise• Opentheprogram:

• powertable.py

• Runtheprogramandreviewtheresults

• Makethefollowingchanges:• ChangethevalueofNMAXto6andruntheprogram• Whatchangesinthetable?• ChangethevalueofNMAXbackto4• ChangethevalueofXMAXto4• Whatchangesinthetable?

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NestedLoopExamples

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HandTracingtheLoop

• i willhavethevalues:• 0,1,2,3– Sowewillhavefourlinesofstars

• j willhavethevalues• 0- Sowewillhaveonestar• 0,1- Sowewillhavetwostars• 0,1,2- Sowewillhavethreestars• 0,1,2,3- Sowewillhavefourstars

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NestedLoopExamples (2)

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SecondProblemStatement• Printthefollowingpatternofbrackets:[][][][][][][][][][][][]

• Thepatternconsistsof:• Threerows• Eachrowhasfourpairsofbrackets

• Whatdoweknow?• Weneedtwonestedloops

• Thefirstloop(theouterloop)willprinteachofthethreerows• Thesecondloop(theinnerloop)willprintthefourpairsofbrackets

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PseudocodeCode,ResultsFor i = 1 to 3For j = 1 to 4Print “[]”

Print a new line

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ExamAveragesProblemStatement• Itiscommontorepeatedlyreadandprocessmultiplegroupsofvalues:

• Writeaprogramthatcancomputetheaverageexamgradeformultiplestudents.

• Eachstudenthasthesamenumberofexamgrades• Prompttheuserforthenumberofexams• Whenyoufinishastudentprompttheusertoseeiftherearemorestudentstoprocess

• Whatdoweknow?

• Whatdoweneedtocompute?

• Whatisouralgorithm/approach?

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StepOne:UnderstandtheProblem• Tocomputetheaveragegradeforastudent,wemustreadandtallyallofthegradesforthatstudent• Wecanusealooptodothis.(wehaveworkingcodetodothisportion)

• Weneedtocomputegradesformultiplestudents• ThatimpliesasetofnestedLoops

• Theouterloopprocesseseachstudent• Theinnerloopprocessthestudent’sgrades

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StepTwo• Computethegradeforonestudent

• Setupthevariablesandloop

• Weknowhowmanygradestoprocess,sowecanuseacount-controlledloop

total score = 0For i in range (1, number of exams + 1) :Read the next exam scoreAdd the exam score to the total score

Compute the exam averagePrint the exam average

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StepThree• Repeattheprocessforeachstudent

• Sincewedon’tknowhowmanystudentsthereare,wewilluseawhileloopwithasentinelvalue• Forsimplicitywewilluse“Y”asthesentinelvalue

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StepFour:Translate toPython

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ExamAverages Example• Openthefile:

• examaverages.py

• Noticethatthesecondloop(thefor loop)isnestedinsidethewhile loop

• Youshouldseealine(theindentguide)connectingthefor looponline17downtothestatementonline21• Thelineisshowingyouthestatementsthatareincludedinthefor loop

• Ifyoudon’tseetheindentguide:• Clickontheedittab• Select“Preferences…”• UnderEditor,selectIndention• Clickthe“ShowIndentGuides”box• ClicktheApplybutton• ClicktheOkayButton

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TurningtheIndentGuidesOn

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ProcessingStrings• Acommonuseofloopsistoprocessorevaluatestrings.

• Forexample,youmayneedtocountthenumberofoccurrencesofoneormorecharactersinastringorverifythatthecontentsofastringmeetcertaincriteria.

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ProcessingStrings

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StringProcessingExamples• CountingMatches

• FindingAllMatches

• FindingtheFirstorLastMatch

• ValidatingaString

• BuildingaNewString

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CountingMatches• Supposeyouneedtocountthenumberofuppercaseletterscontainedinastring.

• Wecanuseaforlooptocheckeachcharacterinthestringtoseeifitisuppercase

• Theloopbelowsetsthevariablecharequaltoeachsuccessivecharacterinthestring

• Eachpassthroughtheloopteststhenextcharacterinthestringtoseeifitisuppercase

uppercase = 0for char in string :

if char.isupper() :uppercase = uppercase + 1

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CountingVowels• Supposeyouneedtocountthevowelswithinastring

• Wecanuseaforlooptocheckeachcharacterinthestringtoseeifitisinthestringofvowels“aeiuo”

• Theloopbelowsetsthevariablecharequaltoeachsuccessivecharacterinthestring

• Eachpassthroughtheloopteststhelowercaseofthenextcharacterinthestringtoseeifitisinthestring“aeiou”

vowels = 0for char in word :

if char.lower() in "aeiou" :vowels = vowels + 1

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FindingAllMatchesExample• Whenyouneedtoexamineeverycharacterinastring,independentofitspositionwecanuseaforstatementtoexamineeachcharacter

• Ifweneedtoprintthepositionofeachuppercaseletterinasentencewecantesteachcharacterinthestringandprintthepositionofalluppercasecharacters

• Wesettherangetobethelengthofthestring• Wetesteachcharacter• Ifit isuppercase weprintI,its position inthestring

sentence = input("Enter a sentence: ")for i in range(len(sentence)) :

if sentence[i].isupper() :print(i)

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FindingtheFirstMatch• Thisexamplefindsthepositionofthefirstdigitinastring.

found = Falseposition = 0while not found and position < len(string) :

if string[position].isdigit() :found = True

else :position = position + 1

if found :print("First digit occurs at position", position)

else :print("The string does not contain a digit.")

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FindingtheLastMatch• Hereisaloopthatfindsthepositionofthelastdigitinthestring.

• Thisapproachusesawhilelooptostartatthelastcharacterinastringandtesteachvaluemovingfromtheendofthestringtothestartofthestring• Position issettothe length ofthestring - 1• Ifthecharacter isnotadigit,wedecrease position by1• Untilwefindadigit,orprocessall thecharacters

found = Falseposition = len(string) - 1while not found and position >= 0 :

if string[position].isdigit() :found = True

else :position = position - 1

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ValidatingaString• IntheUnitedStates,telephonenumbersconsistofthreeparts––areacodeexchange,andlinenumber––whicharecommonlyspecifiedintheform(###)###-####.

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ValidatingaString (code)• Wecanexamineastringtoensurethatitcontainsacorrectlyformattedphonenumber.(e.g.,(703)321-6753)

• Thelooptesteachcharactertoseeititiscorrectforitsposition,oranumber

valid = len(string) == 13position = 0while valid and position < len(string) :

valid = ((position == 0 and string[position] != "(")or (position == 4 and string[position] != ")")or (position == 8 and string[position] != "-")or (position != 0 and position != 4 and position != 8

and string[position].isdigit())) :position = position + 1

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Building aNewString• Oneoftheminorannoyancesofonlineshoppingisthatmanywebsitesrequireyoutoenteracreditcardwithoutspacesordashes,whichmakesdouble-checkingthenumberrathertedious.

• Howhardcanitbetoremovedashesorspacesfromastring?

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Building aNewString (code)• Thecontentsofastringcannotbechanged.

• Butnothingpreventsusfrombuildinganewstring.

• Hereisaloopthatbuildsanewstringcontainingacreditcardnumberwithspacesanddashesremoved:• Wereadthecreditcardnumber• Weinitializeanewstringtotheemptystring• Wetesteachcharacterintheuserinput

• Ifthecharacterisnotaspaceordashweappendittothenewstring

userInput = input("Enter a credit card number: ")creditCardNumber = ""for char in userInput :

if char != " " and char != "-" :creditCardNumber = creditCardNumber + char

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Application: RandomNumbersandSimulations

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RandomNumbers/Simulations• Gamesoftenuserandomnumberstomakethingsinteresting

• RollingDice• Spinningawheel• Pickacard

• Asimulationusuallyinvolvesloopingthroughasequenceofevents• Days• Events

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GeneratingRandomNumbers• ThePythonlibraryhasarandomnumbergeneratorthatproducesnumbersthatappear toberandom• Thenumbersarenotcompletelyrandom.Thenumbersaredrawnfromasequenceofnumbersthatdoesnotrepeatforalongtime

• random()returnsanumberthatis>=0and<1

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SimulatingDieTosses• Goal:

• Togeneratearandomintegerinagivenrangeweusetherandint()function

• Randinthastwoparameters,therange(inclusive)ofnumbersgenerated

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TheMonteCarloMethod• Usedtofindapproximatesolutionstoproblemsthatcannotbepreciselysolved

• Example:ApproximatePIusingtherelativeareasofacircleinsideasquare• Usessimplearithmetic• Hitsareinsidecircle• Triesaretotalnumberoftries• Ratiois4xHits/Tries

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MonteCarloExample

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ImageProcessing

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Manipulating Images• Digitalimageprocessingistheuseofalgorithmstomanipulatedigitalimages

• Itisusedin:• Digital photography• Datacompression• Computer graphics• Computer vision• Robotics

• We’lllearnhowtomanipulateimageswiththeezgraphics package

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Representing Images• Adigitalimageiscomposedofpixelsarrangedinagridofrowsandcolumns• Computer images appear “smooth” because verysmallpoints onthescreen(veryclose together) areused toreproducethe individual pixels

• Pixelsstoredatarepresentingacolorfromthevisualspectrum• Thediscrete RGBcolormodel isthemostusedmodel• Thethree individual colorsarespecified bytheamount ofred,green,andblue light needed toproduceagivencolor

• Thevaluesaregivenas integers between 0(nolightpresent) and255(maximum light present)

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FilteringanImage• Filteringanimagemodifiesthecolorcomponentvaluesofeachpixelinsomeway

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ProcessinganImage• Westartbyloadingtheimageintoourprogram

• Inezgraphicsanimage isstored inaninstance oftheGraphicsImage classfilename = "queen-mary.gif"image = GraphicsImage(filename)

• WedrawtheimageonthecanvasofaGraphicsWindowwin = GraphicsWindow()canvas = win.canvas()canvas.drawImage(image)win.wait()

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FilteringanImage• Tofilteranimage,youmustgetthered,green,andbluecomponentvaluesforeachpixel.• Thepixels areorganized intoatwo-dimensional gridofsizewidth× height:• Therowsandcolumns arenumbered sequentially startingat0,withpixel(0,0)intheupper-left corner.

• Therownumbers rangefrom0toheight– 1;thecolumnnumbers from0towidth– 1.

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AccessingtheComponentValuesofaPixel• WeusethegetRed,getGreen andgetBluemethodsred = image.getRed(0, 4)green = image.getGreen(0, 4)blue = image.getBlue(0, 4)

• Tocreatethenegativeofanimage:

newRed = 255 - rednewGreen = 255 - greennewBlue = 255 – blue

• Andthenupdatethepixel

image.setPixel(0,4,newRed,newGreen,newBlue)

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ThePseudocodewidth = image.width()height = image.height()for row in range(height) :

for col in range(width) :Get the current pixel color.Filter the pixel.Set the pixel to the new color.

image.save("negative" + filename)

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GraphicsImage Methods

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ProblemSolving:SolveaSimplerProblemFirst

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SimplifyaComplexProblem• Aswelearnmoreaboutprogramming,thecomplexityofthetaskswearesolvingincreases

• Whenwearefacedwithacomplextaskweshouldapplyacriticalskill:• Simplifying theproblem andsolving thesimpler problem first

• Oursimplification(AKAproblemdecomposition)skillsimprovewithpractice

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ASampleProblem• Ourassignmentistoarrangepictures,liningthemupalongthetopedges,separatingthemwithsmallgaps,andstartinganewrowwheneveryourunoutofroominthecurrentrow.• Thissounds simple, right?

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ASimplePlan• Let’sdevelopaplanthatsolvesasetofsimpler(increasingincomplexity)problems

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Increase theComplexity

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ImplementingOurPlan1. Specifythecanvascoordinateswheretheupperleftcornerofthefirst

imageshouldbeplaced

2. Thenplacethenextpictureafterthefirstafterthefirst• Itneedstobedrawnsothatitsleft-mostedgeispositionedattheright-mostx-coordinateoftheprecedingpicture

• Thiscanbedeterminedbyobtainingthewidthofthefirstpictureandusingthatvalueasthex-coordinateforthesecondpicture

3. Separatethetwopictureswithagap

4. Todrawthethirdpicture,it’snotsufficienttoknowthewidthoftheprecedingpicture.• Wealsoneedtoknowthex-coordinatewhereitwasdrawnsowecanaddthatvaluetothewidthoftheprecedingimage,plusthegapbetweentheimages

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ImplementingourPlan5. Nowlet’sputallofthepicturesinarow

• Loadthepicturesinaloop,andthenputeachpicturetotherightoftheonethatprecededit.

• Ineachiteration,youneedtotracktwopictures:theonethatisbeingloaded,andtheonethatprecededit

6. Wedon’twanttohaveallpicturesinasinglerow• TherightmarginofapictureshouldnotextendpastMAX_WIDTH• Iftheimagedoesn’tfitweneedtoputitonthenextrow,belowallthepicturesinthecurrentrow

• We’llsetavariablemaxY tothemaximumy-coordinateofallplacedpictures,updatingitwheneveranewpictureisplaced

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Summary

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Summary: TwoTypesofLoops• while Loops

• for Loops

• while loopsareverycommonlyused(generalpurpose)

• Usesofthefor loop:• Thefor loopcanbeusedtoiterateoverthecontentsofanycontainer.

• Afor loopcanalsobeusedasacount-controlledloopthatiteratesoverarangeofintegervalues.

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Summary• Eachlooprequiresthefollowingsteps:

• Initialization(setupvariablestostartlooping)• Condition(testifweshouldexecuteloopbody)• Update(changesomethingeachtimethrough)

• AloopexecutesinstructionsrepeatedlywhileaconditionisTrue.

• Anoff-by-oneerrorisacommonerrorwhenprogrammingloops.• Thinkthroughsimpletestcasestoavoidthistypeoferror.

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Summary• Asentinelvaluedenotestheendofadataset,butitisnotpartofthedata.

• Youcanuseabooleanvariabletocontrolaloop.• SetthevariabletoTrue beforeenteringtheloop• SetittoFalse toleavetheloop.

• Loopscanbeusedinconjunctionwithmanystringprocessingtasks

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Summary• Inasimulation,youusethecomputertosimulateanactivity.

• Youcanintroduce randomness bycallingtherandomnumbergenerator.

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