Data and Expressions in Python programming

Data and Expressions in Python programming

1. Chapter 2: Data and Expressions
Withthischapter,webeginadetaileddiscussionoftheconceptsandtechniquesof
computerprogramming.Westartbylookingatissuesrelatedtotherepresentation,
manipulation,andinput/outputofdata—fundamentaltoallcomputing.
1Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons

2. Thegeneration,collection,andanalysisofdataisadrivingforceintoday’s
world.Thesheeramountofdatabeingcreatedisstaggering.
Chainstoresgenerateterabytesofcustomerinformation,lookingforshopping
patternsofindividuals.Facebookusershavecreated40billionphotosrequiring
morethanapetabyteofstorage.Acertainradiotelescopeisexpectedto
generateanexabyteofinformationeveryfourhours.Alltold,thecurrent
amountofdatacreatedeachyearisestimatedtobealmosttwozettabytes,
morethandoublingeverytwoyears.
Inthischapter,welookathowdataisrepresentedandoperatedoninPython.
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Motivation

3. 3Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons

4. Totakesomethingliterallyistotakeitat“facevalue.”Thesameistrue
ofliteralsinprogramming.Aliteralisasequenceofoneofmore
charactersthatstandsforitself,suchastheliteral12.Welookat
numericliteralsinPython.
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Literals

5. Numeric Literals
Anumericliteralisaliteralcontainingonlythedigits0–9,anoptional
signcharacter(+or-),andapossibledecimalpoint.(Thelettereis
alsousedinexponentialnotation,shownnext).
Ifanumericliteralcontainsadecimalpoint,thenitdenotesa
floating-pointvalue,or“float”(e.g.,10.24);otherwise,itdenotesan
integervalue(e.g.,10).
Commasareneverusedinnumericliterals.
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Example Numerical Values
Sincenumericliteralswithoutaprovidedsigncharacterdenotepositivevalues,
anexplicitpositivesignisrarelyused.

7. Let’s Try It
7
WhichofthefollowingarevalidnumericliteralsinPython?
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8. 8
Limits of Range in Floating-Point Representation
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.1 Literals
ThereisnolimittothesizeofanintegerthatcanberepresentedinPython.
Floatingpointvalues,however,havebothalimitedrangeandalimited
precision.
Pythonusesadouble-precisionstandardformat(IEEE754)providinga
rangeof10
-308
to10
308
with16to17digitsofprecision.Todenotesucha
rangeofvalues,floating-pointscanberepresentedinscientificnotation.

9. 9
Itisimportanttounderstandthelimitationsoffloating-point
representation.Forexample,themultiplicationoftwovaluesmayresultin
arithmeticoverflow,aconditionthatoccurswhenacalculatedresultistoo
largeinmagnitude(size)toberepresented,
>>>1.5e200*2.0e210
inf
Thisresultsinthespecialvalueinf(“infinity”)ratherthanthe
arithmeticallycorrectresult3.0e410,indicatingthatarithmeticoverflowhas
occurred.
Similarly,thedivisionoftwonumbersmayresultinarithmeticunderflow,a
conditionthatoccurswhenacalculatedresultistoosmallinmagnitudeto
berepresented,
>>>1.0e-300/1.0e100
0.0
Thisresultsin0.0ratherthanthearithmeticallycorrectresult1.0e-400,
indicatingthatarithmeticunderflowhasoccurred.
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.1 Literals

10. Let’s Try It
10
Whatdoeachofthefollowingarithmeticexpressions
evaluateto?
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11. 11
Limits of Precision in Floating-Point Representation
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.1 Literals
Arithmeticoverflowandarithmeticunderflowareeasilydetected.Thelossof
precisionthatcanresultinacalculatedresult,however,isamuchmoresubtleissue.
Forexample,1/3isequaltotheinfinitelyrepeatingdecimal.33333333...,whichalso
hasrepeatingdigitsinbasetwo,.010101010....Sinceanyfloating-point
representationnecessarilycontainsonlyafinitenumberofdigits,whatisstoredfor
manyfloating-pointvaluesisonlyanapproximationofthetruevalue,ascanbe
demonstratedinPython,
>>>1/3
.3333333333333333
Here,therepeatingdecimalendsafterthe16thdigit.Consideralsothefollowing,
>>>3*(1/3)
1.0
Giventhevalueof1/3aboveas.3333333333333333,wewouldexpecttheresultto
be.9999999999999999,sowhatishappeninghere?

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TheansweristhatPythondisplaysaroundedresulttokeepthenumberofdigits
displayedmanageable.However,therepresentationof1/3as.3333333333333333
remainsthesame,asdemonstratedbythefollowing,
>>>1/3+1/3+1/3+1/3+1/31+1/3
1.9999999999999998
Inthiscasewegetaresultthatreflectstherepresentationof1/3asanapproximation,
sincethelastdigitis8,andnot9.However,ifweusemultiplicationinstead,weagain
gettheroundedvaluedisplayed,
>>>6*(1/3)
2.0
Thebottomline,therefore,isthatnomatterhowPythonchoosestodisplay
calculatedresults,thevaluestoredislimitedinboththerangeofnumbersthatcan
berepresentedandthedegreeofprecision.Formosteverydayapplications,this
slightlossinaccuracyisofnopracticalconcern.However,inscientificcomputingand
otherapplicationsinwhichprecisecalculationsarerequired,thisissomethingthat
theprogrammermustbekeenlyawareof.

13. Let’s Try It
13
Whatdoeachofthefollowingarithmeticexpressions
evaluateto?
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14. 14
Built-in Format Function
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Becausefloating-pointvaluesmaycontainanarbitrarynumberofdecimalplaces,the
built-informatfunctioncanbeusedtoproduceanumericstringversionofthevalue
containingaspecificnumberofdecimalplaces,
>>>12/5 >>>5/7
2.4 0.7142857142857143
>>>format(12/5,'.2f')>>>format(5/7,'.2f')
'2.40' '0.71'
Intheseexamples,formatspecifier'.2f'roundstheresulttotwodecimalplacesof
accuracyinthestringproduced.
For very large (or very small) values 'e' can be used as a format specifier.
>>> format(2 ** 100, '.6e')
'1.267651e+30'
Here,thevalueisformattedinscientificnotation,withsixdecimalplacesofprecision.

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Formattednumericstringvaluesareusefulwhendisplayingresultsinwhich
onlyacertainnumberofdecimalplacesneedtobedisplayed:
Withoutuseofformatspecifier:
>>>tax=0.08
>>>print('Yourcost:$',(1+tax)*12.99)
Yourcost:$14.029200000000001
Withuseofformatspecifier:
>>> print('Your cost: $', format((1 + tax) * 12.99, '.2f'))
Yourcost:$14.03
Finally,acommaintheformatspecifieraddscommaseparatorstotheresult.
>>>format(13402.25,',.2f')
13,402.24

16. Let’s Try It
16
Whatdoeachofthefollowingusesoftheformatfunction
produce?
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17. String Literals
Stringliterals,or“strings,”representasequenceofcharacters.
'Hello' 'Smith, John' "Baltimore, Maryland 21210"
InPython,stringliteralsmaybedelimited(surrounded)byamatching
pairofeithersingle(')ordouble(")quotes.Stringsmustbecontained
allononeline(exceptwhendelimitedbytriplequotes,discussedlater).
WehavealreadyseentheuseofstringsinChapter1fordisplaying
screenoutput,
>>>print('WelcometoPython!')
WelcometoPython!
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18. Astringmaycontainzeroormorecharacters,includingletters,digits,
specialcharacters,andblanks.Astringconsistingofonlyapairof
matchingquotes(withnothinginbetween)iscalledtheemptystring,
whichisdifferentfromastringcontainingonlyblankcharacters.Both
blankstringsandtheemptystringhavetheiruses,aswewillsee.
Stringsmayalsocontainquotecharactersaslongasdifferentquotes
(singlevs.double)areusedtodelimitthestring.
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19. Let’s Try It
19
Whatwillbedisplayedbyeachofthefollowing?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.1 Literals

20. The Representation of Character Values
Thereneedstobeawaytoencode(represent)characterswithina
computer.Althoughvariousencodingschemeshavebeendeveloped,
theUnicodeencodingschemeisintendedtobeauniversalencoding
scheme.
Unicodeisactuallyacollectionofdifferentencodingschemesutilizing
between8and32bitsforeachcharacter.Thedefaultencodingin
PythonusesUTF-8,an8-bitencodingcompatiblewithASCII,anolder,
stillwidelyusedencodingscheme.
Currently,thereareover100,000Unicode-definedcharactersformany
ofthelanguagesaroundtheworld.Unicodeiscapableofdefiningmore
thanfourbillioncharacters.Thus,alltheworld’slanguages,bothpast
andpresent,canpotentiallybeencodedwithinUnicode.
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21. Partial listing of the ASCII-compatible UTF-8 encoding scheme
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UTF-8encodescharactersthathaveanorderingwithsequential
numericalvalues.Forexample,'A'isencodedas01000001(65),'B'is
encodedas01000010(66),andsoon.Thisisalsotruefordigit
characters,‘0’isencodedas48,‘1’as49,etc.

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Notethedifferencebetweenanumericrepresentation(thatcanbeused
inarithmeticcalculations)vs.anumberrepresentedasastringofdigit
characters(notusedincalculations).
Here,thebinaryrepresentationof124isthebinarynumberforthat
value.Thestringrepresentation‘124’consistsofalongersequenceof
bits,eightbits(onebyte)foreachdigitcharacter.

23. Pythonhasameansofconvertingbetweenacharacteranditsencoding.
TheordfunctiongivestheUTF-8(ASCII)encodingofagivencharacter.
Forexample,
ord('A')is65
Thechrfunctiongivesthecharacterforagivenencodingvalue,thus
chr(65)is'A'
Whileingeneralthereisnoneedtoknowthespecificencodingofa
givencharacter,therearetimeswhensuchknowledgecanbeuseful.
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Converting Between a Character and Its Encoding

24. Let’s Try It
24
Whatistheresultofeachofthefollowingconversions?
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25. Controlcharactersarespecialcharactersthatarenotdisplayed,but
rathercontrolthedisplayofoutput,amongotherthings.Control
charactersdonothaveacorrespondingkeyboardcharacter,andthusare
representedbyacombinationofcharacterscalledanescapesequence.
Escapesequencesbeginwithanescapecharacterthatcausesthe
charactersfollowingitto“escape”theirnormalmeaning.Thebackslash
(\)servesastheescapecharacterinPython.Forexample,'\n',
representsthenewlinecontrolcharacter,thatbeginsanewscreenline,
print('Hello\nJenniferSmith')
whichisdisplayedasfollows:
Hello
JenniferSmith
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Control Characters

26. Let’s Try It
26
Whatisdisplayedbyeachofthefollowing?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.1 Literals

27. Built-infunctionformatcanbeusedforcontrollinghowstringsare
displayed,inadditiontocontrollingthedisplayofnumericalvalues,
format(value,format_specifier)
wherevalueisthevaluetobedisplayed,andformat_specifiercan
containacombinationofformattingoptions.
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String Formatting

28. Forexample,thefollowingproducesthestring'Hello'left-justifiedina
fieldwidthof20characters,
format('Hello', '<20')➝'Hello '
Toright-justifythestring,thefollowingwouldbeused,
format('Hello', '>20')➝' Hello'
Formattedstringsareleft-justifiedbydefault.Therefore,thefollowing
producethesameresult,
format('Hello', '<20')➝'Hello '
format('Hello', '20')➝ 'Hello '
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29. Tocenterastringthe'^'characterisused:
format('Hello', '^20')
Anotheruseoftheformatfunctionistocreateastringofblank
characters,whichissometimesuseful,
format('','15')➝' '
Finallyblanks,bydefault,arethefillcharacterforformattedstrings.
However,aspecificfillcharactercanbespecifiedasshownbelow,
>>>print('Hello', format('.','.<30'),'HaveaNiceDay!')
Hello.............................. HaveaNiceDay!
Here,asingleperiodisthecharacterprintedwithinafieldwidthof30,
thereforeultimatelyprintingout30periods.
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30. Let’s Try It
30
Whatisdisplayedbyeachofthefollowing?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.1 Literals

31. SometimesaprogramlinemaybetoolongtofitinthePython-
recommendedmaximumlengthof79characters.Therearetwowaysin
Pythontodealwithsuchsituations:
•implicitlinejoining
•explicitlinejoining
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Implicit and Explicit Line Joining

32. Therearecertaindelimitingcharactersthatallowalogicalprogramlinetospan
morethanonephysicalline.Thisincludesmatchingparentheses,squarebrackets,
curlybraces,andtriplequotes.
Forexample,thefollowingtwoprogramlinesaretreatedasonelogicalline:
print('Name:',student_name, 'Address:', student_address,
'Number of Credits:', total_credits, 'GPA:', current_gpa)
Matchingquotes(exceptfortriplequotes)mustbeonthesamephysicalline.For
example,thefollowingwillgenerateanerror:
print('This program will calculate a restaurant tab for a couple
with a gift certificate, and a restaurant tax of 3% ')
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Implicit Line Joining
open quote
close quote

33. Inadditiontoimplicitlinejoining,programlinesmaybeexplicitlyjoined
byuseofthebackslash(\)character.Programlinesthatendwitha
backslashthatarenotpartofaliteralstring(thatis,withinquotes)continue
onthefollowingline.
numsecs_1900_dob=((year_birth21900)*avg_numsecs_year)+\
((month_birth21)*avg_numsecs_month)+\
(day_birth*numsecs_day)
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Explicit Line Joining

34. Itisalongtraditionincomputersciencetodemonstrateaprogramthat
simplydisplays“HelloWorld!”asanexampleofthesimplestprogram
possibleinaparticularprogramminglanguage.InPython,thecomplete
HelloWorldprogramiscomprisedofoneprogramline:
print('HelloWorld!')
WetakeatwistonthistraditionandgiveaPythonprogramthatdisplaysthe
Unicodeencodingforeachofthecharactersinthestring“HelloWorld!”
instead.Thisprogramutilizesthefollowingprogrammingfeatures:
➤stringliterals➤print ➤ordfunction
34Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.1 Literals
Hello World Unicode Encoding
Let’s Apply It

35. 35Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.1 Literals
Thestatementsonlines1,3,and6arecommentstatements.Theprint
functiononline4displaysthemessage‘HelloWorld!’.Doublequotesareused
todelimitthecorrespondingstring,sincethesinglequoteswithinitaretobe
takenliterally.Theuseofprintonline7printsouttheUnicodeencoding,one-
by-one,foreachofthecharactersinthe“HelloWorld!”string.Notefromthe
programexecutionthatthereisaUnicodeencodingfortheblankcharacter
(32),aswellastheexclamationmark(33).

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44. Sofar,wehaveonlylookedatliteralvaluesinprograms.However,the
trueusefulnessofacomputerprogramistheabilitytooperateon
differentvalueseachtimetheprogramisexecuted.Thisisprovidedby
thenotionofavariable.Welookatvariablesandidentifiersnext.
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Variables and Identifiers

45. What Is a Variable?
Avariableisaname(identifier)thatisassociatedwithavalue,
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Avariablecanbeassigneddifferentvaluesduringaprogram’s
execution—hence,thename“variable.”

46. Whereveravariableappearsinaprogram(exceptontheleft-handside
ofanassignmentstatement),itisthevalueassociatedwiththevariable
thatisused,andnotthevariable’sname,
46Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
Variablesareassignedvaluesbyuseoftheassignmentoperator,=,

47. Assignmentstatementsoftenlookwrongtonoviceprogrammers.
Mathematically,num=num+1doesnotmakesense.Incomputing,
however,itisusedtoincrementthevalueofagivenvariablebyone.Itis
moreappropriate,therefore,tothinkofthe=symbolasanarrow
symbol
47Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
Whenthoughtofthisway,itmakesclearthattherightsideofan
assignmentisevaluatedfirst,thentheresultisassignedtothe
variableontheleft.Anarrowsymbolisnotusedsimplybecausethere
isnosuchcharacteronastandardcomputerkeyboard.

48. Variablesmayalsobeassignedtothevalueofanothervariable,
48Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
Variables numand kare both associated with the same literal value 10 in
memory. One way to see this is by use of built-in function id,
Theidfunctionproducesauniquenumberidentifyingaspecificvalue
(object)inmemory.Sincevariablesaremeanttobedistinct,itwould
appearthatthissharingofvalueswouldcauseproblems.

49. Ifthevalueofnumchanged,wouldvariablekchangealongwithit?
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Thiscannothappeninthiscasebecausethevariablesrefertointeger
values,andintegervaluesareimmutable.Animmutablevalueisavalue
thatcannotbechanged.Thus,bothwillcontinuetorefertothesame
valueuntilone(orboth)ofthemisreassigned,
Ifnoothervariablereferencesthememorylocationoftheoriginalvalue,
thememorylocationisdeallocated(thatis,itismadeavailableforreuse).

50. Finally,inPythonthesamevariablecanbeassociatedwithvaluesof
differenttypeduringprogramexecution,
50Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
(Theabilityofavariabletobeassignedvaluesofdifferenttypeisreferred
toasdynamictyping,introducedlaterinthediscussionsofdatatypes.)

51. Let’s Try It
51
Whatdoeachofthefollowingevaluateto?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers

52. Variable Assignment and Keyboard Input
Thevaluethatisassignedtoagivenvariabledoesnothavetobe
specifiedintheprogram.Thevaluecancomefromtheuserbyuseofthe
inputfunctionintroducedinChapter1,
>>>name=input('Whatisyourfirstname?')
Whatisyourfirstname?John
Inthiscase,thevariablenameisassignedthestring'John'.Iftheuser
hitreturnwithoutenteringanyvalue,namewouldbeassignedtothe
emptystring('').
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53. Theinputfunctionreturnsastringtype.Forinputofnumericvalues,the
responsemustbeconvertedtotheappropriatetype.Pythonprovides
built-intypeconversionfunctionsint()andfloat()forthispurpose,
line=input('Howmanycreditsdoyouhave?')
num_credits=int(line)
line=input('Whatisyourgradepointaverage?')
gpa=float(line)
Theenterednumberofcredits,say'24',isconvertedtotheequivalent
integervalue,24,beforebeingassignedtovariablenum_credits.The
inputvalueofthegpa,say'3.2',isconvertedtotheequivalentfloating-
pointvalue,3.2.
Notethattheprogramlinesabovecouldbecombinedasfollows,
num_credits=int(input('Howmanycreditsdoyouhave?'))
gpa=float(input('What isyourgradepointaverage?'))
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54. Let’s Try It
54
Whatisdisplayedbyeachofthefollowing?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers

55. What Is an Identifier?
Anidentifierisasequenceofoneormorecharactersusedtoprovidea
nameforagivenprogramelement.Variablenamesline,
num_credits,andgpaareeachidentifiers.
Pythoniscasesensitive,thus,Lineisdifferentfromline.Identifiers
maycontainlettersanddigits,butcannotbeginwithadigit.
Theunderscorecharacter,_,isalsoallowedtoaidinthereadabilityof
longidentifiernames.Itshouldnotbeusedasthefirstcharacter,
however,asidentifiersbeginningwithanunderscorehavespecial
meaninginPython.
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56. Spacesarenotallowedaspartofanidentifier.Thisisacommonerror
sincesomeoperatingsystemsallowspaceswithinfilenames.In
programminglanguages,however,spacesareusedtodelimit(separate)
distinctsyntacticentities.Thus,anyidentifiercontainingaspace
characterwouldbeconsideredtwoseparateidentifiers.
ExamplesofvalidandinvalididentifiersinPython
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57. Let’s Try It
57
Whatisdisplayedbyeachofthefollowing?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers

58. Keywords and Other
Predefined Identifiers in Python
Akeywordisanidentifierthathaspredefinedmeaninginaprogramming
language.Therefore,keywordscannotbeusedas“regular”identifiers.
Doingsowillresultinasyntaxerror,asdemonstratedintheattempted
assignmenttokeywordandbelow,
>>>and=10
SyntaxError:invalidsyntax
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59. ThekeywordsinPythonarelistedbelow.
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TodisplaythekeywordsinPython,typehelp()inthePythonshell,then
typekeywords(type'q'toquit).

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61. 61Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
Thereareotherpredefinedidentifiersthatcanbeusedasregular
identifiers,butshouldnotbe.Thisincludesfloat,int,print,exit,and
quit,forexample.
Asimplewaytocheckwhetheraspecificidentifierisakeywordin
Pythonisasfollows
>>> 'exit' in dir(__builtins__)
True
>>> 'exit_program' in dir(__builtins__)
False

62. Let’s Try It
62
Whatisdisplayedbyeachofthefollowing?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers

63. Theprogrambelowcalculatesarestauranttabforacouplebasedontheuse
ofagiftcertificateandtheitemsordered.
Thisprogramutilizesthefollowingprogrammingfeatures:
➤variables
➤keyboardinput
➤built-informatfunction
➤typeconversionfunctions
63Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
Restaurant Tab Calculation
Let’s Apply It

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Example Execution

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Example Program Execution
Line5providestherequired
initializationofvariables,with
variabletaxassignedto8%
(.08)usedinlines9,35,and
39.Tochangetherestaurant
tax,onlythislineofthe
programneedstobechanged.
Lines8–9displaywhatthe
programdoes.Lines30and31
totalthecostoftheordersfor
eachperson,assignedto
variablesamt_person1and
amt_person2.Lines34and
35computethetab,including
thetax(storedinvariable
tab).
Finally,lines38–41displaythe
costoftheordereditems,
followedbytheadded
restauranttaxandtheamount
dueafterdeductingthe
amountofthegiftcertificate.

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73. Anoperatorisasymbolthatrepresentsanoperationthatmaybe
performedononeormoreoperands.Forexample,the+symbol
representstheoperationofaddition.Anoperandisavaluethatagiven
operatorisappliedto,suchasoperands2and3intheexpression2+3.
Aunaryoperatoroperatesononlyoneoperand,suchasthenegation
operatorintheexpression-12.
Abinaryoperatoroperatesontwooperands,aswiththeaddition
operator.Mostoperatorsinprogramminglanguagesarebinary
operators.WelookatthearithmeticoperatorsinPythonnext.
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Operators

74. Arithmetic Operators
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The+,-,*(multiplication)and/(division)arithmeticoperatorsperformtheusual
operations.Notethatthe-symbolisusedbothasaunaryoperator(fornegation)anda
binaryoperator(forsubtraction),
20-5➝15 (-asbinaryoperator)
-10*2➝-20 (-asunaryoperator)
Pythonalsoincludesanexponentiation(**)operator.

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Pythonprovidestwoformsofdivision.“True”divisionisdenotedbyasingle
slash,/.Thus,25/10evaluatesto2.5.Truncatingdivisionisdenotedbyadouble
slash,//,providingatruncatedresultbasedonthetypeofoperandsappliedto.
Whenbothoperandsareintegervalues,theresultisatruncatedintegerreferred
toasintegerdivision.Whenasleastoneoftheoperandsisafloattype,theresult
isatruncatedfloatingpoint.Thus,25//10evaluatesto2,while25.0//10
evaluatesto2.0.

76. 76Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
Asexampleuseofintegerdivision,thenumberofdozendoughnutsforvariable
numDoughnuts=29is:numDoughnuts//12➝29//12➝2
Lastly,themodulusoperator(%)givestheremainderofthedivisionofits
operands,resultinginacycleofvalues.
Themodulusandtruncating(integer)divisionoperatorsarecomplementsof
eachother.Forexample,29//12givesthenumberofdozendoughnuts,
while29%12givesthenumberofleftoverdoughnuts(5).

77. Let’s Try It
77
Whatdoeachofthefollowingarithmeticexpressions
evaluateto?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers

78. Thefollowingprogramcalculatestheapproximatenumberofatomsthatthe
averagepersoncontains,andthepercentageoftheuniversethatthey
comprise.
Thisprogramutilizesthefollowingprogrammingfeatures:
➤floating-pointscientificnotation
➤built-informatfunction
78Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
Your Place in the Universe
Let’s Apply It

79. Neededvariablesnum_
atoms_universe,weight_
avg_person,andnum_
atoms_avg_personare
initializedinlines7–9.The
programgreetingisonline
12.
Line15inputstheperson’s
weight.Line18converts
theweighttokilogramsfor
thecalculationsonlines
21–22,whichcomputethe
desiredresults.
Finally,lines25–27display
theresults.
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86. 86Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers

87. Nowthatwehavelookedatarithmeticoperators,wewillseehow
operatorsandoperandscanbecombinedtoformexpressions.In
particular,wewilllookathowarithmeticexpressionsareevaluatedin
Python.Wealsointroducethenotionofadatatype.
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Expressions and Data Types

88. What Is an Expression?
88Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Anexpressionisacombinationofsymbolsthatevaluatestoavalue.Expressions,
mostcommonly,consistofacombinationofoperatorsandoperands,
4+(3*k)
Anexpressioncanalsoconsistofasingleliteralorvariable.Thus,4,3,andkare
eachexpressions.Thisexpressionhastwosubexpressions,4and(3*k).
Subexpression(3*k)itselfhastwosubexpressions,3andk.
Expressionsthatevaluatetoanumerictypearecalledarithmeticexpressions.A
subexpressionisanyexpressionthatispartofalargerexpression.Subexpressions
maybedenotedbytheuseofparentheses,asshownabove.Thus,forthe
expression4+(3*2),thetwooperandsoftheadditionoperatorare4and(3*2),
andthustheresultisequalto10.Iftheexpressionwereinsteadwrittenas
(4+3)*2,thenitwouldevaluateto14.

89. Let’s Try It
89
Whatdoeachofthefollowingarithmeticexpressions
evaluateto?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types

90. Operator Precedence
90Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Thewaywecommonlyrepresentexpressions,inwhichoperatorsappearbetween
theiroperands,isreferredtoasinfixnotation.Forexample,theexpression4+3is
ininfixnotationsincethe+operatorappearsbetweenitstwooperands,4and3.
Thereareotherwaysofrepresentingexpressionscalledprefixandpostfixnotation,
inwhichoperatorsareplacedbeforeandaftertheiroperands,respectively.
Theexpression4+(3*5)isalsoininfixnotation.Itcontainstwooperators,
+and*.Theparenthesesdenotethat(3*5)isasubexpression.Therefore,4and
(3*5)aretheoperandsoftheadditionoperator,andthustheoverallexpression
evaluatesto19.Whatiftheparentheseswereomitted,asgivenbelow?
4+3*5
Howwouldthisbeevaluated?Thesearetwopossibilities.

91. 91Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
4+3*5➝4+15➝19 4+3*5➝7*5➝35
Somemightsaythatthefirstversionisthecorrectonebytheconventionsof
mathematics.However,eachprogramminglanguagehasitsownrulesforthe
orderthatoperatorsareapplied,calledoperatorprecedence,definedinan
operatorprecedencetable.Thismayormaynotbethesameasinmathematics,
althoughittypicallyis.
BelowistheoperatorprecedencetableforthePythonoperatorsdiscussedsofar.

92. 92Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Inthetable,higher-priorityoperatorsareplacedabovelower-priorityones.Thus,
weseethatmultiplicationisperformedbeforeadditionwhennoparenthesesare
included,
4+3*5➝4+15➝19
Inourexample,therefore,iftheadditionistobeperformedfirst,parentheses
wouldbeneeded,
(4+3)*5➝7*5➝35

93. 93Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Asanotherexample,considertheexpressionbelow.
4+2**5//10➝4+32//10➝4+3➝7
FollowingPython’srulesofoperatorprecedence,theexponentiationoperatoris
appliedfirst,thenthetruncatingdivisionoperator,andfinallytheaddition
operator.
Operatorprecedenceguaranteesaconsistentinterpretationofexpressions.
However,itisgoodprogrammingpracticetouseparenthesesevenwhennot
neededifitaddsclarityandenhancesreadability,withoutoverdoingit.Thus,the
previousexpressionwouldbebetterwrittenas,
4+(2**5)//10

94. Let’s Try It
94
Whatdoeachofthefollowingarithmeticexpressions
evaluatetousingoperatorprecedenceofPython?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types

95. Operator Associativity
95Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Aquestionthatyoumayhavealreadyhadis,“Whatiftwooperatorshavethe
samelevelofprecedence,whichoneisappliedfirst?”Foroperatorsfollowingthe
associativelaw(suchasaddition)theorderofevaluationdoesn’tmatter,
(2+3)+4➝92+(3+4)➝9
Inthiscase,wegetthesameresultsregardlessoftheorderthattheoperatorsare
applied.Divisionandsubtraction,however,donotfollowtheassociativelaw,
(a)(8-4)-2➝4-2➝28-(4-2)➝8-2➝6
(b)(8/4)/2➝2/2➝18/(4/2)➝8/2➝4
(c)2**(3**2)➝512 (2**3)**2➝64
Here,theorderofevaluationdoesmatter.

96. 96Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Toresolvetheambiguity,eachoperatorhasaspecifiedoperatorassociativitythat
definestheorderthatitandotheroperatorswiththesamelevelofprecedence
areapplied.Alloperatorsgivenbelow,exceptforexponentiation,haveleft-to-
rightassociativity—exponentiationhasright-to-leftassociativity.

97. Let’s Try It
97
Whatdoeachofthefollowingarithmeticexpressions
evaluateto?
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types

98. Data Types
98Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Adatatypeisasetofvalues,andasetofoperatorsthatmaybeapplied
tothosevalues.Forexample,theintegerdatatypeconsistsofthesetof
integers,andoperatorsforaddition,subtraction,multiplication,and
division,amongothers.Integers,floats,andstringsarepartofasetof
predefineddatatypesinPythoncalledthebuilt-intypes.
Forexample,itdoesnotmakesensetotrytodivideastringbytwo,
'Hello'/2.Theprogrammerknowsthisbycommonsense.Pythonknows
itbecause'Hello'belongstothestringdatatype,whichdoesnotinclude
thedivisionoperation.

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Theneedfordatatypesresultsfromthefactthatthesameinternal
representationofdatacanbeinterpretedinvariousways,
Thesequenceofbitsinthefigurecanbeinterpretedasacharacter('A')oran
integer(65).Ifaprogramminglanguagedidnotkeeptrackoftheintendedtypeof
eachvalue,thentheprogrammerwouldhaveto.Thiswouldlikelyleadto
undetectedprogrammingerrors,andwouldprovideevenmoreworkforthe
programmer.Wediscussthisfurtherinthefollowingsection.

100. 100Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Finally,therearetwoapproachestodatatypinginprogramminglanguages.In
statictyping,avariableisdeclaredasacertaintypebeforeitisused,andcan
onlybeassignedvaluesofthattype.
Indynamictyping,thedatatypeofavariabledependsonlyonthetypeofvalue
thatthevariableiscurrentlyholding.Thus,thesamevariablemaybeassigned
valuesofdifferenttypeduringtheexecutionofaprogram.
Pythonusesdynamictyping.

101. Mixed-Type Expressions
101Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Amixed-typeexpressionisanexpressioncontainingoperandsof
differenttype.TheCPUcanonlyperformoperationsonvalueswiththe
sameinternalrepresentationscheme,andthusonlyonoperandsofthe
sametype.Operandsofmixed-typeexpressionsthereforemustbe
convertedtoacommontype.Valuescanbeconvertedinoneoftwo
ways—byimplicit(automatic)conversion,calledcoercion,orbyexplicit
typeconversion.

102. 102Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Coercionistheimplicit(automatic)conversionofoperandstoacommontype.
Coercionisautomaticallyperformedonmixed-typeexpressionsonlyifthe
operandscanbesafelyconverted,thatis,ifnolossofinformationwillresult.
Theconversionofinteger2tofloating-point2.0belowisasafeconversion—the
conversionof4.5tointeger4isnot,sincethedecimaldigitwouldbelost,
2+4.5➝2.0+4.5➝6.5safe(automaticconversionofinttofloat)
int float float float float

103. 103Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.3 Expressions and Data Types
Typeconversionistheexplicitconversionofoperandstoaspecifictype.Type
conversioncanbeappliedeveniflossofinformationresults.Pythonprovides
built-intypeconversionfunctionsint()andfloat(),withtheint()
functiontruncatingresults
2 + 4.5 ➝float(2) + 4.5 ➝2.0 + 4.5 ➝6.5 No loss of information
2 + 4.5 ➝2 + int(4.5) ➝2 + 4 ➝6 Loss of information
intfloat float float floatfloatfloat
intfloatint int intint int

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Typeconversionfunctionsint()andfloat()
Notethatnumericstringscanalsobeconvertedtoanumerictype.Infact,we
havealreadybeendoingthiswhenusingintorfloatwiththeinput
function,
num_credits=int(input('Howmanycreditsdoyouhave?'))

105. ThefollowingPythonprogramrequestsfromtheuseratemperaturein
degreesFahrenheit,anddisplaystheequivalenttemperatureindegrees
Celsius.
Thisprogramutilizesthefollowingprogrammingfeatures:
➤arithmeticexpressions
➤operatorassociativity
➤built-informatfunction
105Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.2 Variables and Identifiers
Temperature Conversion Program
Let’s Apply It

106. Line10readstheFahrenheittemperatureentered,assignedtovariablefahren.Eitheranintegerora
floating-pointvaluemaybeentered,sincetheinputisconvertedtofloattype.Line13performsthe
calculationforconvertingFahrenheittoCelsius.Recallthatthedivisionandmultiplicationoperatorshave
thesamelevelofprecedence.Sincetheseoperatorsassociateleft-to-right,themultiplicationoperatoris
appliedfirst.Becauseoftheuseofthe“true”divisionoperator/,theresultoftheexpressionwillhave
floating-pointaccuracy.Finally,lines16–17outputtheconvertedtemperatureindegreesCelsius.
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114. 114
Welookattheproblemofcalculatingan
individual’sageinseconds.Itisnotfeasibleto
determineagivenperson’sagetotheexact
second.Thiswouldrequireknowing,tothe
second,whentheywereborn.Itwouldalso
involveknowingthetimezonetheywereborn
in,issuesofdaylightsavingstime,
considerationofleapyears,andsoforth.
Therefore,theproblemistodeterminean
approximationofageinseconds.Theprogram
willbetestedagainstcalculationsofagefrom
onlineresources.
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Age in Seconds Program

115. Age in Seconds
The Problem
115
Theproblemistodeterminetheapproximateageofanindividualinseconds
within99%accuracyofresultsfromonlineresources.Theprogrammust
workfordatesofbirthfromJanuary1,1900tothepresent.
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program

116. Age in Seconds
Problem Analysis
116
Thefundamentalcomputationalissueforthisproblemisthedevelopmentof
analgorithmincorporatingapproximationsforinformationthatisimpractical
toutilize(timeofbirthtothesecond,daylightsavingstime,etc.),while
producingaresultthatmeetstherequireddegreeofaccuracy.
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program

117. Age in Seconds
Program Design
117
MeetingtheProgramRequirements
Thereisnorequirementfortheforminwhichthedateofbirthistobeentered.We
willthereforedesigntheprogramtoinputthedateofbirthasintegervalues.Also,
theprogramwillnotperforminputerrorchecking,sincewehavenotyetcoveredthe
programmingconceptsforthis.
DataDescription
Theprogramneedstorepresenttwodates,theuser’sdateofbirth,andthecurrent
date.Sinceeachpartofthedatemustbeabletobeoperatedonarithmetically,dates
willberepresentedbythreeintegers.Forexample,May15,1992wouldbe
representedasfollows:
year= 1992 month= 5 day= 15
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118. 118
Algorithmic Approach
PythonStandardLibrarymoduledatetimewillbeusedtoobtainthecurrentdate.
Weconsiderhowthecalculationscanbeapproximatedwithoutgreatlyaffectingthe
accuracyoftheresults.
Westartwiththeissueofleapyears.Sincethereisaleapyearonceeveryfouryears
(withsomeexceptions),wecalculatetheaveragenumberofsecondsinayearovera
four-yearperiodthatincludesaleapyear.Sincenon-leapyearshave365days,and
leapyearshave366,weneedtocompute,
numsecs_day= (hours per day) * (minsper hour) * (secsper minute)
numsecs_year = (days per year) * numsecs_day
avg_numsecs_year= (4 * numsecs_year) + numsecs_day) // 4(one extra day for leap year)
avg_numsecs_month= avgnumsecs_year// 12
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119. 119
Tocalculatesomeone’sageinseconds,weuseJanuary1,1900asabasis.Thus,we
computetwovalues—thenumberofsecondsfromJanuary1,1900tothegivendate
ofbirth,andthenumberofsecondsfromJanuary1,1900tothecurrentdate.
Subtractingtheformerfromthelattergivestheapproximateage,
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Notethatifwedirectlydeterminedthenumberofsecondsbetweenthedateof
birthandcurrentdate,themonthsanddaysofeachwouldneedtobecompared
toseehowmanyfullmonthsandyearstherewerebetweenthetwo.Using1900
asabasisavoidsthesecomparisons.Thus,therestofouralgorithmfollows.

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121. 121Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
The Overall Steps of the Program

122. Age in Seconds
Program Implementation
122
First,wedecideonthevariablesneededfortheprogram.Fordateofbirth,
weusevariablesmonth_birth,day_birth,andyear_birth.
Similarly,forthecurrentdateweusevariablescurrent_month,
current_day,andcurrent_year.Thefirststageoftheprogramassignseach
ofthesevalues.
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Stage 1—Getting the Date of Birth and Current Date

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124. 124Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Stage 1 Testing
Weaddteststatementsthatdisplaythevaluesoftheassignedvariables.
Thisistoensurethatthedateswearestartingwitharecorrect;otherwise,
theresultswillcertainlynotbecorrect.Thetestrunbelowindicatesthatthe
inputisbeingcorrectlyread.
Enter month born (1-12): 4
Enter day born (1-31): 12
Enter year born (4-digit): 1981
The date of birth read is: 4 12 1981
The current date read is: 1 5 2010
>>>

125. Program Implementation
125
Nextwedeterminetheapproximatenumberofsecondsinagivenyearand
month,andtheexactnumberofsecondsinadaystoredinvariables
avg_numsecs_year,avg_numsecs_month,andnumsecs_day,respectively.
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Stage 2—Approximating the Number of Seconds in a Year/Month/Day

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Thelinesofcodepromptingforinputarecommentedout(lines6–9and11–14).
Sinceitiseasytocommentout(anduncomment)blocksofcodeinIDLE,wedoso;
theinputvaluesareirrelevanttothispartoftheprogramtesting

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Stage 2 Testing
Followingistheoutputofthistestrun.Checkingonlinesources,wefindthat
thenumberofsecondsinaregularyearis31,536,000andinaleapyearis
31,622,400.Thus,ourapproximationof31,557,600astheaveragenumber
ofsecondsoverfouryears(includingaleapyear)isreasonable.The
avg_num_seconds_monthisdirectlycalculatedfromvariableavg_numsecs_
year,andnumsecs_dayisfoundtobecorrect.
numsecs_day86400
avg_numsecs_month = 2629800
avg_numsecs_year 5 31557600
>>>

128. Program Implementation
128
Finally,wecompletetheprogrambycalculatingtheapproximatenumberof
secondsfrom1900toboththecurrentdateandtheprovideddateofbirth.
Thedifferenceofthesetwovaluesgivestheapproximateageinseconds.
Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Final Stage—Calculating the Number of Seconds from 1900

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130. 130Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Wedevelopasetoftestcasesforthisprogram.Wefollowthetestingstrategyof
including“average”aswellas“extreme”or“specialcase”testcasesinthetestplan.
The“correct”ageinsecondsforeachwasobtainedfromanonlinesource.January1,
1900wasincludedsinceitistheearliestdatethattheprogramisrequiredtoworkfor.
April12,1981wasincludedasanaveragecaseinthe1900s,andJanuary4,2000as
anaveragecaseinthe2000s.December31,2009wasincludedsinceitisthelastday
ofthelastmonthoftheyear,andabirthdayonthedaybeforethecurrentdateas
specialcases.Sincethesevaluesarecontinuouslychangingbythesecond,weconsider
anyresultwithinoneday’sworthofseconds(±84,000)tobeanexactresult.

131. 131Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Theprogramresultsareobviouslyincorrect,sincetheresultisapproximatelyequal
totheaveragenumberofsecondsinamonth.Theonlycorrectresultisfortheday
beforethecurrentdate.Theinaccuracyofeachresultwascalculatedasfollowsfor
April12,1981,
((abs(expected_results–actual_results)–86,400)/expected_results)*100=
((917,110,352–518,433)–86400)/917,110,352)*100=99.93%
ExampleoutputofresultsforabirthdayofApril12,1981.

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Eitherouralgorithmicapproachisflawed,oritisnotcorrectlyimplemented.Sincewe
didn’tfindanyerrorsinthedevelopmentofthefirstandsecondstagesoftheprogram,
theproblemmustbeinthecalculationoftheapproximateageinlines29–37.These
linesdefinethreevariables:numsecs_1900_dob,numsecs_1900_today,and
age_in_secs.Wecaninspectthevaluesofthesevariablesafterexecutionofthe
programtoseeifanythingirregularpopsoutatus.
This program computes the approximate age in seconds of an
individual based on a provided date of birth. Only ages for
dates of birth from 1900 and after can be computed
Enter month born (1-12): 4
Enter day born (1-31): 12
Enter year born: (4-digit)1981
You are approximately 604833 seconds old
>>>
>>> numsecs_1900_dob
-59961031015
>>> numsecs_1900_today
-59960426182
>>>

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Clearly,thisiswheretheproblemis,sincewearegettingnegativevaluesforthetimes
between1900anddateofbirth,andfrom1900totoday.We“workbackwards”and
considerhowtheexpressionscouldgivenegativeresults.Thiswouldbeexplainedif,for
somereason,thesecondoperandofthesubtractionweregreaterthanthefirst.That
wouldhappeniftheexpressionwereevaluated,forexample,as
numsecs_1900_dob=(year_birth-(1900*avg_numsecs_year))+\
(month_birth-(1*avg_numsecs_month))+\
(day_birth*numsecs_day)
ratherthanthefollowingintendedmeansofevaluation,
numsecs_1900_dob=((year_birth-1900)*avg_numsecs_year)+\
((month_birth-1)*avg_numsecs_month)+\
(day_birth*numsecs_day)
Nowwerealize!Becausewedidnotuseparenthesestoexplicitlyindicatetheproper
orderofoperators,bytherulesofoperatorprecedencePythonevaluatedthe
expressionasthefirstwayabove,notthesecondasitshouldbe.Thiswouldalso
explainwhytheprogramgavethecorrectresultforadateofbirthonedaybeforethe
currentdate.

134. 134Introduction to Computer Science Using Python –DierbachCopyright 2013 John Wiley and Sons Section 2.5 Age in Seconds Program
Oncewemakethecorrectionsandre-runthetestplan,wegetthefollowingresults,
Theseresultsdemonstratethatourapproximationofthenumberofsecondsina
yearwassufficienttogetwellwithinthe99%degreeofaccuracyrequiredforthis
program.Wewouldexpectmorerecentdatesofbirthtogivelessaccurateresults
giventhatthereislesstimethatisapproximated.Still,fortestcaseDecember31,
2009theinaccuracyislessthan.05percent.Therefore,wewereabletodevelopa
programthatgaveveryaccurateresultswithoutinvolvingalltheprogramlogicthat
wouldbeneededtoconsiderallthedetailsrequiredtogiveanexactresult.