Think Python - Denison University

Think PythonHowto Think LikeaComputer ScientistVersion 1.1.28

Think PythonHowto Think LikeaComputer ScientistVersion 1.1.28AllenDowneyGreenTeaPressNeedham, Massachusetts

Copyright©2008 AllenDowney.Printinghistory:April 2002: Firsteditionof How toThink LikeaComputer Scientist.August 2007: Majorrevision, changed titleto How toThinkLike a(Python) Programmer.June2008: Major revision,changed titleto Think Python: How toThinkLike aComputer Scientist.Green Tea Press9Washburn AveNeedham MA02492Permission is granted to copy, distribute, and/or modify this document under the terms of the GNU Free DocumentationLicense, Version 1.1 or any later version published by the Free Software Foundation; with noInvariant Sections,no Front-CoverTexts,and withno Back-Cover Texts.The GNU Free Documentation License is available from www.gnu.org or by writing to the Free SoftwareFoundation, Inc., 59Temple Place, Suite330, Boston,MA02111-1307, USA.The original form of this book is LATEX source code. Compiling this LATEX source has the effect of generatingadevice-independent representation of atextbook, whichcan be converted toother formatsand printed.TheLATEX sourcefor thisbook isavailable fromhttp://www.thinkpython.com

PrefaceThe strangehistoryof thisbookIn January 1999 I was preparing to teach an introductory programming class in Java. I had taughtit three times and I was getting frustrated. The failure rate in the class was too high and, even forstudents who succeeded, the overall level of achievement was too low.OneoftheproblemsIsawwasthebooks. Theyweretoobig,withtoomuchunnecessarydetailaboutJava,andnotenoughhigh-levelguidanceabouthowtoprogram. Andtheyallsufferedfromthetrapdooreffect: theywouldstartouteasy,proceedgradually,andthensomewherearoundChapter5thebottom would fall out. The students would get too much new material, too fast, and I would spendtherest ofthe semester picking up thepieces.Two weeks before thefirst day of classes,Idecided towritemy own book. Mygoals were:• Keep itshort. Itisbetter for students toread 10 pages than not read 50 pages.• Be careful withvocabulary. I triedtominimize the jargon and define each termat firstuse.• Build gradually. To avoid trap doors, I took the most difficult topics and split them into aseries ofsmall steps.• Focusonprogramming,nottheprogramminglanguage. Iincludedtheminimumusefulsubsetof Java and left out the rest.Ineeded atitle,soon awhim I chose How toThink Like aComputer Scientist.My first version was rough, but it worked. Students did the reading, and they understood enoughthat I could spend class time on the hard topics, the interesting topics and (most important) lettingthestudents practice.IreleasedthebookundertheGNUFreeDocumentationLicense,whichallowsuserstocopy,modify,and distributethebook.Whathappenednextisthecoolpart. JeffElkner,ahighschoolteacherinVirginia,adoptedmybookandtranslateditintoPython. Hesentmeacopyofhistranslation,andIhadtheunusualexperienceof learning Python by reading myown book.Jeff and I revised the book, incorporated a case study by Chris Meyers, and in 2001 we releasedHow to Think Like a Computer Scientist: Learning with Python, also under the GNU Free DocumentationLicense. As Green Tea Press, I published the book and started selling hard copiesthrough Amazon.com and college book stores. Other books from Green Tea Press are available atgreenteapress.com.

viChapter 0. PrefaceIn 2003 I started teaching at Olin College and I got to teach Python for the first time. The contrastwith Java was striking. Students struggled less, learned more, worked on more interesting projects,and generally had alot morefun.Over the last five years I have continued to develop the book, correcting errors, improving some oftheexamplesandaddingmaterial,especiallyexercises. In2008Istartedworkonamajorrevision—at the same time, I was contacted by an editor at Cambridge University Press who was interested inpublishing the next edition. Good timing!The resultisthis book, now withthe lessgrandiose titleThink Python. Some of thechanges are:• I added a section about debugging at the end of each chapter. These sections present generaltechniques forfinding and avoiding bugs, and warnings about Python pitfalls.• I removed the material in the last few chapters about the implementation of lists and trees. Istilllove those topics, but Ithought they were incongruent withthe restof thebook.• Iaddedmoreexercises,rangingfromshorttestsofunderstandingtoafewsubstantialprojects.• I added a series of case studies—longer examples with exercises, solutions, and discussion.SomeofthemarebasedonSwampy,asuiteofPythonprogramsIwroteforuseinmyclasses.Swampy, code examples, and somesolutions are available fromthinkpython.com.• I expanded thediscussion ofprogram development plans and basic design patterns.• The use of Python is more idiomatic. The book is still about programming, not Python, butnow Ithink thebook gets moreleverage from thelanguage.Ihopeyouenjoyworkingwiththisbook,andthatithelpsyoulearntoprogramandthink,atleastalittlebit,likeacomputer scientist.AllenB. DowneyNeedham MAAllen Downey is an Associate Professor of Computer Science at the Franklin W. Olin College ofEngineering.AcknowledgementsFirstandmostimportantly,IthankJeffElkner,whotranslatedmyJavabookintoPython,whichgotthisproject startedand introduced me towhat has turned out tobe myfavoritelanguage.I also thank Chris Meyers, who contributed several sections to How to Think Like a ComputerScientist.And I thank the Free Software Foundation for developing the GNU Free Documentation License,which helped make my collaboration withJeffand Chris possible.Ialsothank theeditors at Lulu who worked on How toThink Like aComputer Scientist.Ithankallthestudentswhoworkedwithearlierversionsofthisbookandallthecontributors(listedbelow) who sent incorrections and suggestions.AndIthankmywife,Lisa,forherworkonthisbook,andGreenTeaPress,andeverythingelse,too.

viiContributor ListMore than 100 sharp-eyed and thoughtful readers have sent in suggestions and corrections over thepast few years. Their contributions, and enthusiasm for thisproject, have been ahuge help.If you have a suggestion or correction, please send email to feedback@thinkpython.com. If Imake a change based on your feedback, I will add you to the contributor list (unless you ask to beomitted).If you include at least part of the sentence the error appears in, that makes it easy for me to search.Page and section numbers arefine, too, but not quite as easytowork with. Thanks!• Lloyd HughAllen sentinacorrection toSection8.4.• Yvon Boulianne sentinacorrection of a semanticerror inChapter 5.• Fred Bremmer submittedacorrection inSection 2.1.• Jonah Cohenwrote thePerlscriptstoconvert theLaTeX sourcefor thisbook intobeautiful HTML.• Michael Conlon sent in a grammar correction in Chapter 2 and an improvement in style in Chapter 1,and he initiateddiscussiononthe technical aspects of interpreters.• BenoitGirard sentinacorrection toahumorous mistakeinSection 5.6.• CourtneyGleasonandKatherineSmithwrotehorsebet.py,whichwasusedasacasestudyinanearlierversion ofthe book. Their program can nowbe foundon thewebsite.• Lee Harr submitted more corrections than we have room to list here, and indeed he should be listed asone of the principaleditors of the text.• James Kaylin is astudentusingthe text. He has submittednumerous corrections.• David Kershaw fixed thebrokencatTwice function inSection 3.10.• Eddie Lam has sent in numerous corrections to Chapters 1, 2, and 3. He also fixed the Makefile so thatitcreates an indexthe firsttimeitis runand helped us setup aversioningscheme.• Man-Yong Lee sentinacorrection to theexample code in Section2.4.• David Mayo pointed out that the word “unconsciously” in Chapter 1 needed to be changed to “subconsciously”.• ChrisMcAloon sentinseveral corrections toSections 3.9and 3.10.• MatthewJ.Moelterhasbeenalong-timecontributorwhosentinnumerouscorrectionsandsuggestionsto thebook.• Simon Dicon Montford reported a missing function definition and several typos in Chapter 3. He alsofound errorsintheincrement functioninChapter 13.• JohnOuzts corrected thedefinition of “returnvalue” inChapter 3.• Kevin Parks sent in valuable comments and suggestions as to how to improve the distribution of thebook.• David Pool sentinatypo intheglossaryof Chapter 1,as well as kindwords of encouragement.• Michael Schmitt sentinacorrection tothe chapter onfiles andexceptions.• Robin Shaw pointed out an error in Section 13.1, where the printTime function was used in an examplewithout being defined.• Paul Sleigh found an error in Chapter 7 and a bug in Jonah Cohen’s Perl script that generates HTMLfromLaTeX.• Craig T. Snydal is testing the text in a course at Drew University. He has contributed several valuablesuggestions and corrections.• Ian Thomas and his students are using the text in a programming course. They are the first ones to testthe chapters in thelatter half of thebook, andthey have made numerous corrections and suggestions.

viiiChapter 0. Preface• Keith Verheyden sentin acorrection inChapter 3.• Peter Winstanley letus know about alongstanding error inour LatininChapter 3.• ChrisWrobel made corrections tothecode inthe chapter onfileI/O andexceptions.• Moshe Zadka has made invaluable contributions to this project. In addition to writing the first draft ofthe chapter onDictionaries, he providedcontinual guidance inthe earlystages of the book.• Christoph Zwerschke sent several corrections and pedagogic suggestions, and explained the differencebetween gleich and selbe.• JamesMayersentusawholeslewofspellingandtypographicalerrors,includingtwointhecontributorlist.• Hayden McAfee caught apotentially confusinginconsistency between twoexamples.• Angel Arnal is part of an international team of translators working on the Spanish version of the text.He has alsofound severalerrorsin theEnglishversion.• TauhidulHoqueandLexBerezhnycreatedtheillustrationsinChapter1andimprovedmanyoftheotherillustrations.• Dr. Michele Alzetta caught an error in Chapter 8 and sent some interesting pedagogic comments andsuggestions about Fibonacci and OldMaid.• Andy Mitchell caught atypoin Chapter 1and abroken example inChapter 2.• Kalin Harvey suggested aclarification inChapter 7andcaught some typos.• Christopher P.Smithcaught several typos and helped usupdate thebook forPython 2.2.• David Hutchins caught atypo intheForeword.• Gregor Lingl is teaching Python at a high school in Vienna, Austria. He is working on a Germantranslation of thebook, andhe caught acouple of bad errorsin Chapter 5.• JuliePeters caught a typointhe Preface.• FlorinOprina sentinan improvement inmakeTime, acorrection inprintTime, and anice typo.• D. J.Webre suggestedaclarification inChapter 3.• Ken found afistfulof errors inChapters 8,9and 11.• Ivo Wever caught a typoinChapter 5 andsuggested aclarification inChapter 3.• CurtisYanko suggestedaclarification inChapter 2.• BenLogan sentinanumber of typos and problems withtranslatingthe book intoHTML.• JasonArmstrongsawthe missingword inChapter 2.• Louis Cordier noticed aspotinChapter 16where the code didn’tmatch thetext.• BrianCainsuggestedseveral clarifications inChapters 2and3.• RobBlack sentinapasselof corrections,including some changes forPython 2.2.• Jean-Philippe Rey at Ecole Centrale Paris sent a number of patches, including some updates for Python2.2 andother thoughtfulimprovements.• JasonMader at George Washington University made anumber of usefulsuggestions and corrections.• JanGundtofte-Bruun reminded usthat “a error”isan error.• AbelDavidandAlexisDinnoremindedusthatthepluralof“matrix”is“matrices”,not“matrixes”. Thiserrorwasinthebookforyears,buttworeaderswiththesameinitialsreporteditonthesameday. Weird.• Charles Thayer encouraged us to get rid of the semi-colons we had put at the ends of some statementsand toclean up our useof “argument” and “parameter”.• Roger Sperberg pointed outatwisted piece of logicin Chapter 3.• Sam Bullpointed out aconfusingparagraph inChapter 2.• Andrew Cheungpointed outtwo instances of “usebefore def.”

ix• C.CoreyCapelspotted themissingword intheThirdTheorem of Debugging and atypo inChapter 4.• Alessandra helped clear upsomeTurtleconfusion.• Wim Champagne found abrain-oinadictionary example.• Douglas Wrightpointed out aproblem withfloor divisioninarc.• Jared Spindor foundsomejetsam attheend of asentence.• LinPeiheng sentanumber of very helpfulsuggestions.• RayHagtvedt sentintwoerrors andanot-quite-error.• TorstenHübsch pointed outan inconsistencyinSwampy.• Inga Petuhhov corrected anexample inChapter 14.• Arne Babenhauserheide sentseveralhelpful corrections.• MarkE.Casidais isgood atspottingrepeated words.• Scott Tyler filledin athatwas missing. Andthen sentinaheap of corrections.• Gordon Shephard sentinseveral corrections,all inseparateemails.• Andrew Turnerspottedan error inChapter 8.• Adam Hobart fixed aproblem withfloor divisioninarc.• Daryl Hammond and Sarah Zimmerman pointed out that I served up math.pi too early. And Zimspotted atypo.• George SassfoundabuginaDebugging section.• BrianBinghamsuggested Exercise11.9.• Leah Engelbert-Fenton pointed out that I used tuple as a variable name, contrary to my own advice.And then foundabunch of typos and a“use beforedef.”• JoeFunke spottedatypo.• Chao-chao Chenfound aninconsistency inthe Fibonacci example.• Jeff Paine knows the difference between space and spam.• Lubos Pintes sentinatypo.• Gregg Lindand Abigail Heithoff suggestedExercise 14.6.• Max Hailperin has sent in a number of corrections and suggestions. Max is one of the authors of theextraordinary Concrete Abstractions,which youmight want toreadwhen you aredone withthis book.• Chotipat Pornavalai foundan errorin anerror message.• Stanislaw Antolsentalistof very helpfulsuggestions.• EricPashman sentanumber of corrections for Chapters 4–11.• Miguel Azevedo foundsometypos.• Jianhua Liusentinalong listof corrections.• Nick King foundamissingword.• MartinZuther sentalonglistof suggestions.• Adam Zimmerman foundan inconsistencyin myinstance of an“instance” andseveral other errors.• Ratnakar Tiwarisuggestedafootnoteexplaining degenerate triangles.• Anurag Goel suggested another solution for is_abecedarian and sent some additional corrections.And he knows how tospellJaneAusten.• Kelli Kratzer spottedone of thetypos.• MarkGriffiths pointed outaconfusing example inChapter 3.• Roydan Ongie foundan errorin myNewton’s method.

xChapter 0. Preface• Patryk Wolowiec helped mewith aproblem intheHTML version.• MarkChonofskytoldme about anew keyword inPython 3.0.• RussellColeman helped me withmygeometry.• Wei Huang spottedseveraltypographical errors.• Karen Barber spottedthe theoldest typointhe book.• Nam Nguyen found a typo and pointed out that I used the Decorator pattern but didn’t mention it byname.• Stéphane Morinsentin severalcorrections andsuggestions.• Paul Stoopcorrected a typoinuses_only.• EricBronner pointed outaconfusioninthediscussionof theorder ofoperations.• Alexandros Gezerlis setanewstandardforthenumber andqualityofsuggestionshesubmitted. We aredeeply grateful!• Gray Thomas knows his rightfromhis left.• Giovanni Escobar Sosasentalong listof corrections and suggestions.• Alix Etiennefixed one of theURLs.• Kuang Hefound atypo.• Daniel Neilson corrected an errorabout the order of operations.• Will McGinnis pointed outthatpolylinewas defined differentlyintwo places.• Swarup Sahoo spottedamissingsemi-colon.

ContentsPrefacev1 The way of the program 11.1 The Python programming language . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 What isaprogram? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 What isdebugging? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Formal and natural languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 The first program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.7 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Variables, expressions and statements 92.1 Values and types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Variable names and keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 Operators and operands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.6 Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.7 Order of operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.8 String operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.9 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.10 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.11 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

xiiContents3 Functions 173.1 Function calls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Type conversion functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Math functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.5 Adding new functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.6 Definitions and uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.7 Flow of execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.8 Parameters and arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.9 Variables and parameters arelocal . . . . . . . . . . . . . . . . . . . . . . . . . 223.10 Stack diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.11 Fruitful functions and void functions . . . . . . . . . . . . . . . . . . . . . . . . 243.12 Why functions? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.13 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.14 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.15 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Case study: interface design 294.1 TurtleWorld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2 Simple repetition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.4 Encapsulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.5 Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.6 Interface design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.7 Refactoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.8 A development plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.9 docstring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.10 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.11 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Contentsxiii5 Conditionals and recursion 395.1 Modulus operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.2 Boolean expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.3 Logical operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.4 Conditional execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.5 Alternative execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.6 Chained conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.7 Nested conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.8 Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.9 Stack diagrams for recursive functions . . . . . . . . . . . . . . . . . . . . . . . 435.10 Infinite recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.11 Keyboard input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.12 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.13 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.14 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 Fruitful functions 516.1 Return values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.2 Incremental development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.3 Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.4 Boolean functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.5 More recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.6 Leap of faith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.7 One more example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.8 Checking types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.9 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.10 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

xivContents7 Iteration 637.1 Multipleassignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637.2 Updating variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647.3 Thewhilestatement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647.4 break . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.5 Square roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667.6 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677.7 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687.8 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698 Strings 718.1 A stringisasequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718.2 len . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 728.3 Traversal withaforloop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 728.4 String slices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 738.5 Strings areimmutable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 748.6 Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 748.7 Looping and counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758.8 stringmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758.9 Theinoperator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 768.10 String comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778.11 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778.12 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798.13 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 799 Case study: word play 819.1 Reading wordlists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829.3 Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839.4 Looping withindices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849.5 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859.6 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Contentsxv10 Lists 8910.1 A listisasequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8910.2 Listsaremutable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8910.3 Traversing alist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9110.4 Listoperations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9110.5 Listslices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9210.6 Listmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9210.7 Map, filter and reduce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9310.8 Deleting elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9410.9 Listsand strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9510.10 Objects and values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9510.11 Aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9610.12 Listarguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9710.13 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9810.14 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9910.15 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10011 Dictionaries 10311.1 Dictionary as a setof counters . . . . . . . . . . . . . . . . . . . . . . . . . . . 10411.2 Looping and dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10611.3 Reverse lookup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10611.4 Dictionaries and lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10711.5 Memos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10911.6 Global variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11011.7 Long integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11111.8 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11211.9 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11211.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

xviContents12 Tuples 11512.1 Tuples are immutable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11512.2 Tuple assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11612.3 Tuples as returnvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11712.4 Variable-length argument tuples . . . . . . . . . . . . . . . . . . . . . . . . . . 11712.5 Listsand tuples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11812.6 Dictionaries and tuples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11912.7 Comparing tuples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12112.8 Sequences of sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12112.9 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12212.10 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12312.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12313 Case study: data structure selection 12513.1 Word frequency analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12513.2 Random numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12613.3 Word histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12713.4 Most common words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12813.5 Optional parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12813.6 Dictionary subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12913.7 Random words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12913.8 Markov analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13013.9 Data structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13113.10 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13213.11 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13313.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13414 Files 13514.1 Persistence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13514.2 Reading and writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13514.3 Format operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13614.4 Filenames and paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Contentsxvii14.5 Catching exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13814.6 Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13914.7 Pickling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13914.8 Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14014.9 Writingmodules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14114.10 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14214.11 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14314.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14315 Classes and objects 14515.1 User-defined types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14515.2 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14615.3 Rectangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14715.4 Instances as returnvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14815.5 Objects aremutable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14815.6 Copying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14915.7 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15015.8 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15115.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15116 Classes and functions 15316.1 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15316.2 Pure functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15416.3 Modifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15516.4 Prototyping versus planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15616.5 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15716.6 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15816.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

xviiiContents17 Classes and methods 15917.1 Object-oriented features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15917.2 Printing objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16017.3 Another example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16117.4 A more complicated example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16217.5 The init method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16217.6 The str method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16317.7 Operator overloading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16317.8 Type-based dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16417.9 Polymorphism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16517.10 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16617.11 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16617.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16718 Inheritance 16918.1 Card objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16918.2 Class attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17018.3 Comparing cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17118.4 Decks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17218.5 Printing thedeck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17218.6 Add, remove, shuffle and sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17318.7 Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17418.8 Class diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17518.9 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17618.10 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17718.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17819 Case study: Tkinter 18119.1 GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18119.2 Buttons and callbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18219.3 Canvas widgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18319.4 Coordinate sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Contentsxix19.5 More widgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18419.6 Packing widgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18519.7 Menus and Callables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18819.8 Binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18919.9 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19119.10 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19119.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192A Debugging 195A.1 Syntax errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195A.2 Runtime errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197A.3 Semantic errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

xxContents

Chapter 1The way ofthe programThe goal of this book is to teach you to think like a computer scientist. This way of thinking combinessome of the best features of mathematics, engineering, and natural science. Like mathematicians,computer scientists use formal languages to denote ideas (specifically computations). Likeengineers, they design things, assembling components into systems and evaluating tradeoffs amongalternatives. Like scientists, they observe the behavior of complex systems, form hypotheses, andtestpredictions.Thesinglemostimportantskillforacomputerscientistisproblemsolving. Problemsolvingmeanstheabilitytoformulateproblems,thinkcreativelyaboutsolutions,andexpressasolutionclearlyandaccurately. Asitturnsout,theprocessoflearningtoprogramisanexcellentopportunitytopracticeproblem-solving skills. That’s why thischapter iscalled, “The way of theprogram.”Ononelevel,youwillbelearningtoprogram,ausefulskillbyitself. Onanotherlevel,youwilluseprogramming as ameans toan end. As wego along, that end willbecome clearer.1.1 ThePython programming languageTheprogramminglanguageyouwilllearnisPython. Pythonisanexampleofahigh-levellanguage;other high-level languages you might have heard of areC, C++, Perl, and Java.There are also low-level languages, sometimes referred to as “machine languages” or “assemblylanguages.” Looselyspeaking,computerscanonlyexecuteprogramswritteninlow-levellanguages.So programs written in a high-level language have to be processed before they can run. This extraprocessing takes sometime, which isasmall disadvantage of high-level languages.Theadvantagesareenormous. First,itismucheasiertoprograminahigh-levellanguage. Programswritten in a high-level language take less time to write, they are shorter and easier to read, and theyaremorelikelytobecorrect. Second, high-level languages areportable, meaningthattheycanrunon different kinds of computers with few or no modifications. Low-level programs can run on onlyone kind of computer and have toberewritten torun onanother.Due to these advantages, almost all programs are written in high-level languages. Low-level languagesareused only forafew specialized applications.Two kinds of programs process high-level languages into low-level languages: interpreters andcompilers. An interpreter reads a high-level program and executes it, meaning that it does what the

2 Chapter 1. The way of theprogramprogram says. It processes the program a little at a time, alternately reading lines and performingcomputations.SOURCECODEINTERPRETEROUTPUTAcompilerreadstheprogramandtranslatesitcompletelybeforetheprogramstartsrunning. Inthiscontext, the high-level program is called the source code, and the translated program is called theobject code or the executable. Once a program is compiled, you can execute it repeatedly withoutfurther translation.SOURCECODECOMPILEROBJECTCODEEXECUTOROUTPUTPython is considered an interpreted language because Python programs are executed by an interpreter.There are two ways to use the interpreter: interactive mode and script mode. In interactivemode, you type Python programs and theinterpreter printstheresult:>>> 1 + 12The chevron, >>>, is the prompt the interpreter uses to indicate that it is ready. If you type 1 + 1,theinterpreter replies2.Alternatively, you can store code in a file and use the interpreter to execute the contents of the file,which iscalled a script. Byconvention, Python scriptshave names that end with.py.To execute the script, you have to tell the interpreter the name of the file. In a UNIX commandwindow, you would type python dinsdale.py. In other development environments, the details ofexecutingscriptsaredifferent. YoucanfindinstructionsforyourenvironmentatthePythonwebsitepython.org.Workingininteractivemodeisconvenientfortestingsmallpiecesofcodebecauseyoucantypeandexecute them immediately. But for anything more than a few lines, you should save your code as ascriptsoyou can modifyand execute itinthefuture.1.2 Whatis aprogram?A program is a sequence of instructions that specifies how to perform a computation. The computationmight be something mathematical, such as solving a system of equations or finding the rootsof a polynomial, but it can also be a symbolic computation, such as searching and replacing text inadocument or (strangelyenough) compiling aprogram.The details look different in different languages, but a few basic instructions appear in just aboutevery language:input: Get data from thekeyboard, afile, or someother device.

4 Chapter 1. The way of theprogram1.3.3 SemanticerrorsThe third type of error is the semantic error. If there is a semantic error in your program, it willrun successfully in the sense that the computer will not generate any error messages, but it will notdo theright thing. Itwilldo something else. Specifically, itwilldo what you toldittodo.Theproblemisthattheprogramyouwroteisnottheprogramyouwantedtowrite. Themeaningofthe program (its semantics) is wrong. Identifying semantic errors can be tricky because it requiresyou to work backward by looking at the output of the program and trying to figure out what it isdoing.1.3.4 ExperimentaldebuggingOne of the most important skills you will acquire is debugging. Although it can be frustrating,debugging isone of the mostintellectually rich,challenging, and interestingparts of programming.In some ways, debugging is like detective work. You are confronted with clues, and you have toinfer theprocesses and events that ledtotheresultsyou see.Debugging is also like an experimental science. Once you have an idea about what is going wrong,you modify your program and try again. If your hypothesis was correct, then you can predict theresult of the modification, and you take a step closer to a working program. If your hypothesis waswrong, you have to come up with a new one. As Sherlock Holmes pointed out, “When you haveeliminated the impossible, whatever remains, however improbable, must be the truth.” (A. ConanDoyle, The Sign of Four)For some people, programming and debugging are the same thing. That is, programming is theprocess of gradually debugging a program until it does what you want. The idea is that you shouldstartwithaprogramthatdoessomethingandmakesmallmodifications, debugging themasyougo,sothat you always have aworking program.For example, Linux is an operating system that contains thousands of lines of code, but it startedout as a simple program Linus Torvalds used to explore the Intel 80386 chip. According to LarryGreenfield, “One of Linus’s earlier projects was a program that would switch between printingAAAA and BBBB. This laterevolved toLinux.” (TheLinux Users’Guide BetaVersion 1).Later chapters will make moresuggestions about debugging and other programming practices.1.4 Formaland natural languagesNatural languages are the languages people speak, such as English, Spanish, and French. Theywere not designed by people (although people try to impose some order on them); they evolvednaturally.Formallanguagesarelanguagesthataredesignedbypeopleforspecificapplications. Forexample,the notation that mathematicians use is a formal language that is particularly good at denoting relationshipsamong numbers and symbols. Chemists use a formal language to represent the chemicalstructureof molecules. And most importantly:Programming languages are formal languages that have been designed to expresscomputations.

1.4. Formal and natural languages 5Formallanguagestendtohavestrictrulesaboutsyntax. Forexample,3+3=6isasyntacticallycorrectmathematical statement, but 3+=3$6 is not. H 2 O is a syntactically correct chemical formula,but 2 Zz isnot.Syntax rules come in two flavors, pertaining to tokens and structure. Tokens are the basic elementsof the language, such as words, numbers, and chemical elements. One of the problems with 3+=3$6isthat$isnotalegaltokeninmathematics(atleastasfarasIknow). Similarly, 2 Zzisnotlegalbecause there isno element withtheabbreviation Zz.The second type of syntax error pertains to the structure of a statement; that is, the way the tokensarearranged. Thestatement3+=3$6isillegalbecauseeventhough+and=arelegaltokens,youcan’t have one right after the other. Similarly, in a chemical formula the subscript comes after theelement name, not before.Exercise 1.1 Write a well-structured English sentence with invalid tokens in it. Then write anothersentence withall validtokens but withinvalidstructure.When you read a sentence in English or a statement in a formal language, you have to figure outwhat the structure of the sentence is (although in a natural language you do this subconsciously).This process iscalled parsing.For example, when you hear the sentence, “The penny dropped,” you understand that “the penny”is the subject and “dropped” is the predicate. Once you have parsed a sentence, you can figure outwhat it means, or the semantics of the sentence. Assuming that you know what a penny isand whatitmeans todrop, you willunderstand thegeneral implication of thissentence.Although formal and natural languages have many features in common—tokens, structure, syntax,and semantics—there are somedifferences:ambiguity: Natural languages are full of ambiguity, which people deal with by using contextualcluesandotherinformation. Formallanguagesaredesignedtobenearlyorcompletelyunambiguous,which means that any statement has exactly one meaning, regardless ofcontext.redundancy: In order to make up for ambiguity and reduce misunderstandings, natural languagesemploy lots of redundancy. As a result, they are often verbose. Formal languages are lessredundant and more concise.literalness: Natural languages arefullofidiomandmetaphor. IfIsay,“The penny dropped,” thereisprobably no penny and nothing dropping 1 . Formal languages mean exactly what they say.People who grow up speaking a natural language—everyone—often have a hard time adjusting toformal languages. In some ways, the difference between formal and natural language is like thedifference between poetry and prose, but more so:Poetry: Words areused fortheirsounds as wellas fortheir meaning, and thewhole poem togethercreates an effect or emotional response. Ambiguity isnot only common but oftendeliberate.Prose: Theliteralmeaningofwordsismoreimportant,andthestructurecontributesmoremeaning.Prose ismoreamenable toanalysis than poetry but stilloftenambiguous.Programs: Themeaningofacomputerprogramisunambiguousandliteral,andcanbeunderstoodentirely by analysis of thetokens and structure.1 This idiommeans that someonerealized somethingafter aperiodof confusion.

6 Chapter 1. The way of theprogramHerearesomesuggestionsforreadingprograms(andotherformallanguages). First,rememberthatformallanguagesaremuchmoredensethannaturallanguages,soittakeslongertoreadthem. Also,the structure is very important, so it is usually not a good idea to read from top to bottom, left toright. Instead, learn to parse the program in your head, identifying the tokens and interpreting thestructure. Finally, the details matter. Small errors in spelling and punctuation, which you can getaway withinnatural languages, can make abig difference inaformal language.1.5 Thefirst programTraditionally, the first program you write in a new language is called “Hello, World!” because all itdoes isdisplay thewords, “Hello, World!” InPython, itlooks like this:print 'Hello, World!'Thisisanexampleofaprintstatement 2 ,whichdoesn’tactuallyprintanythingonpaper. Itdisplaysavalue on thescreen. Inthiscase, theresult isthewordsHello, World!The quotation marks in the program mark the beginning and end of the text to be displayed; theydon’t appear inthe result.Some people judge the quality of a programming language by the simplicity of the “Hello, World!”program. By thisstandard, Python does about as well aspossible.1.6 DebuggingIt is a good idea to read this book in front of a computer so you can try out the examples as yougo. You can run most of the examples in interactive mode, but if you put the code into a script, it iseasier totryout variations.Wheneveryouareexperimentingwithanewfeature,youshouldtrytomakemistakes. Forexample,in the “Hello, world!” program, what happens if you leave out one of the quotation marks? What ifyou leave out both? What if you spellprintwrong?This kind of experiment helps you remember what you read; it also helps with debugging, becauseyou get to know what the error messages mean. It is better to make mistakes now and on purposethan later and accidentally.Programming, and especially debugging, sometimes brings out strong emotions. If you are strugglingwithadifficult bug, you might feel angry, despondent or embarrassed.There is evidence that people naturally respond to computers as if they were people 3 . When theyworkwell,wethinkofthemasteammates,andwhentheyareobstinateorrude,werespondtothemthesame way werespond torude, obstinate people.Preparing for these reactions might help you deal with them. One approach is to think of the computeras an employee with certain strengths, like speed and precision, and particular weaknesses,likelack of empathy and inabilitytograspthe bigpicture.2 InPython3.0,printisafunction,notastatement,sothesyntaxisprint(’Hello, World!’). Wewillgettofunctionssoon!3 SeeReevesandNass, TheMediaEquation: HowPeopleTreat Computers, Television, andNewMediaLike RealPeopleandPlaces.

1.7. Glossary 7Your job is to be a good manager: find ways to take advantage of the strengths and mitigate theweaknesses. And find ways to use your emotions to engage with the problem, without letting yourreactions interferewithyour ability towork effectively.Learning to debug can be frustrating, but it is a valuable skill that is useful for many activitiesbeyond programming. At the end of each chapter there is a debugging section, like this one, withmythoughts about debugging. I hope they help!1.7 Glossaryproblem solving: The process of formulating a problem, finding a solution, and expressing thesolution.high-level language: A programming language like Python that is designed to be easy for humanstoread and write.low-level language: Aprogramminglanguagethatisdesignedtobeeasyforacomputertoexecute;alsocalled “machine language” or “assembly language.”portability: A property of aprogram that can runon morethan one kindof computer.interpret: To execute aprogram inahigh-level language bytranslating itone lineat atime.compile: To translate a program written in a high-level language into a low-level language all atonce, inpreparation forlater execution.source code: A program inahigh-level language before being compiled.object code: The output of thecompiler after ittranslates theprogram.executable: Another name forobject code that isready tobeexecuted.prompt: Characters displayed by the interpreter to indicate that it is ready to take input from theuser.script: A program storedinafile(usually one that willbe interpreted).interactive mode: A way of using the Python interpreter by typing commands and expressions atthe prompt.script mode: A way ofusing thePython interpreter toread and execute statements inascript.program: A set ofinstructions that specifies acomputation.algorithm: A general process forsolving acategory of problems.bug: An errorinaprogram.debugging: The process of finding and removing any ofthe threekinds of programming errors.syntax: The structureof aprogram.syntax error: An error in a program that makes it impossible to parse (and therefore impossible tointerpret).exception: Anerror that isdetected whilethe program isrunning.

8 Chapter 1. The way of theprogramsemantics: The meaning of aprogram.semantic error: Anerrorinaprogramthatmakesitdosomethingotherthanwhattheprogrammerintended.natural language: Any one of thelanguages that people speak that evolved naturally.formal language: Any one of the languages that people have designed for specific purposes, suchas representing mathematical ideas or computer programs; all programming languages areformal languages.token: One of the basic elements of the syntactic structure of a program, analogous to a word in anatural language.parse: To examine aprogram and analyze thesyntactic structure.print statement: AninstructionthatcausesthePythoninterpretertodisplayavalueonthescreen.1.8 ExercisesExercise 1.2 Use a web browser to go to the Python website python.org. This page containsinformation about Python and links to Python-related pages, and it gives you the ability to searchthePython documentation.Forexample,ifyouenterprintinthesearchwindow,thefirstlinkthatappearsisthedocumentationof the print statement. At this point, not all of it will make sense to you, but it is good to knowwhere itis.Exercise 1.3 Start the Python interpreter and type help() to start the online help utility. Or youcan typehelp('print')toget informationabout theprintstatement.If this example doesn’t work, you may need to install additional Python documentation or set anenvironment variable; the details depend on your operating systemand version ofPython.Exercise 1.4 Start the Python interpreter and use it as a calculator. Python’s syntax for math operationsis almost the same as standard mathematical notation. For example, the symbols +, - and /denote addition, subtraction and division, asyou would expect. The symbol formultiplication is*.If you run a 10 kilometer race in 43 minutes 30 seconds, what is your average time per mile? Whatisyour average speed inmilesper hour? (Hint: thereare 1.61kilometers inamile).

Chapter 2Variables,expressions andstatements2.1 Valuesand typesA value is one of the basic things a program works with, like a letter or a number. The values wehave seen sofarare1,2,and'Hello, World!'.Thesevaluesbelongtodifferenttypes: 2isaninteger,and'Hello, World!'isastring,so-calledbecause it contains a “string” of letters. You (and the interpreter) can identify strings because theyareenclosed inquotation marks.The print statement alsoworks forintegers.>>> print 44Ifyou arenot surewhat type a value has, the interpreter can tell you.>>> type('Hello, World!')>>> type(17)Notsurprisingly,stringsbelongtothetypestrandintegersbelongtothetypeint. Lessobviously,numberswithadecimalpointbelongtoatypecalledfloat,becausethesenumbersarerepresentedinaformat called floating-point.>>> type(3.2)What about values like'17' and'3.2'? They look like numbers, but they are in quotation markslikestrings.>>> type('17')>>> type('3.2')

10 Chapter 2. Variables, expressions and statementsThey’re strings.Whenyoutypealargeinteger,youmightbetemptedtousecommasbetweengroupsofthreedigits,as in1,000,000. Thisis not alegal integer inPython, but itislegal:>>> print 1,000,0001 0 0Well, that’s not what we expected at all! Python interprets 1,000,000 as a comma-separated sequenceofintegers, which itprints withspaces between.Thisisthefirstexamplewehaveseenofasemanticerror: thecoderunswithoutproducinganerrormessage, but itdoesn’t do the“right” thing.2.2 VariablesOneofthemostpowerfulfeaturesofaprogramminglanguageistheabilitytomanipulatevariables.A variable isaname that referstoavalue.Anassignment statement creates new variables and gives them values:>>> message = 'And now for something completely different'>>> n = 17>>> pi = 3.1415926535897932Thisexamplemakesthreeassignments. Thefirstassignsastringtoanewvariablenamedmessage;thesecond gives the integer17ton;thethirdassigns the(approximate) value of π topi.A common way to represent variables on paper is to write the name with an arrow pointing to thevariable’s value. This kind of figure is called a state diagram because it shows what state each ofthe variables is in (think of it as the variable’s state of mind). This diagram shows the result of theprevious example:messagenpi’And now for something completely different’173.1415926535897931To display thevalue of avariable, you can useaprint statement:>>> print n17>>> print pi3.14159265359The type of avariable isthetype of thevalue itrefersto.>>> type(message)>>> type(n)>>> type(pi)

2.3. Variable names and keywords 11Exercise 2.1 Ifyou type an integer withaleading zero, you might get aconfusing error:>>> zipcode = 02492ˆSyntaxError: invalid tokenOther numbers seem towork, but the resultsarebizarre:>>> zipcode = 02132>>> print zipcode1114Can you figure out what isgoing on? Hint: printthe values01,010,0100and01000.2.3 Variablenames and keywordsProgrammers generally choose names for their variables that are meaningful—they document whatthevariable isused for.Variable names can be arbitrarily long. They can contain both letters and numbers, but they have tobegin with a letter. It is legal to use uppercase letters, but it is a good idea to begin variable nameswithalowercase letter(you’ll seewhy later).The underscore character (_) can appear in a name. It is often used in names with multiple words,such asmy_nameorairspeed_of_unladen_swallow.Ifyou give avariable anillegal name, you get asyntax error:>>> 76trombones = 'big parade'SyntaxError: invalid syntax>>> more@ = 1000000SyntaxError: invalid syntax>>> class = 'Advanced Theoretical Zymurgy'SyntaxError: invalid syntax76trombones is illegal because it does not begin with a letter. more@ is illegal because it containsan illegal character,@. But what’s wrong withclass?ItturnsoutthatclassisoneofPython’skeywords. Theinterpreteruseskeywordstorecognizethestructureof theprogram, and they cannot be used as variable names.Python has 31 keywords 1 :and del from not whileas elif global or withassert else if pass yieldbreak except import printclass exec in raisecontinue finally is returndef for lambda tryYoumightwanttokeepthislisthandy. Iftheinterpretercomplainsaboutoneofyourvariablenamesand you don’t know why, seeifitis onthislist.1 InPython3.0,execis nolongerakeyword, butnonlocalis.

12 Chapter 2. Variables, expressions and statements2.4 StatementsA statement is a unit of code that the Python interpreter can execute. We have seen two kinds ofstatements: print and assignment.When you type a statement in interactive mode, the interpreter executes it and displays the result, ifthere isone.A script usually contains a sequence of statements. If there is more than one statement, the resultsappear one at atimeas thestatements execute.For example, thescriptprint 1x = 2print xproduces theoutput12The assignment statement produces nooutput.2.5 Operatorsand operandsOperators are special symbols that represent computations like addition and multiplication. Thevalues the operator isapplied toare called operands.The operators +,-,*,/and ** perform addition, subtraction, multiplication, division and exponentiation,as inthefollowing examples:20+32 hour-1 hour*60+minute minute/60 5**2 (5+9)*(15-7)In some other languages, ˆ is used for exponentiation, but in Python it is a bitwise operator calledXOR. I won’t cover bitwise operators in this book, but you can read about them at wiki.python.org/moin/BitwiseOperators.The division operator might not dowhat you expect:>>> minute = 59>>> minute/600The value of minute is 59, and in conventional arithmetic 59 divided by 60 is 0.98333, not 0. Thereason forthe discrepancy isthat Python isperforming floor division 2 .When both of the operands are integers, the result is also an integer; floor division chops off thefractionpart, sointhisexample itrounds down tozero.Ifeitheroftheoperandsisafloating-pointnumber,Pythonperformsfloating-pointdivision,andtheresultisafloat:>>> minute/60.00.983333333333333282 InPython3.0, theresult ofthis divisionis afloat. Thenew operator//performsintegerdivision.

2.6. Expressions 132.6 ExpressionsAnexpressionisacombinationofvalues,variables,andoperators. Avalueallbyitselfisconsideredan expression, and so is a variable, so the following are all legal expressions (assuming that thevariablexhas been assigned avalue):17xx + 17Ifyou type an expression ininteractive mode, the interpreter evaluates itand displays the result:>>> 1 + 12Butinascript,anexpressionallbyitselfdoesn’tdoanything! Thisisacommonsourceofconfusionforbeginners.Exercise 2.2 Type thefollowing statements inthePython interpreter toseewhat they do:5x = 5x + 1Now put the same statements into a script and run it. What is the output? Modify the script bytransformingeach expression into aprint statement and then run itagain.2.7 OrderofoperationsWhenmorethanoneoperatorappearsinanexpression,theorderofevaluationdependsontherulesofprecedence. Formathematicaloperators,Pythonfollowsmathematicalconvention. TheacronymPEMDAS isauseful way toremember therules:• Parentheseshavethehighestprecedenceandcanbeusedtoforceanexpressiontoevaluateinthe order you want. Since expressions in parentheses are evaluated first, 2 * (3-1) is 4, and(1+1)**(5-2) is 8. You can also use parentheses to make an expression easier to read, as in(minute * 100) / 60,even ifitdoesn’t change the result.• Exponentiation has the next highest precedence, so 2**1+1 is 3, not 4, and 3*1**3 is 3, not27.• Multiplication and Division have the same precedence, which is higher than Addition andSubtraction, which also have the same precedence. So 2*3-1 is 5, not 4, and 6+4/2 is 8, not5.• Operators with the same precedence are evaluated from left to right (except exponentiation).Sointheexpressiondegrees / 2 * pi,thedivisionhappensfirstandtheresultismultipliedbypi. To divide by2π, you can use parentheses or writedegrees / 2 / pi.

14 Chapter 2. Variables, expressions and statements2.8 StringoperationsIn general, you cannot perform mathematical operations on strings, even if the strings look likenumbers, sothefollowing areillegal:'2'-'1' 'eggs'/'easy' 'third'*'a charm'The+operator works with strings, but it might not do what you expect: it performs concatenation,which means joining thestringsby linking them end-to-end. For example:first = 'throat'second = 'warbler'print first + secondThe output of thisprogram isthroatwarbler.The * operator also works on strings; it performs repetition. For example, 'Spam'*3 is'SpamSpamSpam'. Ifone of theoperands isastring,the other has tobean integer.This use of + and * makes sense by analogy with addition and multiplication. Just as 4*3 is equivalentto 4+4+4, we expect 'Spam'*3 to be the same as 'Spam'+'Spam'+'Spam', and it is. Onthe other hand, there is a significant way in which string concatenation and repetition are differentfrom integer addition and multiplication. Can you think of a property that addition has that stringconcatenation does not?2.9 CommentsAsprogramsgetbiggerandmorecomplicated,theygetmoredifficulttoread. Formallanguagesaredense, and itisoften difficult tolook at apiece of code and figure out what itisdoing, orwhy.For this reason, it is a good idea to add notes to your programs to explain in natural language whattheprogram isdoing. These notes arecalled comments, and they startwiththe#symbol:# compute the percentage of the hour that has elapsedpercentage = (minute * 100) / 60Inthiscase,thecommentappearsonalinebyitself. Youcanalsoputcommentsattheendofaline:percentage = (minute * 100) / 60# percentage of an hourEverything from the#totheend of the lineisignored—it has no effect on theprogram.Comments are most useful when they document non-obvious features of the code. It is reasonabletoassume that thereader can figure out what thecode does; itismuch moreuseful toexplain why.This comment isredundant withthe code and useless:v = 5# assign 5 to vThis comment contains useful information that isnot inthe code:v = 5# velocity in meters/second.Goodvariablenamescanreducetheneedforcomments,butlongnamescanmakecomplexexpressionshardtoread, sothereisatradeoff.

2.10. Debugging 152.10 DebuggingAtthispointthesyntaxerroryouaremostlikelytomakeisanillegalvariablename,likeclassandyield,which are keywords, orodd˜jobandUS$,which contain illegal characters.Ifyou put aspace inavariable name, Python thinks itistwooperands without anoperator:>>> bad name = 5SyntaxError: invalid syntaxFor syntax errors, the error messages don’t help much. The most common messages areSyntaxError: invalid syntaxandSyntaxError: invalid token,neitherofwhichisveryinformative.The runtime error you are most likely to make is a “use before def;” that is, trying to use a variablebefore you have assigned avalue. This can happen ifyou spell avariable name wrong:>>> principal = 327.68>>> interest = principle * rateNameError: name 'principle' is not definedVariables names arecase sensitive, soLaTeXisnot thesame aslatex.At this point the most likely cause of a semantic error is the order of operations. For example, toevaluate2π 1 ,you might betempted towrite>>> 1.0 / 2.0 * piBut the division happens first, so you would get π/2, which is not the same thing! There is no wayforPythontoknowwhatyoumeanttowrite,sointhiscaseyoudon’tgetanerrormessage;youjustget the wrong answer.2.11 Glossaryvalue: One ofthe basicunits of data, likeanumber or string,that a program manipulates.type: A category of values. The types we have seen so far are integers (type int), floating-pointnumbers (typefloat),and strings(typestr).integer: A type that represents whole numbers.floating-point: A type that represents numbers withfractional parts.string: A type that represents sequences of characters.variable: A name that referstoavalue.statement: A section of code that represents a command or action. So far, the statements we haveseen are assignments and print statements.assignment: A statement that assigns avalue toavariable.statediagram: A graphical representation of aset ofvariables and thevalues they referto.keyword: A reserved word that is used by the compiler to parse a program; you cannot use keywordslikeif,def,andwhileas variable names.

16 Chapter 2. Variables, expressions and statementsoperator: A special symbol that represents a simple computation like addition, multiplication, orstringconcatenation.operand: One of the values on which anoperator operates.floor division: The operation that divides twonumbers and chops off thefractionpart.expression: Acombinationofvariables,operators,andvaluesthatrepresentsasingleresultvalue.evaluate: To simplifyan expression by performing theoperations inorder toyieldasinglevalue.rules of precedence: The set of rules governing the order in which expressions involving multipleoperators and operands areevaluated.concatenate: To jointwooperands end-to-end.comment: Information in a program that is meant for other programmers (or anyone reading thesource code) and has no effect on theexecution of theprogram.2.12 ExercisesExercise 2.3 Assumethat weexecute the following assignment statements:width = 17height = 12.0delimiter = '.'Foreachofthefollowingexpressions,writethevalueoftheexpressionandthetype(ofthevalueoftheexpression).1. width/22. width/2.03. height/34. 1 + 2 * 55. delimiter * 5UsethePython interpreter tocheck your answers.Exercise 2.4 Practice using thePython interpreter as acalculator:1. The volume of a sphere with radius r is 4 3 πr3 . What is the volume of a sphere with radius 5?Hint: 392.6 iswrong!2. Suppose the cover price of a book is $24.95, but bookstores get a 40% discount. Shippingcosts $3 for the first copy and 75 cents for each additional copy. What is the total wholesalecost for 60 copies?3. If I leave my house at 6:52 am and run 1 mile at an easy pace (8:15 per mile), then 3 miles attempo (7:12per mile) and 1mileat easy pace again, what timedoIget home forbreakfast?

Chapter 3Functions3.1 FunctioncallsIn the context of programming, a function is a named sequence of statements that performs a computation.When you define a function, you specify the name and the sequence of statements. Later,you can “call” the function by name. We have already seen one example of afunction call:>>> type(32)The name of the function is type. The expression in parentheses is called the argument of thefunction. The result, forthisfunction, isthe type ofthe argument.It is common to say that a function “takes” an argument and “returns” a result. The result is calledthereturn value.3.2 Typeconversion functionsPython provides built-in functions that convert values from one type to another. The int functiontakes any value and converts ittoan integer, ifitcan, or complains otherwise:>>> int('32')32>>> int('Hello')ValueError: invalid literal for int(): Helloint can convert floating-point values to integers, but it doesn’t round off; it chops off the fractionpart:>>> int(3.99999)3>>> int(-2.3)-2floatconverts integers and stringstofloating-point numbers:

18 Chapter 3. Functions>>> float(32)32.0>>> float('3.14159')3.14159Finally,strconverts itsargument toastring:>>> str(32)'32'>>> str(3.14159)'3.14159'3.3 MathfunctionsPython has a math module that provides most of the familiar mathematical functions. A module isafile that contains acollection of relatedfunctions.Before wecan use themodule, we have toimport it:>>> import mathThis statement creates a module object named math. If you print the module object, you get someinformation about it:>>> print mathThe module object contains the functions and variables defined in the module. To access one of thefunctions, you have to specify the name of the module and the name of the function, separated by adot (alsoknown as aperiod). This format iscalled dot notation.>>> ratio = signal_power / noise_power>>> decibels = 10 * math.log10(ratio)>>> radians = 0.7>>> height = math.sin(radians)The first example uses log10 to compute a signal-to-noise ratio in decibels (assuming thatsignal_power and noise_power are defined). The math module also provides log, which computeslogarithms basee.The second example finds the sine of radians. The name of the variable is a hint that sin and theothertrigonometricfunctions(cos,tan,etc.) takeargumentsinradians. Toconvertfromdegreestoradians, divide by360 and multiplyby 2π:>>> degrees = 45>>> radians = degrees / 360.0 * 2 * math.pi>>> math.sin(radians)0.707106781187Theexpressionmath.pigetsthevariablepifromthemathmodule. Thevalueofthisvariableisanapproximation ofπ, accurate toabout 15 digits.Ifyouknowyourtrigonometry,youcancheckthepreviousresultbycomparingittothesquarerootof twodivided by two:

3.4. Composition 19>>> math.sqrt(2) / 2.00.7071067811873.4 CompositionSo far, we have looked at the elements of a program—variables, expressions, and statements—inisolation, without talking about how tocombine them.One of the most useful features of programming languages is their ability to take small buildingblocks and compose them. For example, the argument of a function can be any kind of expression,including arithmeticoperators:x = math.sin(degrees / 360.0 * 2 * math.pi)And even function calls:x = math.exp(math.log(x+1))Almost anywhere you can put a value, you can put an arbitrary expression, with one exception: theleftsideofanassignmentstatementhastobeavariablename. Anyotherexpressionontheleftsideisasyntax error 1 .>>> minutes = hours * 60 # right>>> hours * 60 = minutes # wrong!SyntaxError: can't assign to operator3.5 Adding newfunctionsSo far, we have only been using the functions that come with Python, but it is also possible to addnew functions. A function definition specifies the name of a new function and the sequence ofstatements that execute when thefunction iscalled.Here isanexample:def print_lyrics():print "I'm a lumberjack, and I'm okay."print "I sleep all night and I work all day."def is a keyword that indicates that this is a function definition. The name of the function isprint_lyrics. The rules for function names are the same as for variable names: letters, numbersandsomepunctuationmarksarelegal,butthefirstcharactercan’tbeanumber.Youcan’tuseakeyword as the name of a function, and you should avoid having a variable and a function with thesame name.The empty parentheses afterthe name indicate that thisfunction doesn’t take any arguments.The first line of the function definition is called the header; the rest is called the body. The headerhas to end with a colon and the body has to be indented. By convention, the indentation is alwaysfour spaces (seeSection 3.13). The body can contain any number ofstatements.1 We will see exceptions tothis rule later.

20 Chapter 3. FunctionsThestringsintheprintstatementsareenclosedindoublequotes. Singlequotesanddoublequotesdothe same thing; most people use single quotes except in cases like this where a single quote (whichisalsoan apostrophe) appears inthestring.If you type a function definition in interactive mode, the interpreter prints ellipses (...) to let youknow that thedefinition isn’tcomplete:>>> def print_lyrics():... print "I'm a lumberjack, and I'm okay."... print "I sleep all night and I work all day."...To end the function, you have toenter an empty line(thisisnot necessary inascript).Defining afunction creates avariable withthesame name.>>> print print_lyrics>>> print type(print_lyrics)The value ofprint_lyricsisafunction object, which has type'function'.The syntax forcalling the new function isthe sameas forbuilt-infunctions:>>> print_lyrics()I'm a lumberjack, and I'm okay.I sleep all night and I work all day.Onceyouhavedefinedafunction,youcanuseitinsideanotherfunction. Forexample,torepeattheprevious refrain, wecould writeafunction calledrepeat_lyrics:def repeat_lyrics():print_lyrics()print_lyrics()And then callrepeat_lyrics:>>> repeat_lyrics()I'm a lumberjack, and I'm okay.I sleep all night and I work all day.I'm a lumberjack, and I'm okay.I sleep all night and I work all day.But that’s not reallyhow thesong goes.3.6 Definitions and usesPulling together thecode fragments fromthe previous section, the whole program looks likethis:def print_lyrics():print "I'm a lumberjack, and I'm okay."print "I sleep all night and I work all day."

3.7. Flow of execution 21def repeat_lyrics():print_lyrics()print_lyrics()repeat_lyrics()This program contains two function definitions: print_lyrics and repeat_lyrics. Functiondefinitions get executed just like other statements, but the effect is to create function objects. Thestatements inside the function do not get executed until the function is called, and the functiondefinition generates no output.As you might expect, you have to create a function before you can execute it. In other words, thefunction definition has tobe executed beforethe firsttimeitiscalled.Exercise 3.1 Move the last line of this program to the top, so the function call appears before thedefinitions. Run theprogram and see what error message you get.Exercise 3.2 Move the function call back to the bottom and move the definition of print_lyricsafter thedefinition ofrepeat_lyrics. What happens when you runthisprogram?3.7 FlowofexecutionInorder to ensure that a function is defined before itsfirst use, you have to know the order in whichstatements are executed, which iscalled the flow ofexecution.Executionalwaysbeginsatthefirststatementoftheprogram. Statementsareexecutedoneatatime,inorder from toptobottom.Functiondefinitionsdonotaltertheflowofexecutionoftheprogram,butrememberthatstatementsinsidethe function arenot executed until the function iscalled.A function call is like a detour in the flow of execution. Instead of going to the next statement, theflow jumps to the body of the function, executes all the statements there, and then comes back topick up where itleftoff.That sounds simple enough, until you remember that one function can call another. While in themiddle of one function, the program might have to execute the statements in another function. Butwhileexecuting that new function, the program might have toexecute yet another function!Fortunately, Python is good at keeping track of where it is, so each time a function completes, theprogram picks up where it left off in the function that called it. When it gets to the end of theprogram, itterminates.What’sthemoralofthissordidtale? Whenyoureadaprogram,youdon’talwayswanttoreadfromtoptobottom. Sometimes it makes moresenseif you follow theflow of execution.3.8 Parametersand argumentsSome of the built-in functions we have seen require arguments. For example, when you callmath.sin you pass a number as an argument. Some functions take more than one argument:math.powtakes two,the base and theexponent.

22 Chapter 3. FunctionsInside the function, the arguments are assigned to variables called parameters. Here is an exampleof auser-defined function that takes an argument:def print_twice(bruce):print bruceprint bruceThis function assigns the argument to a parameter named bruce. When the function is called, itprintsthe value ofthe parameter (whatever itis)twice.This function works withany value that can beprinted.>>> print_twice('Spam')SpamSpam>>> print_twice(17)1717>>> print_twice(math.pi)3.141592653593.14159265359The same rules of composition that apply to built-in functions also apply to user-defined functions,sowecan use any kind of expression asan argument forprint_twice:>>> print_twice('Spam '*4)Spam Spam Spam SpamSpam Spam Spam Spam>>> print_twice(math.cos(math.pi))-1.0-1.0The argument is evaluated before the function is called, so in the examples the expressions'Spam '*4andmath.cos(math.pi)areonly evaluated once.You can alsouse avariable as an argument:>>> michael = 'Eric, the half a bee.'>>> print_twice(michael)Eric, the half a bee.Eric, the half a bee.Thenameofthevariablewepassasanargument (michael)hasnothing todowiththenameoftheparameter (bruce). It doesn’t matter what the value was called back home (in the caller); here inprint_twice,we call everybodybruce.3.9 Variablesand parametersarelocalWhen you create a variable inside a function, it is local, which means that it only exists inside thefunction. For example:def cat_twice(part1, part2):cat = part1 + part2print_twice(cat)

3.10. Stack diagrams 23Thisfunctiontakestwoarguments,concatenatesthem,andprintstheresulttwice. Hereisanexamplethatusesit:>>> line1 = 'Bing tiddle '>>> line2 = 'tiddle bang.'>>> cat_twice(line1, line2)Bing tiddle tiddle bang.Bing tiddle tiddle bang.Whencat_twiceterminates,thevariablecatisdestroyed. Ifwetrytoprintit,wegetanexception:>>> print catNameError: name 'cat' is not definedParameters are alsolocal. For example, outsideprint_twice,thereisno such thingasbruce.3.10 StackdiagramsTokeeptrackofwhichvariablescanbeusedwhere,itissometimesusefultodrawastackdiagram.Likestatediagrams,stackdiagramsshowthevalueofeachvariable,buttheyalsoshowthefunctioneach variable belongs to.Eachfunctionisrepresentedbyaframe. Aframeisaboxwiththenameofafunctionbesideitandthe parameters and variables of the function inside it. The stack diagram for the previous examplelooks like this:__main__line1line2’Bing tiddle ’’tiddle bang.’cat_twicepart1part2cat’Bing tiddle ’’tiddle bang.’’Bing tiddle tiddle bang.’print_twicebruce’Bing tiddle tiddle bang.’The frames are arranged in a stack that indicates which function called which, and so on. In thisexample,print_twicewas called bycat_twice,andcat_twicewas called by__main__,whichis a special name for the topmost frame. When you create a variable outside of any function, itbelongs to__main__.Each parameter refers to the same value as its corresponding argument. So, part1 has the samevalue asline1,part2has thesamevalue asline2,andbrucehas the samevalue ascat.Ifanerroroccursduringafunctioncall,Pythonprintsthenameofthefunction,andthenameofthefunction that called it,and thename of the function that called that, all theway back to__main__.For example, ifyou trytoaccesscatfrom withinprint_twice,you get aNameError:

24 Chapter 3. FunctionsTraceback (innermost last):File "test.py", line 13, in __main__cat_twice(line1, line2)File "test.py", line 5, in cat_twiceprint_twice(cat)File "test.py", line 9, in print_twiceprint catNameError: name 'cat' is not definedThis list of functions is called a traceback. It tells you what program file the error occurred in, andwhat line, and what functions were executing at the time. It also shows the line of code that causedtheerror.Theorderofthefunctionsinthetracebackisthesameastheorderoftheframesinthestackdiagram.The function that iscurrently running isat thebottom.3.11 Fruitfulfunctions and void functionsSome of the functions we are using, such as the math functions, yield results; for lack of a bettername, I call them fruitful functions. Other functions, like print_twice, perform an action butdon’t returnavalue. They arecalled void functions.When you call a fruitful function, you almost always want to do something with the result; forexample, you might assignittoavariable or useitas part of anexpression:x = math.cos(radians)golden = (math.sqrt(5) + 1) / 2When you call a function ininteractive mode, Python displays theresult:>>> math.sqrt(5)2.2360679774997898But inascript, ifyou call afruitfulfunction all byitself,thereturnvalue islostforever!math.sqrt(5)Thisscriptcomputesthesquarerootof5,butsinceitdoesn’tstoreordisplaytheresult,itisnotveryuseful.Voidfunctionsmightdisplaysomethingonthescreenorhavesomeothereffect,buttheydon’thaveareturnvalue. Ifyou trytoassigntheresult toavariable, you get aspecial value calledNone.>>> result = print_twice('Bing')BingBing>>> print resultNoneThe valueNoneisnot the sameas thestring'None'. Itisaspecial value that has itsown type:>>> print type(None)The functions we have written so far are all void. We will start writing fruitful functions in a fewchapters.

3.12. Why functions? 253.12 Whyfunctions?It may not be clear why it is worth the trouble to divide a program into functions. There are severalreasons:• Creatinganewfunctiongivesyouanopportunitytonameagroupofstatements,whichmakesyour program easier toread and debug.• Functions can make a program smaller by eliminating repetitive code. Later, if you make achange, you only have tomake itinone place.• Dividing a long program into functions allows you to debug the parts one at a time and thenassemble them intoaworking whole.• Well-designed functions are often useful for many programs. Once you write and debug one,you can reuseit.3.13 DebuggingIfyouareusingatexteditortowriteyourscripts,youmightrunintoproblemswithspacesandtabs.The best way to avoid these problems is to use spaces exclusively (no tabs). Most text editors thatknow about Python do thisby default, but some don’t.Tabs and spaces are usually invisible, which makes them hard to debug, so try to find an editor thatmanages indentation foryou.Also, don’t forget to save your program before you run it. Some development environments do thisautomatically, but some don’t. In that case the program you are looking at in the text editor is notthesame as theprogram you are running.Debugging can take along timeifyou keep running the same, incorrect, program over and over!Make sure that the code you are looking at is the code you are running. If you’re not sure, putsomething like print 'hello' at the beginning of the program and run it again. If you don’t seehello,you’re not running theright program!3.14 Glossaryfunction: A named sequence of statements that performs someuseful operation. Functions may ormay not take arguments and may or may not produce a result.function definition: A statement that creates a new function, specifying its name, parameters, andthe statements itexecutes.function object: A value created by a function definition. The name of the function is a variablethat referstoafunction object.header: The firstlineof afunction definition.body: The sequence of statements insideafunction definition.parameter: A name usedinside afunction torefertothe value passedas an argument.

26 Chapter 3. Functionsfunction call: Astatementthatexecutesafunction. Itconsistsofthefunctionnamefollowedbyanargument list.argument: Avalueprovidedtoafunctionwhenthefunctioniscalled. Thisvalueisassignedtothecorresponding parameter inthe function.local variable: A variable defined inside a function. A local variable can only be used inside itsfunction.return value: The result of a function. If a function call is used as an expression, the return valueisthe value ofthe expression.fruitfulfunction: A function that returns avalue.void function: A function that doesn’t returnavalue.module: A filethat contains acollection of related functions and other definitions.import statement: A statement that reads amodule fileand creates a module object.module object: A value created by an import statement that provides access to the values definedinamodule.dot notation: The syntax for calling a function in another module by specifying the module namefollowed byadot (period) and the function name.composition: Using an expression as part of a larger expression, or a statement as part of a largerstatement.flow of execution: The order inwhich statements are executed during aprogram run.stackdiagram: A graphical representation of a stack of functions, their variables, and the valuesthey referto.frame: A box in a stack diagram that represents a function call. It contains the local variables andparameters of the function.traceback: Alistof thefunctions that are executing, printedwhen anexception occurs.3.15 ExercisesExercise3.3 Pythonprovidesabuilt-infunctioncalledlenthatreturnsthelengthofastring,sothevalue oflen('allen')is5.Write a function named right_justify that takes a string named s as a parameter and prints thestringwithenough leading spaces sothat the lastletterof the stringisincolumn 70of the display.>>> right_justify('allen')allenExercise 3.4 A function object is a value you can assign to a variable or pass as an argument. Forexample,do_twiceisafunction that takes a function object as anargument and calls ittwice:def do_twice(f):f()f()

3.15. Exercises 27Here’s an example that usesdo_twicetocall a function namedprint_spamtwice.def print_spam():print 'spam'do_twice(print_spam)1. Type this example intoascriptand testit.2. Modify do_twice so that it takes two arguments, a function object and a value, and calls thefunction twice, passingthe value as an argument.3. Write a more general version of print_spam, called print_twice, that takes a string as aparameter and printsittwice.4. Use the modified version of do_twice to call print_twice twice, passing 'spam' as anargument.5. Define a new function called do_four that takes a function object and a value and calls thefunctionfourtimes,passingthevalueasaparameter. Thereshouldbeonlytwostatementsinthe body of this function, not four.You can see mysolutionatthinkpython.com/code/do_four.py.Exercise 3.5 This exercise 2 can be done using only the statements and other features we havelearned sofar.1. Writeafunction that draws agridlikethe following:+ - - - - + - - - - +| | || | || | || | |+ - - - - + - - - - +| | || | || | || | |+ - - - - + - - - - +Hint: toprint more than one value on aline, you can printacomma-separated sequence:print '+', '-'If the sequence ends with a comma, Python leaves the line unfinished, so the value printednext appears on thesame line.print '+',print '-'The output ofthese statements is'+ -'.Aprintstatement all by itselfends the current lineand goes tothe next line.2 Based onanexercise inOualline, Practical CProgramming, Third Edition, O’Reilly (1997)

28 Chapter 3. Functions2. Usethe previous function todraw a similargridwithfour rows and four columns.You can see mysolutionatthinkpython.com/code/grid.py.

Chapter 4Case study: interfacedesign4.1 TurtleWorldTo accompany this book, I have written a suite of modules called Swampy. One of these modulesis TurtleWorld, which provides a set of functions for drawing lines by steering turtles around thescreen.YoucandownloadSwampyfromthinkpython.com/swampy;followtheinstructionstheretoinstallSwampy on your system.Move into the directory that contains TurtleWorld.py, create a file named polygon.py and typeinthefollowing code:from TurtleWorld import *world = TurtleWorld()bob = Turtle()print bobwait_for_user()The first line is a variation of the import statement we saw before; instead of creating a moduleobject, it imports the functions from the module directly, so you can access them without using dotnotation.The next lines create a TurtleWorld assigned to world and a Turtle assigned to bob. Printing bobyields something like:This means that bob refers to an instance of a Turtle as defined in module TurtleWorld. In thiscontext, “instance” means amember of aset; thisTurtleisone of the setof possibleTurtles.wait_for_usertellsTurtleWorldtowaitfortheusertodosomething, although inthiscasethere’snot much forthe user todoexcept closethewindow.TurtleWorldprovidesseveralturtle-steeringfunctions: fdandbkforforwardandbackward,andltand rt for left and right turns. Also, each Turtle is holding a pen, which is either down or up; if the

30 Chapter 4. Case study: interface designpenisdown,theTurtleleavesatrailwhenitmoves. Thefunctionspuandpdstandfor“penup”and“pen down.”To draw a right angle, add these lines to the program (after creating bob and before callingwait_for_user):fd(bob, 100)lt(bob)fd(bob, 100)The firstlinetellsbobtotake100 stepsforward. The second line tellshim toturnleft.Whenyourunthisprogram,youshouldseebobmoveeastandthennorth,leavingtwolinesegmentsbehind.Now modify theprogram todraw asquare. Don’t goon until you’ve got itworking!4.2 SimplerepetitionChances are you wrote something like this (leaving out the code that creates TurtleWorld and waitsforthe user):fd(bob, 100)lt(bob)fd(bob, 100)lt(bob)fd(bob, 100)lt(bob)fd(bob, 100)We can do the same thing more concisely with a for statement. Add this example to polygon.pyand runit again:for i in range(4):print 'Hello!'You should seesomething likethis:Hello!Hello!Hello!Hello!This is the simplest use of the for statement; we will see more later. But that should be enough tolet you rewriteyour square-drawing program. Don’t goon until you do.Here isaforstatement that draws asquare:for i in range(4):fd(bob, 100)lt(bob)

4.3. Exercises 31The syntax of a for statement is similar to a function definition. It has a header that ends with acolon and anindented body. The body can contain any number of statements.A for statement is sometimes called a loop because the flow of execution runs through the bodyand then loops back tothe top. Inthiscase, itruns thebody four times.This version is actually a little different from the previous square-drawing code because it makesanother turn after drawing the last side of the square. The extra turn takes a little more time, but itsimplifies the code if we do the same thing every time through the loop. This version also has theeffect of leaving theturtleback inthe startingposition, facing inthe startingdirection.4.3 ExercisesThe following is a series of exercises using TurtleWorld. They are meant to be fun, but they have apoint, too. Whileyou are working onthem, thinkabout what the point is.The following sections have solutions to the exercises, so don’t look until you have finished (or atleast tried).1. Write a function called square that takes a parameter named t, which is a turtle. It shoulduse theturtletodraw asquare.Write a function call that passes bob as an argument to square, and then run the programagain.2. Add another parameter, named length, to square. Modify the body so length of the sides islength, and then modify the function call to provide a second argument. Run the programagain. Test your program witharange of values forlength.3. The functions lt and rt make 90-degree turns by default, but you can provide a secondargument that specifies the number of degrees. For example, lt(bob, 45) turns bob 45degrees tothe left.Make a copy of square and change the name to polygon. Add another parameter named nand modify the body so it draws an n-sided regular polygon. Hint: The exterior angles of ann-sided regular polygon are 360.0/n degrees.4. Write a function called circle that takes a turtle, t, and radius, r, as parameters and thatdraws an approximate circle by invoking polygon with an appropriate length and number ofsides. Test your function witharange of values ofr.Hint: figure out the circumference of the circle and make sure that length * n =circumference.Anotherhint: ifbobistooslowforyou,youcanspeedhimupbychangingbob.delay,whichisthe timebetween moves, inseconds. bob.delay = 0.01ought toget him moving.5. Make a more general version ofcirclecalledarcthat takes an additional parameterangle,which determines what fraction of a circle to draw. angle is in units of degrees, so whenangle=360,arcshould draw acomplete circle.

32 Chapter 4. Case study: interface design4.4 EncapsulationThe first exercise asks you to put your square-drawing code into a function definition and then callthefunction, passing theturtleas aparameter. Here isasolution:def square(t):for i in range(4):fd(t, 100)lt(t)square(bob)The innermost statements, fd and lt are indented twice to show that they are inside the for loop,whichisinsidethefunctiondefinition. Thenextline,square(bob),isflushwiththeleftmargin,sothat isthe end of both theforloop and the function definition.Insidethefunction,treferstothesameturtlebobrefersto,solt(t)hasthesameeffectaslt(bob).So why not call the parameter bob? The idea is that t can be any turtle, not just bob, so you couldcreate asecond turtleand pass itas anargument tosquare:ray = Turtle()square(ray)Wrapping a piece of code up in a function is called encapsulation. One of the benefits of encapsulationis that it attaches a name to the code, which serves as a kind of documentation. Anotheradvantage is that if you re-use the code, it is more concise to call a function twice than to copy andpaste thebody!4.5 GeneralizationThe next stepistoadd alengthparameter tosquare. Here isasolution:def square(t, length):for i in range(4):fd(t, length)lt(t)square(bob, 100)Adding a parameter to a function is called generalization because it makes the function more general:inthe previous version, thesquare isalways thesame size;inthis version itcan be any size.The next step is also a generalization. Instead of drawing squares,polygondraws regular polygonswithany number of sides. Hereisasolution:def polygon(t, n, length):angle = 360.0 / nfor i in range(n):fd(t, length)lt(t, angle)polygon(bob, 7, 70)

4.6. Interface design 33This draws a 7-sided polygon with side length 70. If you have more than a few numeric arguments,itiseasytoforgetwhattheyare,orwhatordertheyshouldbein. Itislegal,andsometimeshelpful,toinclude thenames of theparameters intheargument list:polygon(bob, n=7, length=70)Thesearecalledkeywordargumentsbecausetheyincludetheparameternamesas“keywords”(nottobe confused withPython keywords likewhileanddef).This syntax makes the program more readable. It is also a reminder about how arguments andparameters work: when you call afunction, the arguments are assigned totheparameters.4.6 InterfacedesignThe next step is to write circle, which takes a radius, r, as a parameter. Here is a simple solutionthat usespolygontodraw a50-sided polygon:def circle(t, r):circumference = 2 * math.pi * rn = 50length = circumference / npolygon(t, n, length)The first line computes the circumference of a circle with radius r using the formula 2πr. Sincewe use math.pi, we have to import math. By convention, import statements are usually at thebeginning of thescript.n is the number of line segments in our approximation of a circle, so length is the length of eachsegment. Thus,polygondraws a50-sides polygon that approximates acircle withradiusr.One limitation of this solution is that n is a constant, which means that for very big circles, theline segments are too long, and for small circles, we waste time drawing very small segments. Onesolution would be to generalize the function by taking n as a parameter. This would give the user(whoever callscircle)morecontrol, but theinterface would be lessclean.Theinterfaceofafunctionisasummaryofhowitisused: whataretheparameters? Whatdoesthefunctiondo? Andwhatisthereturnvalue? Aninterfaceis“clean”ifitis“assimpleaspossible,butnot simpler. (Einstein)”In this example, r belongs in the interface because it specifies the circle to be drawn. n is lessappropriate because itpertains tothe details of how thecircleshould be rendered.Rather than clutter up the interface, it is better to choose an appropriate value of n depending oncircumference:def circle(t, r):circumference = 2 * math.pi * rn = int(circumference / 3) + 1length = circumference / npolygon(t, n, length)Now the number of segments is (approximately) circumference/3, so the length of each segmentis(approximately)3,whichissmallenoughthatthecircleslookgood,butbigenoughtobeefficient,and appropriate forany sizecircle.

34 Chapter 4. Case study: interface design4.7 RefactoringWhen I wrote circle, I was able to re-use polygon because a many-sided polygon is a good approximationof a circle. But arc is not as cooperative; we can’t use polygon or circle to draw anarc.One alternative is to start with a copy of polygon and transform it into arc. The result might looklikethis:def arc(t, r, angle):arc_length = 2 * math.pi * r * angle / 360n = int(arc_length / 3) + 1step_length = arc_length / nstep_angle = float(angle) / nfor i in range(n):fd(t, step_length)lt(t, step_angle)Thesecondhalfofthisfunctionlookslikepolygon,butwecan’tre-usepolygonwithoutchangingthe interface. We could generalize polygon to take an angle as a third argument, but then polygonwould no longer bean appropriate name! Instead, let’scall themore general functionpolyline:def polyline(t, n, length, angle):for i in range(n):fd(t, length)lt(t, angle)Now wecan rewritepolygonandarctousepolyline:def polygon(t, n, length):angle = 360.0 / npolyline(t, n, length, angle)def arc(t, r, angle):arc_length = 2 * math.pi * r * angle / 360n = int(arc_length / 3) + 1step_length = arc_length / nstep_angle = float(angle) / npolyline(t, n, step_length, step_angle)Finally, wecan rewritecircletousearc:def circle(t, r):arc(t, r, 360)This process—rearranging a program to improve function interfaces and facilitate code re-use—iscalled refactoring. In this case, we noticed that there was similar code in arc and polygon, so we“factored itout” intopolyline.If we had planned ahead, we might have written polyline first and avoided refactoring, but oftenyou don’t know enough at the beginning of a project to design all the interfaces. Once you startcoding, you understand the problem better. Sometimes refactoring is a sign that you have learnedsomething.

4.8. A development plan 354.8 AdevelopmentplanA development plan is a process for writing programs. The process we used in this case study is“encapsulation and generalization.” The steps of thisprocess are:1. Start by writingasmallprogram withno function definitions.2. Once you get the program working, encapsulate it inafunction and give itaname.3. Generalize the function by adding appropriate parameters.4. Repeat steps 1–3 until you have a set of working functions. Copy and paste working code toavoid retyping (and re-debugging).5. Look for opportunities to improve the program by refactoring. For example, if you havesimilarcode inseveral places, consider factoring itintoan appropriately general function.This process has some drawbacks—we will see alternatives later—but it can be useful if you don’tknowaheadoftimehowtodividetheprogramintofunctions. Thisapproachletsyoudesignasyougo along.4.9 docstringA docstring is a string at the beginning of a function that explains the interface (“doc” is short for“documentation”). Here isanexample:def polyline(t, n, length, angle):"""Draw n line segments with the given length andangle (in degrees) between them. t is a turtle."""for i in range(n):fd(t, length)lt(t, angle)This docstring is a triple-quoted string, also known as a multiline string because the triple quotesallow thestringtospan more than one line.It is terse, but it contains the essential information someone would need to use this function. Itexplains concisely what the function does (without getting into the details of how it does it). Itexplainswhateffecteachparameterhasonthebehaviorofthefunctionandwhattypeeachparametershould be (ifit isnot obvious).Writing this kind of documentation is an important part of interface design. A well-designed interfaceshouldbesimpletoexplain;ifyouarehavingahardtimeexplainingoneofyourfunctions,thatmight be asignthat the interface could be improved.4.10 DebuggingAn interface is like a contract between a function and a caller. The caller agrees to provide certainparameters and the function agrees todocertain work.

36 Chapter 4. Case study: interface designFor example, polyline requires four arguments: t has to be a Turtle; n is the number of linesegments, so it has to be an integer; length should be a positive number; and angle has to be anumber, which isunderstood tobe indegrees.These requirements are called preconditions because they are supposed to be true before the functionstartsexecuting.Conversely,conditionsattheendofthefunctionarepostconditions. Postconditionsinclude the intended effect of the function (like drawing line segments) and any side effects(likemoving theTurtleor making other changes intheWorld).Preconditions are the responsibility of the caller. If the caller violates a (properly documented!)precondition and thefunction doesn’t workcorrectly, thebug isinthe caller, not thefunction.4.11 Glossaryinstance: A member of a set. The TurtleWorld in this chapter is a member of the set of Turtle-Worlds.loop: A part of aprogram that can execute repeatedly.encapsulation: The process oftransforming asequence ofstatements intoafunction definition.generalization: The process of replacing something unnecessarily specific (like a number) withsomething appropriately general (likeavariable or parameter).keyword argument: An argument that includes thename ofthe parameter as a“keyword.”interface: Adescriptionofhowtouseafunction,includingthenameanddescriptionsoftheargumentsand returnvalue.refactoring: Theprocessofmodifyingaworkingprogramtoimprovefunctioninterfacesandotherqualities ofthe code.development plan: Aprocess forwritingprograms.docstring: A stringthat appears inafunction definition todocument the function’s interface.precondition: A requirement that should be satisfiedby thecaller before a function starts.postcondition: A requirement that should besatisfied bythe function before itends.4.12 ExercisesExercise 4.1 Download thecode inthischapter fromthinkpython.com/code/polygon.py.1. Writeappropriate docstrings forpolygon,arcandcircle.2. Draw a stack diagram that shows the state of the program while executing circle(bob,radius). You can do the arithmeticby hand or addprintstatements tothecode.3. TheversionofarcinSection4.7isnotveryaccuratebecausethelinearapproximationofthecircle is always outside the true circle. As a result, the turtle ends up a few units away fromthe correct destination. My solution shows a way to reduce the effect of this error. Read thecode and see ifitmakes sensetoyou. Ifyou draw a diagram, you might seehow itworks.

4.12. Exercises 37Exercise 4.2 Writean appropriately general set of functions that can draw flowers likethis:You can download asolution fromthinkpython.com/code/flower.py.Exercise 4.3 Writean appropriately general set of functions that can draw shapes likethis:You can download asolution fromthinkpython.com/code/pie.py.Exercise 4.4 The letters of the alphabet can be constructed from a moderate number of basic elements,like vertical and horizontal lines and a few curves. Design a font that can be drawn with aminimal number of basicelements and then writefunctions that draw lettersofthe alphabet.You should write one function for each letter, with names draw_a,draw_b, etc., and put your functionsin a file named letters.py. You can download a “turtle typewriter” from thinkpython.com/code/typewriter.pytohelp you testyour code.You can download asolution fromthinkpython.com/code/letters.py.

38 Chapter 4. Case study: interface design

Chapter 5Conditionals and recursion5.1 Modulus operatorThemodulusoperatorworksonintegersandyieldstheremainderwhenthefirstoperandisdividedby the second. In Python, the modulus operator is a percent sign (%). The syntax is the same as forother operators:>>> quotient = 7 / 3>>> print quotient2>>> remainder = 7 % 3>>> print remainder1So 7divided by 3is2with1leftover.The modulus operator turns out to be surprisingly useful. For example, you can check whether onenumber is divisibleby another—ifx % yiszero, thenxisdivisiblebyy.Also, you can extract the right-most digit or digits from a number. For example, x % 10 yields theright-mostdigit ofx(inbase 10). Similarlyx % 100yields thelast twodigits.5.2 BooleanexpressionsA boolean expression is an expression that is either true or false. The following examples usethe operator ==, which compares two operands and produces True if they are equal and Falseotherwise:>>> 5 == 5True>>> 5 == 6FalseTrueandFalsearespecial values that belong tothetypebool;they are not strings:

40 Chapter 5. Conditionals and recursion>>> type(True)>>> type(False)The==operator isone of therelational operators; theothers are:x != yx > yx < yx >= yx 0 and x < 10 is true only if x is greaterthan 0and lessthan 10.n%2 == 0 or n%3 == 0 is true if either of the conditions is true, that is, if the number is divisibleby 2or 3.Finally, the not operator negates a boolean expression, so not (x > y) is true if x > y is false,that is,ifxisless thanor equal toy.Strictlyspeaking,theoperandsofthelogicaloperatorsshouldbebooleanexpressions,butPythonisnot very strict. Any nonzero number isinterpreted as“true.”>>> 17 and TrueTrueThis flexibility can be useful, but there are some subtleties to it that might be confusing. You mightwant toavoid it(unless you know what you are doing).5.4 Conditional executionInordertowriteusefulprograms,wealmostalwaysneedtheabilitytocheckconditionsandchangethe behavior of the program accordingly. Conditional statements give us this ability. The simplestform istheifstatement:if x > 0:print 'x is positive'Thebooleanexpressionaftertheifstatementiscalledthecondition. Ifitistrue,thentheindentedstatement gets executed. Ifnot, nothing happens.

5.5. Alternative execution 41if statements have the same structure as function definitions: a header followed by an indentedbody. Statements likethisare called compound statements.Thereisnolimitonthenumberofstatementsthatcanappearinthebody,buttherehastobeatleastone. Occasionally, it is useful to have a body with no statements (usually as a place keeper for codeyou haven’t writtenyet). Inthat case, you can usethepassstatement, which does nothing.if x < 0:pass# need to handle negative values!5.5 AlternativeexecutionAsecondformoftheifstatementisalternativeexecution,inwhichtherearetwopossibilitiesandthecondition determines which one gets executed. The syntax looks likethis:if x%2 == 0:print 'x is even'else:print 'x is odd'If the remainder when x is divided by 2 is 0, then we know that x is even, and the program displaysa message tothat effect. If the condition isfalse, the second set of statements is executed. Since theconditionmustbetrueorfalse,exactlyoneofthealternativeswillbeexecuted. Thealternativesarecalled branches, because they arebranches inthe flow of execution.5.6 Chained conditionalsSometimes there are more than two possibilities and we need more than two branches. One way toexpress acomputation likethat isachained conditional:if x < y:print 'x is less than y'elif x > y:print 'x is greater than y'else:print 'x and y are equal'elifisanabbreviationof“elseif.” Again,exactlyonebranchwillbeexecuted. Thereisnolimitonthe number of elif statements. If there is an else clause, it has to be at the end, but there doesn’thave tobe one.if choice == 'a':draw_a()elif choice == 'b':draw_b()elif choice == 'c':draw_c()Eachconditionischeckedinorder. Ifthefirstisfalse,thenextischecked,andsoon. Ifoneofthemistrue,thecorrespondingbranchexecutes,andthestatementends. Evenifmorethanoneconditionistrue, only thefirsttruebranch executes.

42 Chapter 5. Conditionals and recursion5.7 NestedconditionalsOne conditional can also be nested within another. We could have written the trichotomy examplelikethis:if x == y:print 'x and y are equal'else:if x < y:print 'x is less than y'else:print 'x is greater than y'Theouterconditionalcontainstwobranches. Thefirstbranchcontainsasimplestatement. Thesecondbranch contains another if statement, which has two branches of its own. Those two branchesareboth simplestatements, although they could have been conditional statements as well.Although the indentation of the statements makes the structure apparent, nested conditionals becomedifficult toread very quickly. Ingeneral, itisagood idea toavoid them when you can.Logical operators often provide a way to simplify nested conditional statements. For example, wecan rewritethe following code using asingleconditional:if 0 < x:if x < 10:print 'x is a positive single-digit number.'The print statement is executed only if we make it past both conditionals, so we can get the sameeffect withtheandoperator:if 0 < x and x < 10:print 'x is a positive single-digit number.'5.8 RecursionIt is legal for one function to call another; it is also legal for a function to call itself. It may not beobviouswhythatisagoodthing,butitturnsouttobeoneofthemostmagicalthingsaprogramcando. For example, look at thefollowing function:def countdown(n):if n >> countdown(3)

5.9. Stack diagrams for recursive functions 43The execution of countdown begins with n=3, and since n is greater than 0, it outputs the value 3,and then calls itself...The execution of countdown begins with n=2, and since n is greater than 0, it outputsthe value 2, and then callsitself...The execution of countdown begins with n=1, and since n is greater than 0,itoutputs thevalue 1, and then calls itself...The execution of countdown begins with n=0, and since n is notgreater than 0, itoutputs the word, “Blastoff!” and thenreturns.Thecountdownthat gotn=1returns.Thecountdownthat gotn=2returns.Thecountdownthat gotn=3returns.And then you’reback in__main__. So, thetotal output looks likethis:321Blastoff!A function that calls itselfisrecursive; theprocess iscalled recursion.As another example, we can writeafunction that printsastringntimes.def print_n(s, n):if n

44 Chapter 5. Conditionals and recursion__main__countdownn 3countdownn 2countdownn 1countdownn 0As usual, the top of the stack is the frame for __main__. It is empty because we did not create anyvariables in__main__or pass any arguments toit.The four countdown frames have different values for the parameter n. The bottom of the stack,wheren=0,iscalled the base case. It does not make arecursive call, sothere areno moreframes.Draw astack diagram forprint_ncalled withs = 'Hello'andn=2.Writeafunctioncalleddo_nthattakesafunctionobjectandanumber,n,asarguments,and that callsthe given functionntimes.5.10 Infinite recursionIf a recursion never reaches a base case, it goes on making recursive calls forever, and the programnever terminates. This is known as infinite recursion, and it is generally not a good idea. Here is aminimal program withan infinite recursion:def recurse():recurse()In most programming environments, a program with infinite recursion does not really run forever.Python reports anerror message when the maximum recursion depth isreached:File "", line 2, in recurseFile "", line 2, in recurseFile "", line 2, in recurse...File "", line 2, in recurseRuntimeError: Maximum recursion depth exceededThis traceback is a littlebigger than the one we saw inthe previous chapter. When the error occurs,there are1000recurseframes on thestack!

5.11. Keyboard input 455.11 KeyboardinputThe programs we have written so far are a bit rude in the sense that they accept no input from theuser. They justdo the samething every time.Pythonprovidesabuilt-infunctioncalledraw_inputthatgetsinputfromthekeyboard 1 . Whenthisfunctioniscalled,theprogramstopsandwaitsfortheusertotypesomething. WhentheuserpressesReturnor Enter, theprogram resumes andraw_inputreturns what theuser typed as astring.>>> input = raw_input()What are you waiting for?>>> print inputWhat are you waiting for?Before getting input from the user, it is a good idea to print a prompt telling the user what to input.raw_inputcan take aprompt asan argument:>>> name = raw_input('What...is your name?\n')What...is your name?Arthur, King of the Britons!>>> print nameArthur, King of the Britons!The sequence \n at the end of the prompt represents a newline, which is a special character thatcauses alinebreak. That’s why the user’sinput appears below the prompt.Ifyou expect the user totype aninteger, you can trytoconvert the returnvalue toint:>>> prompt = 'What...is the airspeed velocity of an unladen swallow?\n'>>> speed = raw_input(prompt)What...is the airspeed velocity of an unladen swallow?17>>> int(speed)17But ifthe user types something other than astringofdigits, you get an error:>>> speed = raw_input(prompt)What...is the airspeed velocity of an unladen swallow?What do you mean, an African or a European swallow?>>> int(speed)ValueError: invalid literal for int()We willseehow tohandle thiskind of error later.5.12 DebuggingThe traceback Python displays when an error occurs contains a lot of information, but it can beoverwhelming, especially when there are many frames on the stack. The most useful parts areusually:1 InPython3.0, this functionis namedinput.

46 Chapter 5. Conditionals and recursion• What kind of erroritwas, and• Where itoccurred.Syntax errors are usually easy to find, but there are a few gotchas. Whitespace errors can be trickybecause spaces and tabs are invisibleand weareused toignoring them.>>> x = 5>>> y = 6File "", line 1y = 6ˆSyntaxError: invalid syntaxIn this example, the problem is that the second line is indented by one space. But the error messagepoints to y, which is misleading. In general, error messages indicate where the problem wasdiscovered, but theactual error might be earlier inthecode, sometimes on aprevious line.The same is true of runtime errors. Suppose you are trying to compute a signal-to-noise ratio indecibels. The formula is SNR db = 10log 10 (P signal /P noise ). In Python, you might write somethinglikethis:import mathsignal_power = 9noise_power = 10ratio = signal_power / noise_powerdecibels = 10 * math.log10(ratio)print decibelsBut when you runit,you get anerror message 2 :Traceback (most recent call last):File "snr.py", line 5, in ?decibels = 10 * math.log10(ratio)OverflowError: math range errorThe error message indicates line 5, but there is nothing wrong with that line. To find the real error,it might be useful to print the value of ratio, which turns out to be 0. The problem is in line 4,because dividing two integers does floor division. The solution is to represent signal power andnoise power withfloating-point values.In general, error messages tell you where the problem was discovered, but that is often not where itwas caused.5.13 Glossarymodulus operator: Anoperator,denotedwithapercentsign(%),thatworksonintegersandyieldsthe remainder when one number isdivided by another.boolean expression: Anexpression whose value is eitherTrueorFalse.2 In Python 3.0, you no longer get an error message; the division operator performs floating-point division even withintegeroperands.

5.14. Exercises 47relational operator: Oneof the operators that compares itsoperands: ==,!=,>,=,and

48 Chapter 5. Conditionals and recursion1. Write a function named is_triangle that takes three integers as arguments, and that printseither “Yes” or “No,” depending on whether you can or cannot form a triangle from stickswiththe given lengths.2. Write a function that prompts the user to input three stick lengths, converts them to integers,and usesis_triangletocheck whether stickswiththegiven lengths can form atriangle.The following exercises useTurtleWorld from Chapter 4:Exercise 5.3 Read the following function and see if you can figure out what it does. Then run it(seetheexamples inChapter 4).def draw(t, length, n):if n == 0:returnangle = 50fd(t, length*n)lt(t, angle)draw(t, length, n-1)rt(t, 2*angle)draw(t, length, n-1)lt(t, angle)bk(t, length*n)Exercise 5.4 The Koch curve is afractal that looks something likethis:To draw aKoch curve withlength x, allyou have todois1. Draw aKoch curve withlength x/3.2. Turn left 60degrees.3. Draw aKoch curve withlength x/3.4. Turn right 120 degrees.5. Draw aKoch curve withlength x/3.6. Turn left 60degrees.7. Draw aKoch curve withlength x/3.The only exception isifxislessthan 3. Inthat case, you can justdraw astraight linewithlength x.1. Write a function called koch that takes a turtle and a length as parameters, and that uses theturtletodraw aKoch curve withthe given length.

5.14. Exercises 492. Write a function called snowflake that draws three Koch curves to make the outline of asnowflake.You can seemysolution atthinkpython.com/code/koch.py.3. The Koch curve can be generalized in several ways. See wikipedia.org/wiki/Koch_snowflakefor examples and implement your favorite.

50 Chapter 5. Conditionals and recursion

Chapter 6Fruitfulfunctions6.1 ReturnvaluesSome of the built-in functions we have used, such as the math functions, produce results. Callingthefunctiongeneratesavalue,whichweusuallyassigntoavariableoruseaspartofanexpression.e = math.exp(1.0)height = radius * math.sin(radians)All of the functions we have written so far are void; they print something or move turtles around,but their returnvalue isNone.In this chapter, we are (finally) going to write fruitful functions. The first example is area, whichreturns thearea of acirclewiththe given radius:def area(radius):temp = math.pi * radius**2return tempWe have seen thereturn statement before, but in a fruitful function thereturn statement includesanexpression. Thisstatementmeans: “Returnimmediatelyfromthisfunctionandusethefollowingexpression as a return value.” The expression can be arbitrarily complicated, so we could havewrittenthisfunction more concisely:def area(radius):return math.pi * radius**2Onthe other hand, temporary variables liketempoften make debugging easier.Sometimes itisuseful tohave multiple returnstatements, one ineach branch of aconditional:def absolute_value(x):if x < 0:return -xelse:return x

52 Chapter 6. Fruitful functionsSince thesereturnstatements areinan alternative conditional, only one willbe executed.As soon as a return statement executes, the function terminates without executing any subsequentstatements. Codethatappearsafterareturnstatement,oranyotherplacetheflowofexecutioncannever reach, iscalled dead code.In a fruitful function, it is a good idea to ensure that every possible path through the program hits areturnstatement. For example:def absolute_value(x):if x < 0:return -xif x > 0:return xThis function is incorrect because if x happens to be 0, neither condition is true, and the functionends without hitting a return statement. If the flow of execution gets to the end of a function, thereturnvalue isNone,which isnot the absolute value of0.>>> print absolute_value(0)NoneBy theway, Python provides abuilt-infunction calledabsthat computes absolute values.Exercise 6.1 Writeacomparefunction that returns1ifx > y,0ifx == y,and-1ifx < y.6.2 IncrementaldevelopmentAs you writelarger functions, you might find yourself spending moretimedebugging.To deal with increasingly complex programs, you might want to try a process called incrementaldevelopment. The goal of incremental development is to avoid long debugging sessions by addingand testingonly asmall amount of code at atime.As an example, suppose you want to find the distance between two points, given by the coordinates(x 1 ,y 1 )and (x 2 ,y 2 ). Bythe Pythagorean theorem, thedistance is:√distance= (x 2 −x 1 ) 2 +(y 2 −y 1 ) 2The first step is to consider what a distance function should look like in Python. In other words,what aretheinputs (parameters) and what istheoutput (returnvalue)?Inthiscase,theinputsaretwopoints,whichyoucanrepresentusingfournumbers. Thereturnvalueisthedistance, which isafloating-point value.Already you can writean outline ofthe function:def distance(x1, y1, x2, y2):return 0.0Obviously, this version doesn’t compute distances; it always returns zero. But it is syntacticallycorrect, and itruns,which means that you can testitbefore you make itmore complicated.To testthe new function, call itwithsample arguments:

6.2. Incremental development 53>>> distance(1, 2, 4, 6)0.0I chose these values so that the horizontal distance is 3 and the vertical distance is 4; that way, theresultis5(thehypotenuseofa3-4-5triangle). Whentestingafunction,itisusefultoknowtherightanswer.At this point we have confirmed that the function is syntactically correct, and we can start addingcode to the body. A reasonable next step is to find the differences x 2 −x 1 and y 2 −y 1 . The nextversion storesthose values intemporary variables and printsthem.def distance(x1, y1, x2, y2):dx = x2 - x1dy = y2 - y1print 'dx is', dxprint 'dy is', dyreturn 0.0If the function is working, it should display 'dx is 3' and ’dy is 4’. If so, we know that thefunction is getting the right arguments and performing the first computation correctly. If not, thereareonly afew lines tocheck.Next we compute thesum of squares ofdxanddy:def distance(x1, y1, x2, y2):dx = x2 - x1dy = y2 - y1dsquared = dx**2 + dy**2print 'dsquared is: ', dsquaredreturn 0.0Again, you would run the program at this stage and check the output (which should be 25). Finally,you can usemath.sqrttocompute and returntheresult:def distance(x1, y1, x2, y2):dx = x2 - x1dy = y2 - y1dsquared = dx**2 + dy**2result = math.sqrt(dsquared)return resultIfthatworkscorrectly,youaredone. Otherwise,youmightwanttoprintthevalueofresultbeforethereturn statement.The final version of the function doesn’t display anything when it runs; it only returns a value.The print statements we wrote are useful for debugging, but once you get the function working,you should remove them. Code like that is called scaffolding because it is helpful for building theprogram but isnot part of thefinal product.When you start out, you should add only a line or two of code at a time. As you gain more experience,you might find yourself writing and debugging bigger chunks. Either way, incrementaldevelopment can save you a lotof debugging time.The key aspects of theprocess are:

54 Chapter 6. Fruitful functions1. Start with a working program and make small incremental changes. At any point, if there isan error,you should have agood idea where itis.2. Usetemporary variables tohold intermediate values soyou can displayand check them.3. Once the program is working, you might want to remove some of the scaffolding or consolidatemultiplestatementsintocompoundexpressions,butonlyifitdoesnotmaketheprogramdifficult toread.Exercise 6.2 Use incremental development to write a function called hypotenuse that returns thelength of the hypotenuse of a right triangle given the lengths of the two legs as arguments. Recordeach stageof thedevelopment process as you go.6.3 CompositionAs you should expect by now, you can call one function from within another. This ability is calledcomposition.As an example, we’ll write a function that takes two points, the center of the circle and a point ontheperimeter, and computes the area ofthe circle.Assume that the center point is stored in the variables xc and yc, and the perimeter point is in xpandyp. Thefirststepistofindtheradiusofthecircle,whichisthedistancebetweenthetwopoints.We justwroteafunction,distance,that does that:radius = distance(xc, yc, xp, yp)The next stepistofind thearea of acirclewiththat radius; wejust wrotethat, too:result = area(radius)Encapsulating thesesteps inafunction, weget:def circle_area(xc, yc, xp, yp):radius = distance(xc, yc, xp, yp)result = area(radius)return resultThe temporary variables radius and result are useful for development and debugging, but oncetheprogram isworking, we can make it moreconcise bycomposing the function calls:def circle_area(xc, yc, xp, yp):return area(distance(xc, yc, xp, yp))6.4 BooleanfunctionsFunctions can return booleans, which is often convenient for hiding complicated tests inside functions.For example:def is_divisible(x, y):if x % y == 0:return Trueelse:return False

6.5. More recursion 55It is common to give boolean functions names that sound like yes/no questions; is_divisiblereturns eitherTrueorFalsetoindicate whetherxisdivisible byy.Here isanexample:>>> is_divisible(6, 4)False>>> is_divisible(6, 3)TrueTheresultofthe==operator isaboolean, sowecan writethefunctionmoreconcisely byreturningitdirectly:def is_divisible(x, y):return x % y == 0Boolean functions areoften used inconditional statements:if is_divisible(x, y):print 'x is divisible by y'Itmight be tempting towritesomething like:if is_divisible(x, y) == True:print 'x is divisible by y'But the extra comparison isunnecessary.Exercise 6.3 Write a function is_between(x, y, z) that returns True if x ≤ y ≤ z or Falseotherwise.6.5 MorerecursionWe have only covered a small subset of Python, but you might be interested to know that thissubset is a complete programming language, which means that anything that can be computed canbeexpressedinthislanguage. Anyprogrameverwrittencouldberewrittenusingonlythelanguagefeatures you have learned so far (actually, you would need a few commands to control devices likethekeyboard, mouse, disks,etc., but that’sall).Proving that claim is a nontrivial exercise first accomplished by Alan Turing, one of the first computerscientists(somewouldarguethathewasamathematician,butalotofearlycomputerscientistsstartedasmathematicians). Accordingly,itisknownastheTuringThesis. Foramorecomplete(andaccurate) discussion of the Turing Thesis, I recommend Michael Sipser’s book Introduction to theTheory of Computation.To give you an idea of what you can do with the tools you have learned so far, we’ll evaluate a fewrecursively defined mathematical functions. Arecursive definition issimilartoacircular definition,in the sense that the definition contains a reference to the thing being defined. A truly circulardefinition isnot very useful:frabjous: An adjective used todescribe something that isfrabjous.

56 Chapter 6. Fruitful functionsIfyousaw thatdefinition inthedictionary, you mightbeannoyed. Ontheother hand, ifyoulookedup the definition of the factorial function, denoted with the symbol !, you might get something likethis:0!=1n!=n(n−1)!Thisdefinitionsaysthatthefactorialof0is1,andthefactorialofanyothervalue,n,isnmultipliedby thefactorial of n−1.So3!is3times2!,whichis2times1!,whichis1times0!. Puttingitalltogether,3!equals3times2times 1times1, which is 6.If you can write a recursive definition of something, you can usually write a Python program toevaluate it. The first step is to decide what the parameters should be. In this case it should be clearthatfactorialtakes an integer:def factorial(n):Iftheargument happens tobe 0, all wehave todo isreturn1:def factorial(n):if n == 0:return 1Otherwise, and this is the interesting part, we have to make a recursive call to find the factorial ofn−1and then multiply itby n:def factorial(n):if n == 0:return 1else:recurse = factorial(n-1)result = n * recursereturn resultTheflowofexecutionforthisprogramissimilartotheflowofcountdowninSection5.8. Ifwecallfactorialwiththevalue 3:Since 3 isnot 0, wetake the second branch and calculate the factorial ofn-1...Since 2isnot 0, we take thesecond branch and calculate thefactorial ofn-1...Since 1 is not 0, we take the second branch and calculate the factorial ofn-1...Since 0 is 0, we take the first branch and return 1 without makingany more recursive calls.Thereturnvalue(1)ismultipliedbyn,whichis1,andtheresultisreturned.The return value (1) ismultipliedby n, which is2, and the resultisreturned.Thereturnvalue(2)ismultipliedbyn,whichis3,andtheresult,6,becomesthereturnvalueofthefunction call that startedthe whole process.Here iswhat the stackdiagram looks likeforthis sequence of function calls:

6.6. Leap of faith 57__main__factorialn 3 recurse 2result66factorialn 2recurse 1result22factorialn 1recurse 1result11factorialn 01The return values are shown being passed back up the stack. In each frame, the return value is thevalue ofresult,which isthe product ofnandrecurse.In the last frame, the local variables recurse and result do not exist, because the branch thatcreates them does not execute.6.6 Leapof faithFollowingtheflowofexecutionisonewaytoreadprograms,butitcanquicklybecomelabyrinthine.An alternative is what I call the “leap of faith.” When you come to a function call, instead offollowing the flow of execution, you assume that the function works correctly and returns the rightresult.In fact, you are already practicing this leap of faith when you use built-in functions. When you callmath.cosormath.exp,youdon’texaminethebodiesofthosefunctions. Youjustassumethattheyworkbecause thepeople who wrotethe built-infunctions weregood programmers.The same is true when you call one of your own functions. For example, in Section 6.4, we wrotea function called is_divisible that determines whether one number is divisible by another. Oncewe have convinced ourselves that this function is correct—by examining the code and testing—wecan usethe function without looking at the body again.The same is true of recursive programs. When you get to the recursive call, instead of followingtheflowofexecution,youshouldassumethattherecursivecallworks(yieldsthecorrectresult)andthenaskyourself,“AssumingthatIcanfindthefactorialofn−1,canIcomputethefactorialofn?”Inthiscase, itisclear that you can, bymultiplying by n.Of course, it’s a bit strange to assume that the function works correctly when you haven’t finishedwritingit,but that’swhy it’scalled a leap offaith!6.7 OnemoreexampleAfter factorial, the most common example of a recursively defined mathematical function isfibonacci,which has thefollowing definition 1 :1 Seewikipedia.org/wiki/Fibonacci_number.

58 Chapter 6. Fruitful functionsfibonacci(0)=0fibonacci(1)=1Translated into Python, itlooks likethis:fibonacci(n)=fibonacci(n−1)+fibonacci(n−2);def fibonacci (n):if n == 0:return 0elif n == 1:return 1else:return fibonacci(n-1) + fibonacci(n-2)Ifyoutrytofollowtheflowofexecutionhere,evenforfairlysmallvaluesofn,yourheadexplodes.But according to the leap of faith, if you assume that the two recursive calls work correctly, then itisclear that you get the right resultby adding them together.6.8 CheckingtypesWhat happens ifwecallfactorialand give it1.5as an argument?>>> factorial(1.5)RuntimeError: Maximum recursion depth exceededIt looks like an infinite recursion. But how can that be? There is a base case—when n == 0. But ifnisnot aninteger, we can missthebase case and recurseforever.In the first recursive call, the value of n is 0.5. In the next, it is -0.5. From there, it gets smaller(morenegative), but it willnever be0.We have two choices. We can try to generalize the factorial function to work with floating-pointnumbers, or we can make factorial check the type of its argument. The first option is called thegamma function 2 and it’salittlebeyond thescope of thisbook. Sowe’ll gofor thesecond.We can use the built-in function isinstance to verify the type of the argument. While we’re at it,wecan alsomake suretheargument ispositive:def factorial (n):if not isinstance(n, int):print 'Factorial is only defined for integers.'return Noneelif n < 0:print 'Factorial is not defined for negative integers.'return Noneelif n == 0:return 1else:return n * factorial(n-1)2 Seewikipedia.org/wiki/Gamma_function.

6.9. Debugging 59The first base case handles nonintegers; the second catches negative integers. In both cases, theprogram printsan error message and returnsNonetoindicate that something went wrong:>>> factorial('fred')Factorial is only defined for integers.None>>> factorial(-2)Factorial is not defined for negative integers.NoneIfwegetpastbothchecks,thenweknowthatnispositiveorzero,sowecanprovethattherecursionterminates.This program demonstrates a pattern sometimes called a guardian. The first two conditionals actas guardians, protecting the code that follows from values that might cause an error. The guardiansmake it possibletoprove thecorrectness of thecode.6.9 DebuggingBreaking a large program into smaller functions creates natural checkpoints for debugging. If afunction isnot working, therearethree possibilitiestoconsider:• There is something wrong with the arguments the function is getting; a precondition is violated.• There issomething wrong withthefunction; apostcondition isviolated.• There issomething wrong withthereturnvalue or theway itis being used.To rule out the first possibility, you can add a print statement at the beginning of the function anddisplay the values of the parameters (and maybe their types). Or you can write code that checks thepreconditions explicitly.If the parameters look good, add a print statement before each return statement that displays thereturn value. If possible, check the result by hand. Consider calling the function with values thatmake it easytocheck the result(as inSection 6.2).If the function seems to be working, look at the function call to make sure the return value is beingused correctly (orused at all!).Adding print statements at the beginning and end of a function can help make the flow of executionmore visible. For example, hereisaversion offactorialwithprint statements:def factorial(n):space = ' ' * (4 * n)print space, 'factorial', nif n == 0:print space, 'returning 1'return 1else:recurse = factorial(n-1)result = n * recurseprint space, 'returning', resultreturn result

60 Chapter 6. Fruitful functionsspaceisastringofspacecharactersthatcontrolstheindentationoftheoutput. Hereistheresultoffactorial(5):factorial 5factorial 4factorial 3factorial 2factorial 1factorial 0returning 1returning 1returning 2returning 6returning 24returning 120If you are confused about the flow of execution, this kind of output can be helpful. It takes sometimetodevelop effective scaffolding, but alittlebit of scaffolding can save alot of debugging.6.10 Glossarytemporary variable: A variable usedtostorean intermediate value inacomplex calculation.dead code: Part of a program that can never be executed, often because it appears after a returnstatement.None: A special value returned by functions that have no return statement or a return statementwithout an argument.incremental development: A program development plan intended to avoid debugging by addingand testingonlyasmallamount of code at atime.scaffolding: Code that isused during program development but isnot part of thefinal version.guardian: A programming pattern that uses a conditional statement to check for and handle circumstancesthat might cause an error.6.11 ExercisesExercise 6.4 Draw astackdiagram forthe following program. What does theprogram print?def b(z):prod = a(z, z)print z, prodreturn proddef a(x, y):x = x + 1return x * ydef c(x, y, z):

6.11. Exercises 61sum = x + y + zpow = b(sum)**2return powx = 1y = x + 1print c(x, y+3, x+y)Exercise 6.5 The Ackermann function, A(m,n),isdefined 3 :⎧⎪⎨ n+1 ifm=0A(m,n)= A(m−1,1) ifm>0and n=0⎪⎩A(m−1,A(m,n−1)) ifm>0and n>0.(6.1)Write a function named ack that evaluates Ackerman’s function. Use your function to evaluateack(3, 4),which should be125. What happens for larger values ofmandn?Exercise 6.6 A palindrome is a word that is spelled the same backward and forward, like “noon”and “redivider”. Recursively, a word is a palindrome if the first and last letters are the same and themiddle isapalindrome.The following arefunctions that take astringargument and returnthefirst,last,and middle letters:def first(word):return word[0]def last(word):return word[-1]def middle(word):return word[1:-1]We’ll seehow they work inChapter 8.1. Type these functions into a file named palindrome.py and test them out. What happens ifyou call middle with a string with two letters? One letter? What about the empty string,which iswritten'' and contains noletters?2. Write a function called is_palindrome that takes a string argument and returns True if it isa palindrome and False otherwise. Remember that you can use the built-in function len tocheck thelength of astring.Exercise 6.7 A number, a, is a power of b if it is divisible by b and a/b is a power of b. Write afunction calledis_powerthat takes parametersaandband returnsTrueifaisapower ofb.Exercise6.8 Thegreatestcommondivisor(GCD)ofaandbisthelargestnumberthatdividesbothof them withno remainder 4 .3 Seewikipedia.org/wiki/Ackermann_function.4 ThisexerciseisbasedonanexamplefromAbelsonandSussman’sStructureandInterpretationofComputerPrograms.

62 Chapter 6. Fruitful functionsOne way to find the GCD of two numbers is Euclid’s algorithm, which is based on the observationthat if r is the remainder when a is divided by b, then gcd(a,b)=gcd(b,r). As a base case, we canconsider gcd(a,0)=a.Writeafunctioncalledgcdthattakesparametersaandbandreturnstheirgreatestcommondivisor.Ifyou need help, seewikipedia.org/wiki/Euclidean_algorithm.

Chapter 7Iteration7.1 MultipleassignmentAs you may have discovered, it is legal to make more than one assignment to the same variable. Anewassignmentmakesanexistingvariablerefertoanewvalue(andstopreferringtotheoldvalue).bruce = 5print bruce,bruce = 7print bruceThe output of this program is 5 7, because the first time bruce is printed, its value is 5, and thesecond time, its value is 7. The comma at the end of the first print statement suppresses thenewline, which iswhy both outputs appear on thesame line.Here iswhat multipleassignment looks likeinastatediagram:bruce57With multiple assignment it is especially important to distinguish between an assignment operationandastatementofequality. BecausePythonusestheequalsign(=)forassignment,itistemptingtointerpret astatement likea = bas a statement of equality. Itisnot!First, equality is a symmetric relation and assignment is not. For example, in mathematics, if a=7then 7=a. But inPython, thestatementa = 7islegal and7 = aisnot.Furthermore, in mathematics, a statement of equality is either true or false, for all time. If a = bnow, then a will always equal b. In Python, an assignment statement can make two variables equal,but they don’t have tostaythat way:a = 5b = aa = 3# a and b are now equal# a and b are no longer equal

64 Chapter 7. IterationThethirdlinechangesthevalueofabutdoesnotchangethevalueofb,sotheyarenolongerequal.Although multiple assignment is frequently helpful, you should use it with caution. If the values ofvariables change frequently, itcan make thecode difficult toread and debug.7.2 Updating variablesOne of the most common forms of multiple assignment is an update, where the new value of thevariable depends onthe old.x = x+1This means “get thecurrent value ofx,add one, and then updatexwiththenew value.”Ifyoutrytoupdateavariablethatdoesn’texist,yougetanerror,becausePythonevaluatestherightsidebefore itassigns avalue tox:>>> x = x+1NameError: name 'x' is not definedBefore you can update avariable, you have toinitializeit,usually withasimpleassignment:>>> x = 0>>> x = x+1Updating avariable byadding 1iscalled anincrement; subtracting 1iscalled a decrement.7.3 ThewhilestatementComputers are often used to automate repetitive tasks. Repeating identical or similar tasks withoutmaking errorsissomething that computers dowell and people do poorly.We have seen two programs, countdown and print_n, that use recursion to perform repetition,which is also called iteration. Because iteration is so common, Python provides several languagefeatures to make it easier. One is the for statement we saw in Section 4.2. We’ll get back to thatlater.Another isthewhilestatement. Here isaversion ofcountdownthat uses awhilestatement:def countdown(n):while n > 0:print nn = n-1print 'Blastoff!'You can almost read the while statement as if it were English. It means, “While n is greater than0, display the value of n and then reduce the value of n by 1. When you get to 0, display the wordBlastoff!”Moreformally, here isthe flow of execution forawhilestatement:1. Evaluate thecondition, yieldingTrueorFalse.

7.4. break 652. Iftheconditionisfalse,exitthewhilestatementandcontinueexecutionatthenextstatement.3. Ifthe condition istrue,execute thebody and then goback tostep1.This type of flow iscalled aloop because the thirdsteploops back around tothe top.Thebodyoftheloopshouldchangethevalueofoneormorevariablessothateventuallytheconditionbecomes false and the loop terminates. Otherwise the loop will repeat forever, which is calledaninfiniteloop. Anendlesssourceofamusementforcomputerscientistsistheobservationthatthedirections onshampoo, “Lather, rinse,repeat,” arean infinite loop.In the case of countdown, we can prove that the loop terminates because we know that the value ofn is finite, and we can see that the value of n gets smaller each time through the loop, so eventuallywehave toget to0. Inother cases, itisnot soeasy totell:def sequence(n):while n != 1:print n,if n%2 == 0:n = n/2else:n = n*3+1# n is even# n is oddThe condition for this loop is n != 1, so the loop will continue until n is 1, which makes thecondition false.Eachtimethroughtheloop,theprogramoutputsthevalueofnandthencheckswhetheritisevenorodd. If it is even, n is divided by 2. If it is odd, the value of n is replaced with n*3+1. For example,ifthe argument passed tosequenceis3, the resultingsequence is3, 10, 5, 16, 8, 4, 2, 1.Since n sometimes increases and sometimes decreases, there is no obvious proof that n will everreach 1, or that the program terminates. For some particular values of n, we can prove termination.For example, if the starting value is a power of two, then the value of n will be even each timethrough the loop until it reaches 1. The previous example ends with such a sequence, starting with16.The hard question is whether we can prove that this program terminates for all positive values of n.So far 1 , noone has been abletoprove itor disprove it!Exercise 7.1 Rewrite thefunctionprint_nfrom Section 5.8 usingiterationinstead of recursion.7.4 breakSometimes you don’t know it’s time to end a loop until you get half way through the body. In thatcase you can usethebreakstatement tojump out of theloop.For example, suppose you want totake input from the useruntil they typedone. You could write:while True:line = raw_input('> ')if line == 'done':1 Seewikipedia.org/wiki/Collatz_conjecture.

66 Chapter 7. Iterationbreakprint lineprint 'Done!'The loop condition isTrue,which isalways true, sotheloop runs until ithitsthe break statement.Each time through, it prompts the user with an angle bracket. If the user types done, the breakstatement exits the loop. Otherwise the program echoes whatever the user types and goes back tothetop of theloop. Here’s asample run:> not donenot done> doneDone!This way of writing while loops is common because you can check the condition anywhere inthe loop (not just at the top) and you can express the stop condition affirmatively (“stop when thishappens”) rather than negatively (“keep going until that happens.”).7.5 Square rootsLoops are often used in programs that compute numerical results by starting with an approximateanswer and iteratively improving it.For example, one way of computing square roots is Newton’s method. Suppose that you want toknowthesquarerootofa. Ifyoustartwithalmostanyestimate,x,youcancomputeabetterestimatewiththefollowing formula:For example, ifais4and x is3:y= x+a/x2>>> a = 4.0>>> x = 3.0>>> y = (x + a/x) / 2>>> print y2.16666666667Which is closer to the correct answer ( √ 4=2). If we repeat the process with the new estimate, itgets even closer:>>> x = y>>> y = (x + a/x) / 2>>> print y2.00641025641Afterafew more updates, theestimateisalmost exact:>>> x = y>>> y = (x + a/x) / 2>>> print y

7.6. Algorithms 672.00001024003>>> x = y>>> y = (x + a/x) / 2>>> print y2.00000000003In general we don’t know ahead of time how many steps it takes to get to the right answer, but weknow when we get there because theestimatestops changing:>>> x = y>>> y = (x + a/x) / 2>>> print y2.0>>> x = y>>> y = (x + a/x) / 2>>> print y2.0When y == x, we can stop. Here is a loop that starts with an initial estimate, x, and improves ituntil itstops changing:while True:print xy = (x + a/x) / 2if y == x:breakx = yFor most values of a this works fine, but in general it is dangerous to test float equality. Floatingpointvalues are only approximately right: most rational numbers, like 1/3, and irrational numbers,like √ 2,can’t berepresented exactly withafloat.Ratherthancheckingwhetherxandyareexactlyequal,itissafertousethebuilt-infunctionabstocompute the absolute value, or magnitude, of thedifference between them:if abs(y-x) < epsilon:breakWhereepsilonhas avalue like0.0000001that determines how closeisclose enough.Exercise 7.2 Encapsulate this loop in a function called square_root that takes a as a parameter,chooses a reasonable value ofx,and returns an estimateof thesquare root ofa.7.6 AlgorithmsNewton’s method is an example of an algorithm: it is a mechanical process for solving a categoryof problems (inthiscase, computing square roots).It is not easy to define an algorithm. It might help to start with something that is not an algorithm.When you learned to multiply single-digit numbers, you probably memorized the multiplicationtable. Ineffect, you memorized 100 specific solutions. That kind of knowledge isnot algorithmic.

68 Chapter 7. IterationBut if you were “lazy,” you probably cheated by learning a few tricks. For example, to find theproduct of n and 9, you can write n−1 as the first digit and 10−n as the second digit. This trick isageneral solutionfor multiplying any single-digit number by9. That’s analgorithm!Similarly, the techniques you learned for addition with carrying, subtraction with borrowing, andlong division are all algorithms. One of the characteristics of algorithms is that they do not requireany intelligence to carry out. They are mechanical processes in which each step follows from thelastaccording toasimplesetof rules.In my opinion, it is embarrassing that humans spend so much time in school learning to executealgorithms that, quite literally,require nointelligence.Ontheotherhand,theprocessofdesigningalgorithmsisinteresting,intellectuallychallenging,andacentral part of what we call programming.Some of the things that people do naturally, without difficulty or conscious thought, are the hardestto express algorithmically. Understanding natural language is a good example. We all do it, but sofarno one has been able toexplain how we doit,at least not inthe formof an algorithm.7.7 DebuggingAsyoustartwritingbiggerprograms,youmightfindyourselfspendingmoretimedebugging. Morecode means morechances tomake anerror and more place forbugs tohide.Onewaytocutyourdebuggingtimeis“debuggingbybisection.” Forexample,ifthereare100linesinyour program and you check them one at atime, itwould take 100 steps.Instead, try to break the problem in half. Look at the middle of the program, or near it, for anintermediate value you can check. Add a print statement (or something else that has a verifiableeffect) and run theprogram.If the mid-point check is incorrect, there must be a problem in the first half of the program. If it iscorrect, the problem isinthesecond half.Every time you perform a check like this, you halve the number of lines you have to search. Aftersixsteps(whichisfewerthan100),youwouldbedowntooneortwolinesofcode,atleastintheory.In practice it is not always clear what the “middle of the program” is and not always possible tocheck it. It doesn’t make sense to count lines and find the exact midpoint. Instead, think aboutplaces in the program where there might be errors and places where it is easy to put a check. Thenchoose a spot where you think the chances are about the same that the bug is before or after thecheck.7.8 Glossarymultipleassignment: Makingmorethanoneassignmenttothesamevariableduringtheexecutionof aprogram.update: An assignment where thenew value of thevariable depends on theold.initialization: Anassignment that gives an initialvalue toavariable that willbe updated.increment: An update that increases thevalue of avariable (oftenby one).

7.9. Exercises 69decrement: An update that decreases the value of avariable.iteration: Repeatedexecutionofasetofstatementsusingeitherarecursivefunctioncalloraloop.infinite loop: A loop inwhich theterminating condition isnever satisfied.7.9 ExercisesExercise7.3 Totestthesquarerootalgorithminthischapter,youcouldcompareitwithmath.sqrt.Writeafunction namedtest_square_rootthat prints atablelikethis:1.0 1.0 1.0 0.02.0 1.41421356237 1.41421356237 2.22044604925e-163.0 1.73205080757 1.73205080757 0.04.0 2.0 2.0 0.05.0 2.2360679775 2.2360679775 0.06.0 2.44948974278 2.44948974278 0.07.0 2.64575131106 2.64575131106 0.08.0 2.82842712475 2.82842712475 4.4408920985e-169.0 3.0 3.0 0.0Thefirstcolumnisanumber,a;thesecondcolumnisthesquarerootofacomputedwiththefunctionfrom Exercise 7.2; the third column is the square root computed by math.sqrt; the fourth columnistheabsolute value of the difference between the twoestimates.Exercise 7.4 The built-in functioneval takes a string and evaluates it using the Python interpreter.For example:>>> eval('1 + 2 * 3')7>>> import math>>> eval('math.sqrt(5)')2.2360679774997898>>> eval('type(math.pi)')Write a function called eval_loop that iteratively prompts the user, takes the resulting input andevaluates it usingeval,and printsthe result.It should continue until the user enters 'done', and then return the value of the last expression itevaluated.Exercise7.5 ThebrilliantmathematicianSrinivasaRamanujanfoundaninfiniteseries 2 thatcanbeused togenerate anumerical approximation of π:2 Seewikipedia.org/wiki/Pi.1π = 2√ 29801∞∑k=0(4k)!(1103+26390k)(k!) 4 396 4k

70 Chapter 7. IterationWrite a function called estimate_pi that uses this formula to compute and return an estimate ofπ. It should use a while loop to compute terms of the summation until the last term is smaller than1e-15(which isPython notation for 10 −15 ). You can check theresult bycomparing it tomath.pi.You can see mysolutionatthinkpython.com/code/pi.py.

Chapter 8Strings8.1 Astringis a sequenceA string is a sequence of characters. You can access the characters one at a time with the bracketoperator:>>> fruit = 'banana'>>> letter = fruit[1]The second statement selects character number 1 fromfruitand assigns ittoletter.The expression in brackets is called an index. The index indicates which character in the sequenceyou want (hence thename).But you might not get what you expect:>>> print letteraFormostpeople, thefirstletterof'banana'isb,nota. Butforcomputer scientists,theindexisanoffset fromthe beginning ofthe string,and the offsetof thefirst letteriszero.>>> letter = fruit[0]>>> print letterbSo b is the 0th letter (“zero-eth”) of 'banana', a is the 1th letter (“one-eth”), and n is the 2th(“two-eth”) letter.Youcanuseanyexpression,includingvariablesandoperators,asanindex,butthevalueoftheindexhas tobe an integer. Otherwiseyou get:>>> letter = fruit[1.5]TypeError: string indices must be integers

72 Chapter 8. Strings8.2 lenlenisabuilt-infunction that returnsthe number of characters inastring:>>> fruit = 'banana'>>> len(fruit)6To get the lastletter ofastring,you might be tempted totrysomething likethis:>>> length = len(fruit)>>> last = fruit[length]IndexError: string index out of rangeThe reason for the IndexError is that there is no letter in ’banana’ with the index 6. Since westarted counting at zero, the six letters are numbered 0 to 5. To get the last character, you have tosubtract 1 fromlength:>>> last = fruit[length-1]>>> print lastaAlternatively, you can use negative indices, which count backward from the end of the string. Theexpressionfruit[-1]yields the lastletter,fruit[-2]yields thesecond tolast,and soon.8.3 Traversalwith aforloopA lot of computations involve processing a string one character at a time. Often they start at thebeginning, select each character in turn, do something to it, and continue until the end. This patternof processing iscalled atraversal. One way towriteatraversal iswithawhileloop:index = 0while index < len(fruit):letter = fruit[index]print letterindex = index + 1This loop traverses the string and displays each letter on a line by itself. The loop condition isindex < len(fruit), so when index is equal to the length of the string, the condition is false,and the body of the loop is not executed. The last character accessed is the one with the indexlen(fruit)-1,which isthe lastcharacter inthe string.Exercise 8.1 Write a function that takes a string as an argument and displays the letters backward,one per line.Another way towriteatraversal iswithaforloop:for char in fruit:print charEach time through the loop, the next character in the string is assigned to the variable char. Theloop continues untilno characters are left.

8.4. String slices 73Thefollowingexampleshowshowtouseconcatenation(stringaddition)andaforlooptogeneratean abecedarian series (that is, in alphabetical order). In Robert McCloskey’s book Make Way forDucklings,thenamesoftheducklingsareJack,Kack,Lack,Mack,Nack,Ouack,Pack,andQuack.This loop outputs these names inorder:prefixes = 'JKLMNOPQ'suffix = 'ack'for letter in prefixes:print letter + suffixThe output is:JackKackLackMackNackOackPackQackOf course, that’s not quite rightbecause “Ouack” and “Quack” aremisspelled.Exercise 8.2 Modify theprogram tofix thiserror.8.4 StringslicesA segment ofastringiscalled aslice. Selecting asliceissimilartoselecting acharacter:>>> s = 'Monty Python'>>> print s[0:5]Monty>>> print s[6:12]PythonTheoperator[n:m]returnsthepartofthestringfromthe“n-eth”charactertothe“m-eth”character,including the first but excluding the last. This behavior is counterintuitive, but it might help toimagine the indices pointing between thecharacters, as inthe followingdiagram:fruit’ b a n a n a ’index0 1 2 3 4 5 6If you omit the first index (before the colon), the slice starts at the beginning of the string. If youomit thesecond index, theslicegoes tothe end of thestring:>>> fruit = 'banana'>>> fruit[:3]'ban'>>> fruit[3:]'ana'

74 Chapter 8. StringsIf the first index is greater than or equal to the second the result is an empty string, represented bytwoquotation marks:>>> fruit = 'banana'>>> fruit[3:3]''An empty string contains no characters and has length 0, but other than that, it is the same as anyother string.Exercise 8.3 Given thatfruitisastring,what doesfruit[:] mean?8.5 Stringsare immutableItistemptingtousethe[]operatorontheleftsideofanassignment,withtheintentionofchangingacharacter inastring. For example:>>> greeting = 'Hello, world!'>>> greeting[0] = 'J'TypeError: object does not support item assignmentThe “object” in this case is the string and the “item” is the character you tried to assign. For now,an object is the same thing as a value, but we will refine that definition later. An item is one of thevalues inasequence.The reason for the error is that strings are immutable, which means you can’t change an existingstring. The best you can do iscreate anew stringthat isavariation on theoriginal:>>> greeting = 'Hello, world!'>>> new_greeting = 'J' + greeting[1:]>>> print new_greetingJello, world!Thisexampleconcatenatesanewfirstletterontoasliceofgreeting. Ithasnoeffectontheoriginalstring.8.6 SearchingWhat does the following function do?def find(word, letter):index = 0while index < len(word):if word[index] == letter:return indexindex = index + 1return -1In a sense, find is the opposite of the [] operator. Instead of taking an index and extracting thecorresponding character, it takes a character and finds the index where that character appears. If thecharacter isnot found, the function returns-1.

8.7. Looping and counting 75This is the first example we have seen of a return statement inside a loop. If word[index] ==letter,thefunction breaks out of theloop and returns immediately.Ifthecharacter doesn’t appear inthe string,theprogram exits theloop normally and returns-1.Thispatternofcomputation—traversingasequenceandreturningwhenwefindwhatwearelookingfor—iscalled asearch.Exercise 8.4 Modify find so that it has a third parameter, the index in word where it should startlooking.8.7 Looping and countingThe following program counts the number of timesthe letteraappears inastring:word = 'banana'count = 0for letter in word:if letter == 'a':count = count + 1print countThis program demonstrates another pattern of computation called a counter. The variable count isinitialized to 0 and then incremented each time an a is found. When the loop exits, count containstheresult—thetotal number ofa’s.Exercise 8.5 Encapsulate this code in a function named count, and generalize it so that it acceptsthestringand theletter as arguments.Exercise8.6 Rewritethisfunctionsothatinsteadoftraversingthestring,itusesthethree-parameterversion offindfromthe previous section.8.8 stringmethodsA method is similar to a function—it takes arguments and returns a value—but the syntax is different.For example, the method upper takes a string and returns a new string with all uppercaseletters:Instead ofthe function syntaxupper(word),ituses themethod syntaxword.upper().>>> word = 'banana'>>> new_word = word.upper()>>> print new_wordBANANAThis form of dot notation specifies the name of the method, upper, and the name of the string toapply the method to,word. The empty parentheses indicate that this method takes noargument.Amethodcalliscalledaninvocation;inthiscase,wewouldsaythatweareinvokingupperontheword.As it turns out, there is a string method named find that is remarkably similar to the function wewrote:

76 Chapter 8. Strings>>> word = 'banana'>>> index = word.find('a')>>> print index1Inthisexample, we invokefindonwordand pass theletter wearelooking for asaparameter.Actually, thefind method is more general than our function; it can find substrings, not just characters:>>> word.find('na')2Itcan take as asecond argument theindex where itshould start:>>> word.find('na', 3)4And as athirdargument the index where itshould stop:>>> name = 'bob'>>> name.find('b', 1, 2)-1This search failsbecausebdoes not appear intheindex range from1to2(not including2).Exercise 8.7 There is a string method called count that is similar to the function in the previousexercise. Read the documentation of this method and write an invocation that counts the number ofasin'banana'.8.9 Thein operatorThe word in is a boolean operator that takes two strings and returns True if the first appears as asubstringinthesecond:>>> 'a' in 'banana'True>>> 'seed' in 'banana'FalseFor example, thefollowing function printsall thelettersfromword1that alsoappear inword2:def in_both(word1, word2):for letter in word1:if letter in word2:print letterWith well-chosen variable names, Python sometimes reads like English. You could read this loop,“for (each) letterin(thefirst)word, if(the) letter(appears) in(thesecond) word, print(the) letter.”Here’s what you get ifyou compare apples and oranges:>>> in_both('apples', 'oranges')aes

8.10. String comparison 778.10 StringcomparisonThe relational operators work on strings. To seeiftwostringsareequal:if word == 'banana':print 'All right, bananas.'Other relational operations are useful forputting words inalphabetical order:if word < 'banana':print 'Your word,' + word + ', comes before banana.'elif word > 'banana':print 'Your word,' + word + ', comes after banana.'else:print 'All right, bananas.'Pythondoesnothandleuppercaseandlowercaselettersthesamewaythatpeopledo. Alltheuppercaseletterscome before all thelowercase letters,so:Your word, Pineapple, comes before banana.A common way to address this problem is to convert strings to a standard format, such as all lowercase,before performing the comparison. Keep that in mind in case you have to defend yourselfagainst aman armed withaPineapple.8.11 DebuggingWhen you use indices to traverse the values in a sequence, it is tricky to get the beginning and endof the traversal right. Here is a function that is supposed to compare two words and return True ifone of thewords isthereverse of theother, but itcontains twoerrors:def is_reverse(word1, word2):if len(word1) != len(word2):return Falsei = 0j = len(word2)while j > 0:if word1[i] != word2[j]:return Falsei = i+1j = j-1return TrueThe first if statement checks whether the words are the same length. If not, we can return Falseimmediatelyandthen,fortherestofthefunction,wecanassumethatthewordsarethesamelength.This isan example of theguardian pattern inSection 6.8.i and j are indices: i traverses word1 forward while j traverses word2 backward. If we find twolettersthatdon’tmatch, wecanreturnFalseimmediately. Ifwegetthroughthewholeloopandalltheletters match, we returnTrue.

78 Chapter 8. StringsIf we test this function with the words “pots” and “stop”, we expect the return value True, but weget an IndexError:>>> is_reverse('pots', 'stop')...File "reverse.py", line 15, in is_reverseif word1[i] != word2[j]:IndexError: string index out of rangeFor debugging this kind of error, my first move is to print the values of the indices immediatelybefore thelinewhere the errorappears.while j > 0:print i, j# print hereif word1[i] != word2[j]:return Falsei = i+1j = j-1Now when I runtheprogram again, I get moreinformation:>>> is_reverse('pots', 'stop')0 4...IndexError: string index out of rangeThefirsttimethroughtheloop,thevalueofjis4,whichisoutofrangeforthestring'pots'. Theindex of thelastcharacter is3, sotheinitialvalue forjshould belen(word2)-1.IfIfix that error and runthe program again, I get:>>> is_reverse('pots', 'stop')0 31 22 1TrueThistimewegettherightanswer,butitlookslikethelooponlyranthreetimes,whichissuspicious.To get a better idea of what is happening, it is useful to draw a state diagram. During the firstiteration, theframeforis_reverselooks likethis:word1 ’pots’ word2 ’stop’i 0 j 3Itookalittlelicensebyarrangingthevariablesintheframeandaddingdottedlinestoshowthatthevalues ofiandjindicate characters inword1andword2.Exercise 8.8 Starting with this diagram, execute the program on paper, changing the values of iandjduring each iteration. Find and fixthe second error inthisfunction.

8.12. Glossary 798.12 Glossaryobject: Something a variable can refer to. For now, you can use “object” and “value” interchangeably.sequence: Anorderedset;thatis,asetofvalueswhereeachvalueisidentifiedbyanintegerindex.item: One of thevalues inasequence.index: Aninteger value used toselect an item inasequence, such as acharacter inastring.slice: A part of astringspecified by arange ofindices.empty string: A stringwithnocharacters and length 0, represented by twoquotation marks.immutable: The property of asequence whose items cannot be assigned.traverse: To iteratethrough theitems inasequence, performing a similaroperation on each.search: A pattern of traversal that stops when itfinds what itislooking for.counter: A variable used tocount something, usually initializedtozero and then incremented.method: A function that isassociated withan object and called using dot notation.invocation: A statement that calls amethod.8.13 ExercisesExercise8.9 Astringslicecantakeathirdindexthatspecifiesthe“stepsize;”thatis,thenumberofspaces between successive characters. A step size of 2 means every other character; 3 means everythird,etc.>>> fruit = 'banana'>>> fruit[0:5:2]'bnn'A stepsizeof -1goes through theword backwards, sothe slice[::-1]generates areversed string.Usethisidiom towriteaone-line version ofis_palindromefrom Exercise 6.6.Exercise 8.10 Read the documentation of the string methods at docs.python.org/lib/string-methods.html. You might want to experiment with some of them to make sure you understandhow they work. stripandreplaceare particularly useful.The documentation uses a syntax that might be confusing. For example, infind(sub[, start[, end]]), the brackets indicate optional arguments. So sub is required, butstartis optional, and ifyou includestart,thenendisoptional.Exercise8.11 Thefollowingfunctionsareallintendedtocheck whetherastringcontains anylowercaseletters, but at least some of them are wrong. For each function, describe what the functionactually does (assumingthat theparameter isastring).

80 Chapter 8. Stringsdef any_lowercase1(s):for c in s:if c.islower():return Trueelse:return Falsedef any_lowercase2(s):for c in s:if 'c'.islower():return 'True'else:return 'False'def any_lowercase3(s):for c in s:flag = c.islower()return flagdef any_lowercase4(s):flag = Falsefor c in s:flag = flag or c.islower()return flagdef any_lowercase5(s):for c in s:if not c.islower():return Falsereturn TrueExercise8.12 ROT13isaweakformofencryptionthatinvolves“rotating”eachletterinawordby13places 1 . Torotatealettermeanstoshiftitthroughthealphabet,wrappingaroundtothebeginningifnecessary, so’A’shiftedby 3is’D’and ’Z’shiftedby1is’A’.Write a function called rotate_word that takes a string and an integer as parameters, and thatreturns anew stringthat contains thelettersfrom theoriginal string“rotated” by thegiven amount.For example, “cheer” rotated by 7is“jolly” and “melon” rotated by-10 is“cubed”.Youmightwanttousethebuilt-infunctionsord,whichconvertsacharactertoanumericcode,andchr,which converts numeric codes tocharacters.Potentially offensive jokes on the Internet are sometimes encoded in ROT13. If you are not easilyoffended, find and decode someof them.1 Seewikipedia.org/wiki/ROT13.

Chapter 9Case study: word play9.1 Readingword listsFor the exercises in this chapter we need a list of English words. There are lots of word listsavailableontheWeb,buttheonemostsuitableforourpurposeisoneofthewordlistscollectedandcontributed to the public domain by Grady Ward as part of the Moby lexicon project 1 . It is a list of113,809 official crosswords; that is, words that are considered valid in crossword puzzles and otherword games. In the Moby collection, the filename is 113809of.fic; I include a copy of this file,withthesimpler namewords.txt,along withSwampy.This file is in plain text, so you can open it with a text editor, but you can also read it from Python.Thebuilt-infunctionopentakesthenameofthefileasaparameterandreturnsafileobjectyoucanusetoread thefile.>>> fin = open('words.txt')>>> print finfin is a common name for a file object used for input. Mode'r' indicates that this file is open forreading (as opposed to'w' forwriting).The file object provides several methods for reading, including readline, which reads charactersfrom thefileuntil it gets toanewline and returnsthe resultas astring:>>> fin.readline()'aa\r\n'The first word in this particular list is “aa,” which is a kind of lava. The sequence \r\n representstwowhitespace characters, acarriage returnand anewline, that separate this wordfrom thenext.The file object keeps track of where it is in the file, so if you call readline again, you get the nextword:>>> fin.readline()'aah\r\n'1 wikipedia.org/wiki/Moby_Project.

82 Chapter 9. Casestudy: word playThe next word is “aah,” which is a perfectly legitimate word, so stop looking at me like that. Or, ifit’sthewhitespace that’sbothering you, wecan get ridofit withthe stringmethodstrip:>>> line = fin.readline()>>> word = line.strip()>>> print wordaahedYou can also use a file object as part of a for loop. This program reads words.txt and prints eachword, one per line:fin = open('words.txt')for line in fin:word = line.strip()print wordExercise 9.1 Write a program that reads words.txt and prints only the words with more than 20characters (not counting whitespace).9.2 ExercisesTherearesolutionstotheseexercisesinthenextsection. Youshouldatleastattempteachonebeforeyou read thesolutions.Exercise9.2 In1939ErnestVincentWrightpublisheda50,000wordnovelcalledGadsbythatdoesnot contain theletter “e.” Since “e” isthe most common letterinEnglish, that’s not easy todo.In fact, it is difficult to construct a solitary thought without using that most common symbol. It isslow going at first,but withcaution and hours oftraining you can gradually gain facility.Allright, I’llstopnow.Write a function called has_no_e that returns True if the given word doesn’t have the letter “e” init.Modifyyourprogramfromtheprevioussectiontoprintonlythewordsthathaveno“e”andcomputethepercentage of the words inthelisthave no “e.”Exercise9.3 Writeafunctionnamedavoidsthattakesawordandastringofforbiddenletters,andthat returnsTrueiftheword doesn’t use any of the forbidden letters.Modify your program to prompt the user to enter a string of forbidden letters and then print thenumber of words that don’t contain any of them. Can you find a combination of 5 forbidden lettersthat excludes thesmallestnumber of words?Exercise 9.4 Write a function named uses_only that takes a word and a string of letters, and thatreturns True if the word contains only letters in the list. Can you make a sentence using only thelettersacefhlo? Other than “Hoe alfalfa?”Exercise 9.5 Write a function named uses_all that takes a word and a string of required letters,and that returns True if the word uses all the required letters at least once. How many words arethere that useall thevowelsaeiou? How aboutaeiouy?

9.3. Search 83Exercise 9.6 Write a function called is_abecedarian that returns True if the letters in a wordappear inalphabetical order (double lettersareok). How many abecedarian words are there?9.3 SearchAll of the exercises in the previous section have something in common; they can be solved with thesearch pattern wesaw inSection 8.6. The simplestexample is:def has_no_e(word):for letter in word:if letter == 'e':return Falsereturn TrueThe for loop traverses the characters in word. If we find the letter “e”, we can immediately returnFalse;otherwisewehavetogotothenextletter. Ifweexittheloopnormally,thatmeanswedidn’tfind an “e”, sowereturnTrue.avoidsisamore general version ofhas_no_ebut ithas thesame structure:def avoids(word, forbidden):for letter in word:if letter in forbidden:return Falsereturn TrueWecanreturnFalseassoonaswefindaforbiddenletter;ifwegettotheendoftheloop,wereturnTrue.uses_onlyissimilarexcept that thesense of thecondition isreversed:def uses_only(word, available):for letter in word:if letter not in available:return Falsereturn TrueInsteadofalistofforbiddenletters,wehavealistofavailableletters. Ifwefindaletterinwordthatisnot inavailable,wecan returnFalse.uses_allissimilarexcept that we reverse the roleofthe wordand the stringof letters:def uses_all(word, required):for letter in required:if letter not in word:return Falsereturn TrueInsteadoftraversingthelettersinword,thelooptraversestherequiredletters. Ifanyoftherequiredlettersdo not appear intheword, wecan returnFalse.Ifyouwerereallythinkinglikeacomputerscientist,youwouldhaverecognizedthatuses_allwasan instance of apreviously-solved problem, and you would have written:

84 Chapter 9. Casestudy: word playdef uses_all(word, required):return uses_only(required, word)This is an example of a program development method called problem recognition, which meansthat you recognize the problem you are working on as an instance of a previously-solved problem,and apply apreviously-developed solution.9.4 Looping with indicesI wrote the functions in the previous section withfor loops because I only needed the characters inthestrings;Ididn’t have todoanything withtheindices.Foris_abecedarianwe have tocompare adjacent letters,which isalittletrickywithaforloop:def is_abecedarian(word):previous = word[0]for c in word:if c < previous:return Falseprevious = creturn TrueAnalternative istouse recursion:def is_abecedarian(word):if len(word) word[1]:return Falsereturn is_abecedarian(word[1:])Another option istouse awhileloop:def is_abecedarian(word):i = 0while i < len(word)-1:if word[i+1] < word[i]:return Falsei = i+1return TrueTheloopstartsati=0andendswheni=len(word)-1. Eachtimethroughtheloop,itcomparestheith character (which you can think of as the current character) to the i+1th character (which youcan think of asthe next).If the next character is less than (alphabetically before) the current one, then we have discovered abreak inthe abecedarian trend, and wereturnFalse.If we get to the end of the loop without finding a fault, then the word passes the test. To convinceyourself that the loop ends correctly, consider an example like'flossy'. The length of the wordis 6, so the last time the loop runs is when i is 4, which is the index of the second-to-last character.Onthe lastiteration, itcompares thesecond-to-last character tothe last,which iswhat wewant.

9.5. Debugging 85Here is a version of is_palindrome (see Exercise 6.6) that uses two indices; one starts at thebeginning and goes up; the other startsat theend and goes down.def is_palindrome(word):i = 0j = len(word)-1while i

86 Chapter 9. Casestudy: word play9.6 Glossaryfileobject: A value that represents anopen file.problem recognition: A way of solving a problem by expressing it as an instance of a previouslysolvedproblem.special case: A testcase that isatypical or non-obvious (and lesslikelytobe handled correctly).9.7 ExercisesExercise9.7 ThisquestionisbasedonaPuzzlerthatwasbroadcastontheradioprogramCarTalk 2 :Give me a word with three consecutive double letters. I’ll give you a couple of wordsthat almost qualify, but don’t. For example, the word committee, c-o-m-m-i-t-t-e-e. Itwould be great except for the ‘i’ that sneaks in there. Or Mississippi: M-i-s-s-i-s-s-ip-p-i.If you could take out those i’s it would work. But there is a word that has threeconsecutivepairsoflettersandtothebestofmyknowledgethismaybetheonlyword.Of course thereare probably 500 morebut Ican only think of one. What isthe word?Writeaprogram tofind it. You can see mysolution atthinkpython.com/code/cartalk.py.Exercise 9.8 Here’s another Car Talk Puzzler 3 :“I was driving on the highway the other day and I happened to notice my odometer.Likemostodometers,itshowssixdigits,inwholemilesonly. So,ifmycarhad300,000miles, forexample, I’dsee 3-0-0-0-0-0.“Now, what I saw that day was very interesting. I noticed that the last 4 digits werepalindromic; that is, they read the same forward as backward. For example, 5-4-4-5 isa palindrome, somyodometer could have read3-1-5-4-4-5.“One mile later, the last 5 numbers were palindromic. For example, it could have read3-6-5-4-5-6. Onemileafterthat,themiddle4outof6numberswerepalindromic. Andyou ready forthis? One milelater, all6were palindromic!“The question is,what was onthe odometer when Ifirstlooked?”WriteaPythonprogramthattestsallthesix-digitnumbersandprintsanynumbersthatsatisfytheserequirements. You can seemysolution atthinkpython.com/code/cartalk.py.Exercise 9.9 Here’s another Car Talk Puzzler you can solve withasearch 4 :“Recently I had a visit with my mom and we realized that the two digits that makeup my age when reversed resulted in her age. For example, if she’s 73, I’m 37. Wewonderedhowoftenthishashappenedovertheyearsbutwegotsidetrackedwithothertopics and wenever came upwithan answer.“WhenIgothomeIfiguredoutthatthedigitsofourageshavebeenreversiblesixtimesso far. I also figured out that if we’re lucky it would happen again in a few years, andifwe’rereallyluckyitwouldhappenonemoretimeafterthat. Inotherwords,itwouldhave happened 8times over all. So thequestion is,how old am I now?”2 www.cartalk.com/content/puzzler/transcripts/200725.3 www.cartalk.com/content/puzzler/transcripts/200803.4 www.cartalk.com/content/puzzler/transcripts/200813

9.7. Exercises 87Write a Python program that searches for solutions to this Puzzler. Hint: you might find the stringmethodzfilluseful.You can see mysolutionatthinkpython.com/code/cartalk.py.

88 Chapter 9. Casestudy: word play

Chapter 10Lists10.1 Alist isasequenceLike a string, a list is a sequence of values. In a string, the values are characters; in a list, they canbe any type. The values inalistare called elements orsometimes items.Thereareseveralwaystocreateanewlist;thesimplestistoenclosetheelementsinsquarebrackets([and]):[10, 20, 30, 40]['crunchy frog', 'ram bladder', 'lark vomit']The first example is a list of four integers. The second is a list of three strings. The elements of alist don’t have to be the same type. The following list contains a string, a float, an integer, and (lo!)another list:['spam', 2.0, 5, [10, 20]]A listwithin another listisnested.A listthat contains no elements iscalled anempty list;you can create one withempty brackets,[].As you might expect, you can assign listvalues tovariables:>>> cheeses = ['Cheddar', 'Edam', 'Gouda']>>> numbers = [17, 123]>>> empty = []>>> print cheeses, numbers, empty['Cheddar', 'Edam', 'Gouda'] [17, 123] []10.2 Listsare mutableThe syntax for accessing the elements of a list is the same as for accessing the characters of astring—thebracketoperator. Theexpressioninsidethebracketsspecifiestheindex. Rememberthattheindices startat 0:

90 Chapter 10. Lists>>> print cheeses[0]CheddarUnlikestrings,listsaremutable. Whenthebracketoperatorappearsontheleftsideofanassignment,itidentifies the element of thelistthat willbe assigned.>>> numbers = [17, 123]>>> numbers[1] = 5>>> print numbers[17, 5]The one-eth element ofnumbers,which used tobe 123, is now 5.You can think of a list as a relationship between indices and elements. This relationship is calleda mapping; each index “maps to” one of the elements. Here is a state diagram showing cheeses,numbersandempty:cheeseslist012’Cheddar’’Edam’’Gouda’listnumbers 01171235emptylistLists are represented by boxes with the word “list” outside and the elements of the list inside.cheesesreferstoalistwiththreeelementsindexed0,1and2. numberscontainstwoelements;thediagramshowsthatthevalueofthesecondelementhasbeenreassignedfrom123to5. emptyreferstoalistwithnoelements.Listindices workthe sameway as stringindices:• Any integer expression can beused as an index.• Ifyou trytoread or writean element that does not exist,you get anIndexError.• Ifan index has anegative value, itcounts backward from theend of the list.Theinoperator alsoworks on lists.>>> cheeses = ['Cheddar', 'Edam', 'Gouda']>>> 'Edam' in cheesesTrue>>> 'Brie' in cheesesFalse

10.3. Traversing alist 9110.3 TraversingalistThe most common way to traverse the elements of a list is with a for loop. The syntax is the sameas forstrings:for cheese in cheeses:print cheeseThis works well if you only need to read the elements of the list. But if you want to write or updatethe elements, you need the indices. A common way to do that is to combine the functions rangeandlen:for i in range(len(numbers)):numbers[i] = numbers[i] * 2Thislooptraversesthelistandupdateseachelement. lenreturnsthenumberofelementsinthelist.range returns a list of indices from 0 to n−1, where n is the length of the list. Each time throughthe loop i gets the index of the next element. The assignment statement in the body uses i to readtheold value ofthe element and toassignthe new value.Aforloop over an empty listnever executes thebody:for x in []:print 'This never happens.'Althoughalistcancontainanotherlist,thenestedliststillcountsasasingleelement. Thelengthofthislistisfour:['spam', 1, ['Brie', 'Roquefort', 'Pol le Veq'], [1, 2, 3]]10.4 ListoperationsThe+operator concatenates lists:>>> a = [1, 2, 3]>>> b = [4, 5, 6]>>> c = a + b>>> print c[1, 2, 3, 4, 5, 6]Similarly, the*operator repeats alistagiven number oftimes:>>> [0] * 4[0, 0, 0, 0]>>> [1, 2, 3] * 3[1, 2, 3, 1, 2, 3, 1, 2, 3]The first example repeats [0] four times. The second example repeats the list [1, 2, 3] threetimes.

92 Chapter 10. Lists10.5 ListslicesThe sliceoperator alsoworks on lists:>>> t = ['a', 'b', 'c', 'd', 'e', 'f']>>> t[1:3]['b', 'c']>>> t[:4]['a', 'b', 'c', 'd']>>> t[3:]['d', 'e', 'f']If you omit the first index, the slice starts at the beginning. If you omit the second, the slice goes totheend. Soif you omit both, the sliceisacopy of the whole list.>>> t[:]['a', 'b', 'c', 'd', 'e', 'f']Since lists are mutable, it is often useful to make a copy before performing operations that fold,spindle or mutilatelists.A sliceoperator on theleftsideof an assignment can update multipleelements:>>> t = ['a', 'b', 'c', 'd', 'e', 'f']>>> t[1:3] = ['x', 'y']>>> print t['a', 'x', 'y', 'd', 'e', 'f']10.6 ListmethodsPython provides methods that operate on lists. For example, append adds a new element to the endof alist:>>> t = ['a', 'b', 'c']>>> t.append('d')>>> print t['a', 'b', 'c', 'd']extendtakes a listas an argument and appends all ofthe elements:>>> t1 = ['a', 'b', 'c']>>> t2 = ['d', 'e']>>> t1.extend(t2)>>> print t1['a', 'b', 'c', 'd', 'e']This example leavest2unmodified.sortarranges theelements of the listfrom low tohigh:>>> t = ['d', 'c', 'e', 'b', 'a']>>> t.sort()>>> print t['a', 'b', 'c', 'd', 'e']

10.7. Map, filter and reduce 93List methods are all void; they modify the list and return None. If you accidentally write t =t.sort(),you willbe disappointed withthe result.10.7 Map,filterand reduceTo add up all thenumbers inalist,you can usealoop likethis:def add_all(t):total = 0for x in t:total += xreturn totaltotal is initialized to 0. Each time through the loop, x gets one element from the list. The +=operator provides ashortway toupdate avariable. This augmented assignment statement:total += xisequivalent to:total = total + xAs the loop executes, total accumulates the sum of the elements; a variable used this way issometimes called an accumulator.Adding up the elements of a list is such a common operation that Python provides it as a built-infunction,sum:>>> t = [1, 2, 3]>>> sum(t)6An operation like this that combines a sequence of elements into a single value is sometimes calledreduce.Sometimesyouwanttotraverseonelistwhilebuildinganother. Forexample,thefollowingfunctiontakes a listof stringsand returns anew listthat contains capitalized strings:def capitalize_all(t):res = []for s in t:res.append(s.capitalize())return resres is initialized with an empty list; each time through the loop, we append the next element. Soresisanother kind of accumulator.Anoperationlikecapitalize_allissometimescalledamapbecauseit“maps”afunction(inthiscase themethodcapitalize)onto each of theelements inasequence.Anothercommonoperationistoselectsomeoftheelementsfromalistandreturnasublist. Forexample,thefollowingfunctiontakesalistofstringsandreturnsalistthatcontainsonlytheuppercasestrings:

94 Chapter 10. Listsdef only_upper(t):res = []for s in t:if s.isupper():res.append(s)return resisupperisastringmethod that returnsTrueifthestringcontains only upper case letters.An operation like only_upper is called a filter because it selects some of the elements and filtersout the others.Most common list operations can be expressed as a combination of map, filter and reduce. Becausethese operations are so common, Python provides language features to support them, including thebuilt-infunctionmapand an operator called a“listcomprehension.”Exercise 10.1 Write a function that takes a list of numbers and returns the cumulative sum; thatis, a new list where the ith element is the sum of the first i+1 elements from the original list. Forexample, the cumulative sum of[1, 2, 3]is[1, 3, 6].10.8 DeletingelementsThere are several ways to delete elements from a list. If you know the index of the element youwant, you can usepop:>>> t = ['a', 'b', 'c']>>> x = t.pop(1)>>> print t['a', 'c']>>> print xbpop modifies the list and returns the element that was removed. If you don’t provide an index, itdeletes and returns thelastelement.Ifyou don’t need the removed value, you can use thedeloperator:>>> t = ['a', 'b', 'c']>>> del t[1]>>> print t['a', 'c']Ifyou know theelement you want toremove (but not theindex), you can useremove:>>> t = ['a', 'b', 'c']>>> t.remove('b')>>> print t['a', 'c']The returnvalue fromremoveisNone.To remove more than one element, you can usedelwithasliceindex:

10.9. Listsand strings 95>>> t = ['a', 'b', 'c', 'd', 'e', 'f']>>> del t[1:5]>>> print t['a', 'f']As usual, thesliceselects allthe elements up to,but not including, the second index.10.9 Listsand stringsA string is a sequence of characters and a list is a sequence of values, but a list of characters is notthesame as astring. To convert from astringtoalistof characters, you can uselist:>>> s = 'spam'>>> t = list(s)>>> print t['s', 'p', 'a', 'm']Becauselististhenameofabuilt-infunction,youshouldavoidusingitasavariablename. Ialsoavoidlbecause itlooks too much like1. Sothat’s why I uset.The list function breaks a string into individual letters. If you want to break a string into words,you can use thesplitmethod:>>> s = 'pining for the fjords'>>> t = s.split()>>> print t['pining', 'for', 'the', 'fjords']An optional argument called a delimiter specifies which characters to use as word boundaries. Thefollowing example uses a hyphen as adelimiter:>>> s = 'spam-spam-spam'>>> delimiter = '-'>>> s.split(delimiter)['spam', 'spam', 'spam']joinistheinverseofsplit. Ittakesalistofstringsandconcatenatestheelements. joinisastringmethod, soyou have toinvoke itonthe delimiter and pass thelistas aparameter:>>> t = ['pining', 'for', 'the', 'fjords']>>> delimiter = ' '>>> delimiter.join(t)'pining for the fjords'In this case the delimiter is a space character, so join puts a space between words. To concatenatestringswithout spaces, you can use theempty string,'', as adelimiter.10.10 Objectsand valuesIfweexecute theseassignment statements:

96 Chapter 10. Listsa = 'banana'b = 'banana'Weknowthataandbbothrefertoastring,butwedon’tknowwhethertheyrefertothesamestring.There aretwo possiblestates:ab’banana’’banana’ab’banana’In one case,aandbrefer to two different objects that have the same value. In the second case, theyrefer tothe sameobject.To check whether twovariables refertothe sameobject, you can use theisoperator.>>> a = 'banana'>>> b = 'banana'>>> a is bTrueInthisexample, Python only created one stringobject, and bothaandbrefertoit.But when you create twolists,you get two objects:>>> a = [1, 2, 3]>>> b = [1, 2, 3]>>> a is bFalseSo thestatediagram looks likethis:ab[ 1, 2, 3 ][ 1, 2, 3 ]In this case we would say that the two lists are equivalent, because they have the same elements,but not identical, because they are not the same object. If two objects are identical, they are alsoequivalent, but ifthey are equivalent, they arenot necessarily identical.Until now, we have been using “object” and “value” interchangeably, but it is more precise to saythat an object has a value. If you execute [1,2,3], you get a list object whose value is a sequenceofintegers. Ifanotherlisthasthesameelements,wesayithasthesamevalue,butitisnotthesameobject.10.11 AliasingIfareferstoan object and you assignb = a,then both variables refertothe sameobject:>>> a = [1, 2, 3]>>> b = a>>> b is aTrue

10.12. Listarguments 97The statediagram looks likethis:ab[ 1, 2, 3 ]The association of a variable with an object is called a reference. In this example, there are tworeferences tothesame object.Anobjectwithmorethanonereferencehasmorethanonename,sowesaythattheobjectisaliased.Ifthealiased object ismutable, changes made withone alias affect the other:>>> b[0] = 17>>> print a[17, 2, 3]Although this behavior can be useful, it is error-prone. In general, it is safer to avoid aliasing whenyou are working withmutable objects.For immutable objects likestrings,aliasing isnot as much ofaproblem. Inthisexample:a = 'banana'b = 'banana'Italmost never makes adifference whetheraandbrefertothe samestringor not.10.12 ListargumentsWhen you pass a list to a function, the function gets a reference to the list. If the function modifiesa list parameter, the caller sees the change. For example, delete_head removes the first elementfrom alist:def delete_head(t):del t[0]Here’s how itisused:>>> letters = ['a', 'b', 'c']>>> delete_head(letters)>>> print letters['b', 'c']The parameter t and the variable letters are aliases for the same object. The stack diagram lookslikethis:__main__letterslist0’a’delete_headt12’b’’c’

98 Chapter 10. ListsSince the listisshared by twoframes, Idrew itbetween them.It is important to distinguish between operations that modify lists and operations that create newlists. For example, theappendmethod modifies a list,but the+operator creates anew list:>>> t1 = [1, 2]>>> t2 = t1.append(3)>>> print t1[1, 2, 3]>>> print t2None>>> t3 = t1 + [3]>>> print t3[1, 2, 3]>>> t2 is t3FalseThisdifferenceisimportantwhenyouwritefunctionsthataresupposedtomodifylists. Forexample,thisfunction does not delete thehead of alist:def bad_delete_head(t):t = t[1:]# WRONG!Thesliceoperatorcreatesanewlistandtheassignmentmakestrefertoit,butnoneofthathasanyeffect on the listthat was passed as an argument.An alternative is to write a function that creates and returns a new list. For example, tail returnsall but thefirst element of alist:def tail(t):return t[1:]This function leaves the original listunmodified. Here’s how itisused:>>> letters = ['a', 'b', 'c']>>> rest = tail(letters)>>> print rest['b', 'c']Exercise 10.2 Write a function called chop that takes a list and modifies it, removing the first andlastelements, and returnsNone.Then write a function called middle that takes a list and returns a new list that contains all but thefirstand last elements.10.13 DebuggingCarelessuseoflists(andothermutableobjects)canleadtolonghoursofdebugging. Herearesomecommon pitfallsand ways toavoid them:1. Don’tforgetthatmostlistmethodsmodifytheargumentandreturnNone. Thisistheoppositeof the stringmethods, which returnanew stringand leave theoriginal alone.Ifyou areused towritingstringcode likethis:

10.14. Glossary 99word = word.strip()Itis tempting towritelistcode likethis:t = t.sort()# WRONG!BecausesortreturnsNone,thenext operation you perform withtislikelytofail.Beforeusinglistmethodsandoperators,youshouldreadthedocumentationcarefullyandthentestthemininteractivemode. Themethodsandoperatorsthatlistssharewithothersequences(like strings) are documented at docs.python.org/lib/typesseq.html. The methods andoperators that only apply to mutable sequences are documented at docs.python.org/lib/typesseq-mutable.html.2. Pick an idiom and stickwithit.Part of the problem with lists is that there are too many ways to do things. For example, toremove anelement fromalist,you can usepop,remove,del,oreven asliceassignment.To add an element, you can use the append method or the + operator. Assuming that t is alistandxisalistelement, these areright:t.append(x)t = t + [x]And these arewrong:t.append([x])t = t.append(x)t + [x]t = t + x# WRONG!# WRONG!# WRONG!# WRONG!Try out each of these examples in interactive mode to make sure you understand what theydo. Notice that only the last one causes a runtime error; the other three are legal, but they dothe wrong thing.3. Make copies toavoid aliasing.If you want to use a method like sort that modifies the argument, but you need to keep theoriginal listas well, you can make a copy.orig = t[:]t.sort()In this example you could also use the built-in function sorted, which returns a new, sortedlistandleavestheoriginalalone. Butinthatcaseyoushouldavoidusingsortedasavariablename!10.14 Glossarylist: A sequence of values.element: One of the values inalist(orother sequence), alsocalled items.index: Aninteger value that indicates an element inalist.

100 Chapter 10. Listsnested list: A listthat isan element of another list.listtraversal: The sequential accessing ofeach element inalist.mapping: A relationship in which each element of one set corresponds to an element of anotherset. For example, alistisamapping from indices toelements.accumulator: A variable used inaloop toadd up oraccumulate aresult.augmented assignment: Astatementthatupdatesthevalueofavariableusinganoperatorlike+=.reduce: A processing pattern that traverses a sequence and accumulates the elements into a singleresult.map: A processing pattern that traverses asequence and performs an operation oneach element.filter: Aprocessingpatternthattraversesalistandselectstheelementsthatsatisfysomecriterion.object: Something a variable can refer to. An object has atype and avalue.equivalent: Having thesame value.identical: Being the sameobject (whichimplies equivalence).reference: The association between avariable and itsvalue.aliasing: A circumstance where twoor morevariables refer tothesame object.delimiter: A character or stringusedtoindicate where astringshould be split.10.15 ExercisesExercise 10.3 Write a function called is_sorted that takes a list as a parameter and returns TrueifthelistissortedinascendingorderandFalseotherwise. Youcanassume(asaprecondition)thattheelements of the listcan be compared withthe relational operators,etc.For example, is_sorted([1,2,2]) should return True and is_sorted(['b','a']) should returnFalse.Exercise 10.4 Two words are anagrams if you can rearrange the letters from one to spell the other.Writeafunction calledis_anagramthat takes twostringsand returnsTrueif they areanagrams.Exercise 10.5 The (so-called) Birthday Paradox:1. Write a function called has_duplicates that takes a list and returns True if there is anyelement that appears more than once. It should not modify theoriginal list.2. If there are 23 students in your class, what are the chances that two of you have the samebirthday? Youcanestimatethisprobabilitybygeneratingrandomsamplesof23birthdaysandcheckingformatches. Hint: youcangeneraterandombirthdayswiththerandintfunctionintherandommodule.You can read about this problem at wikipedia.org/wiki/Birthday_paradox, and you can seemysolution atthinkpython.com/code/birthday.py.

10.15. Exercises 101Exercise 10.6 Write a function called remove_duplicates that takes a list and returns a new listwithonly theunique elements from theoriginal. Hint: they don’t have tobe inthe sameorder.Exercise10.7 Writeafunctionthatreadsthefilewords.txtandbuildsalistwithoneelementperword. Write two versions of this function, one using the append method and the other using theidiomt = t + [x]. Which one takes longer torun? Why?You can see mysolutionatthinkpython.com/code/wordlist.py.Exercise 10.8 To check whether a word is in the word list, you could use the in operator, but itwould be slow because itsearches through thewords inorder.Because the words are in alphabetical order, we can speed things up with a bisection search (alsoknownasbinarysearch),whichissimilartowhatyoudowhenyoulookawordupinthedictionary.You start in the middle and check to see whether the word you are looking for comes before thewordinthemiddleofthelist. Ifso,thenyousearchthefirsthalfofthelistthesameway. Otherwiseyou search thesecond half.Either way, you cut the remaining search space in half. If the word list has 113,809 words, it willtake about 17 steps tofind theword orconclude that it’snot there.Writeafunctioncalledbisectthattakesasortedlistandatargetvalueandreturnstheindexofthevalue inthelist,ifit’sthere, orNoneifit’snot.Or you could read thedocumentation of thebisectmodule and usethat!Exercise 10.9 Two words are a “reverse pair” if each is the reverse of the other. Write a programthat finds all thereverse pairs intheword list.Exercise 10.10 Two words “interlock” if taking alternating letters from each forms a new word 1 .For example, “shoe” and “cold” interlock toform“schooled.”1. Writeaprogram that finds all pairsof words that interlock. Hint: don’t enumerate all pairs!2. Canyoufindanywordsthatarethree-wayinterlocked;thatis,everythirdletterformsaword,startingfrom thefirst,second orthird?1 This exercise is inspired byanexampleatpuzzlers.org.

102 Chapter 10. Lists

Chapter 11DictionariesAdictionaryislikealist,butmoregeneral. Inalist,theindiceshavetobeintegers;inadictionarythey can be(almost)any type.You can think of a dictionary as a mapping between a set of indices (which are called keys) and aset of values. Each key maps to a value. The association of a key and a value is called a key-valuepair or sometimes an item.As an example, we’ll build a dictionary that maps from English to Spanish words, so the keys andthevalues areall strings.The function dict creates a new dictionary with no items. Because dict is the name of a built-infunction, you should avoid using itas avariable name.>>> eng2sp = dict()>>> print eng2sp{}The squiggly-brackets, {}, represent an empty dictionary. To add items to the dictionary, you canusesquare brackets:>>> eng2sp['one'] = 'uno'Thislinecreatesanitemthatmapsfromthekey’one’tothevalue'uno'. Ifweprintthedictionaryagain, weseeakey-value pair withacolon between the key and value:>>> print eng2sp{'one': 'uno'}This output format is also an input format. For example, you can create a new dictionary with threeitems:>>> eng2sp = {'one': 'uno', 'two': 'dos', 'three': 'tres'}But ifyou printeng2sp,you might besurprised:>>> print eng2sp{'one': 'uno', 'three': 'tres', 'two': 'dos'}

104 Chapter 11. DictionariesTheorderofthekey-valuepairsisnotthesame. Infact,ifyoutypethesameexampleonyourcomputer,youmightgetadifferentresult.Ingeneral,theorderofitemsinadictionaryisunpredictable.Butthat’snotaproblembecausetheelementsofadictionaryareneverindexedwithintegerindices.Instead, you usethekeys tolook up thecorresponding values:>>> print eng2sp['two']'dos'The key’two’always maps tothe value'dos'sotheorder ofthe itemsdoesn’t matter.Ifthekey isn’tinthedictionary, you get an exception:>>> print eng2sp['four']KeyError: 'four'Thelenfunction works ondictionaries; itreturns thenumber of key-value pairs:>>> len(eng2sp)3Theinoperatorworksondictionaries;ittellsyouwhethersomethingappearsasakeyinthedictionary(appearing as avalue isnot good enough).>>> 'one' in eng2spTrue>>> 'uno' in eng2spFalseToseewhethersomethingappearsasavalueinadictionary,youcanusethemethodvalues,whichreturns thevalues as a list,and then usetheinoperator:>>> vals = eng2sp.values()>>> 'uno' in valsTrueThe in operator uses different algorithms for lists and dictionaries. For lists, it uses a searchalgorithm, as in Section 8.6. As the list gets longer, the search time gets longer in direct proportion.For dictionaries, Python uses an algorithm called a hashtable that has a remarkableproperty: the in operator takes about the same amount of time no matter how many items thereare in a dictionary. I won’t explain how that’s possible, but you can read more about it atwikipedia.org/wiki/Hash_table.Exercise 11.1 Write a function that reads the words in words.txt and stores them as keys in adictionary. It doesn’t matter what the values are. Then you can use the in operator as a fast way tocheck whether a stringisinthedictionary.IfyoudidExercise10.8,youcancomparethespeedofthisimplementationwiththelistinoperatorand the bisection search.11.1 DictionaryasasetofcountersSuppose you are given a string and you want to count how many times each letter appears. Thereareseveral ways you could doit:

11.1. Dictionary as asetof counters 1051. Youcouldcreate26variables,oneforeachletterofthealphabet. Thenyoucouldtraversethestringand,foreachcharacter,incrementthecorresponding counter,probablyusingachainedconditional.2. You could create a list with 26 elements. Then you could convert each character to a number(using the built-in function ord), use the number as an index into the list, and increment theappropriate counter.3. Youcouldcreateadictionarywithcharactersaskeysandcountersasthecorrespondingvalues.The first time you see a character, you would add an item to the dictionary. After that youwould increment thevalue of an existingitem.Eachoftheseoptionsperformsthesamecomputation,buteachofthemimplementsthatcomputationinadifferent way.An implementation is a way of performing a computation; some implementations are better thanothers. For example, an advantage of the dictionary implementation is that we don’t have to knowahead of time which letters appear in the string and we only have to make room for the letters thatdo appear.Here iswhat the code might look like:def histogram(s):d = dict()for c in s:if c not in d:d[c] = 1else:d[c] += 1return dThe name of the function is histogram, which is a statistical term for a set of counters (or frequencies).The first line of the function creates an empty dictionary. The for loop traverses the string. Eachtimethroughtheloop,ifthecharactercisnotinthedictionary,wecreateanewitemwithkeycandtheinitialvalue1(sincewehaveseenthisletteronce). Ifcisalreadyinthedictionaryweincrementd[c].Here’s how itworks:>>> h = histogram('brontosaurus')>>> print h{'a': 1, 'b': 1, 'o': 2, 'n': 1, 's': 2, 'r': 2, 'u': 2, 't': 1}The histogram indicates that theletters’a’and'b'appear once;'o'appears twice, and soon.Exercise11.2 Dictionarieshaveamethodcalledgetthattakesakeyandadefaultvalue. Ifthekeyappearsinthedictionary,getreturnsthecorrespondingvalue;otherwiseitreturnsthedefaultvalue.For example:>>> h = histogram('a')>>> print h{'a': 1}

106 Chapter 11. Dictionaries>>> h.get('a', 0)1>>> h.get('b', 0)0Usegettowritehistogrammoreconcisely. You should be able toeliminatetheifstatement.11.2 Looping and dictionariesIf you use a dictionary in a for statement, it traverses the keys of the dictionary. For example,print_histprints each key and thecorresponding value:def print_hist(h):for c in h:print c, h[c]Here’s what theoutput looks like:>>> h = histogram('parrot')>>> print_hist(h)a 1p 1r 2t 1o 1Again, the keys areinno particular order.Exercise 11.3 Dictionaries have a method called keys that returns the keys of the dictionary, in noparticular order,as alist.Modifyprint_histtoprint thekeys and their values inalphabetical order.11.3 ReverselookupGivenadictionarydandakeyk,itiseasytofindthecorrespondingvaluev = d[k]. Thisoperationiscalled alookup.But what if you have v and you want to find k? You have two problems: first, there might be morethanonekeythatmapstothevaluev. Dependingontheapplication,youmightbeabletopickone,or you might have to make a list that contains all of them. Second, there is no simple syntax to do areverse lookup; you have tosearch.Here isafunction that takes avalue and returnsthe firstkey that maps tothat value:def reverse_lookup(d, v):for k in d:if d[k] == v:return kraise ValueError

11.4. Dictionaries and lists 107This function is yet another example of the search pattern, but it uses a feature we haven’t seenbefore, raise. The raise statement causes an exception; in this case it causes a ValueError,which generally indicates that thereissomething wrong withthevalue of aparameter.Ifwegettotheendoftheloop,thatmeansvdoesn’tappearinthedictionaryasavalue,soweraisean exception.Here isanexample of asuccessful reverse lookup:>>> h = histogram('parrot')>>> k = reverse_lookup(h, 2)>>> print krAnd an unsuccessful one:>>> k = reverse_lookup(h, 3)Traceback (most recent call last):File "", line 1, in ?File "", line 5, in reverse_lookupValueErrorThe result when you raise an exception is the same as when Python raises one: it prints a tracebackand an errormessage.Theraisestatement takes adetailed error message as anoptional argument. For example:>>> raise ValueError, 'value does not appear in the dictionary'Traceback (most recent call last):File "", line 1, in ?ValueError: value does not appear in the dictionaryAreverselookupismuchslowerthanaforwardlookup;ifyouhavetodoitoften,orifthedictionarygets big, the performance of your program will suffer.Exercise11.4 Modifyreverse_lookupsothatitbuildsandreturnsalistofallkeysthatmaptov,or an empty listifthere arenone.11.4 Dictionariesand listsLists can appear as values in a dictionary. For example, if you were given a dictionary that mapsfrom letters to frequencies, you might want to invert it; that is, create a dictionary that maps fromfrequenciestoletters. Sincetheremightbeseveralletterswiththesamefrequency,eachvalueintheinverted dictionary should bealistof letters.Here isafunction that inverts adictionary:def invert_dict(d):inv = dict()for key in d:val = d[key]if val not in inv:inv[val] = [key]

108 Chapter 11. Dictionarieselse:inv[val].append(key)return invEach time through the loop, key gets a key from d and val gets the corresponding value. If valis not in inv, that means we haven’t seen it before, so we create a new item and initialize it with asingleton (a list that contains a single element). Otherwise we have seen this value before, so weappend thecorresponding key tothe list.Here isanexample:>>> hist = histogram('parrot')>>> print hist{'a': 1, 'p': 1, 'r': 2, 't': 1, 'o': 1}>>> inv = invert_dict(hist)>>> print inv{1: ['a', 'p', 't', 'o'], 2: ['r']}And here isadiagram showinghistandinv:dictdictlisthist’a’ 1inv10’a’’p’11’p’’r’ 22 ’t’’t’13’o’’o’ 1list2 0’r’A dictionary is represented as a box with the type dict above it and the key-value pairs inside. Ifthe values are integers, floats or strings, I usually draw them inside the box, but I usually draw listsoutside thebox, justtokeep thediagram simple.Lists can be values in a dictionary, as this example shows, but they cannot be keys. Here’s whathappens ifyou try:>>> t = [1, 2, 3]>>> d = dict()>>> d[t] = 'oops'Traceback (most recent call last):File "", line 1, in ?TypeError: list objects are unhashableI mentioned earlier that a dictionary is implemented using a hashtable and that means that the keyshave tobe hashable.A hash is a function that takes a value (of any kind) and returns an integer. Dictionaries use theseintegers, called hashvalues, tostoreand look up key-value pairs.This system works fine if the keys are immutable. But if the keys are mutable, like lists, bad thingshappen. For example, when you create a key-value pair, Python hashes the key and stores it in the

11.5. Memos 109corresponding location. If you modify the key and then hash it again, it would go to a differentlocation. In that case you might have two entries for the same key, or you might not be able to findakey. Either way, thedictionary wouldn’t workcorrectly.That’s why the keys have to be hashable, and why mutable types like lists aren’t. The simplest waytoget around thislimitationistousetuples, which wewillseeinthe next chapter.Since dictionaries aremutable, they can’t be used as keys, but they can be used as values.Exercise 11.5 Read the documentation of the dictionary method setdefault and use it to write amore concise version ofinvert_dict.11.5 MemosIfyouplayedwiththefibonaccifunctionfromSection6.7,youmighthavenoticedthatthebiggerthe argument you provide, the longer the function takes to run. Furthermore, the run time increasesvery quickly.To understand why, consider this call graph forfibonacciwithn=4:fibonaccin 4fibonaccin 3fibonaccin 2fibonaccin 2fibonaccin 1fibonaccin 1fibonaccin 0fibonaccin 1fibonaccin 0A call graph shows a set of function frames, with lines connecting each frame to the frames of thefunctions it calls. At the top of the graph, fibonacci with n=4 calls fibonacci with n=3 and n=2.Inturn,fibonacciwithn=3callsfibonacciwithn=2andn=1. And soon.Counthowmanytimesfibonacci(0)andfibonacci(1)arecalled. Thisisaninefficientsolutiontotheproblem, and it gets worseas theargument gets bigger.One solution is to keep track of values that have already been computed by storing them in a dictionary.A previously computed value that is stored for later use is called a memo 1 . Here is animplementation offibonacciusingmemos:known = {0:0, 1:1}def fibonacci(n):if n in known:return known[n]res = fibonacci(n-1) + fibonacci(n-2)1 Seewikipedia.org/wiki/Memoization.

110 Chapter 11. Dictionariesknown[n] = resreturn resknownis a dictionary that keeps track of the Fibonacci numbers we already know. It starts with twoitems: 0maps to0and 1maps to1.Wheneverfibonacciiscalled,itchecksknown. Iftheresultisalreadythere,itcanreturnimmediately.Otherwiseithas tocompute thenew value, add ittothe dictionary, and returnit.Exercise 11.6 Run this version of fibonacci and the original with a range of parameters andcompare their runtimes.11.6 Global variablesIn the previous example, known is created outside the function, so it belongs to the special framecalled__main__. Variablesin__main__aresometimescalledglobalbecausetheycanbeaccessedfrom any function. Unlike local variables, which disappear when their function ends, global variablespersistfrom one function call tothenext.Itiscommontouseglobalvariablesforflags;thatis,booleanvariablesthatindicate(“flag”)whethera condition is true. For example, some programs use a flag named verbose to control the level ofdetail inthe output:verbose = Truedef example1():if verbose:print 'Running example1'If you try to reassign a global variable, you might be surprised. The following example is supposedtokeep trackof whether the function has been called:been_called = Falsedef example2():been_called = True# WRONGBut if you run it you will see that the value of been_called doesn’t change. The problem is thatexample2 creates a new local variable named been_called. The local variable goes away whenthefunction ends, and has noeffect on theglobal variable.To reassign a global variable inside a function you have to declare the global variable before youuseit:been_called = Falsedef example2():global been_calledbeen_called = TrueThe global statement tells the interpreter something like, “In this function, when I saybeen_called,Imean the global variable; don’t create alocal one.”Here’s an example that triestoupdate aglobal variable:

11.7. Long integers 111count = 0def example3():count = count + 1# WRONGIfyou runit you get:UnboundLocalError: local variable 'count' referenced before assignmentPython assumes that count is local, which means that you are reading it before writing it. Thesolution, again, istodeclarecountglobal.def example3():global countcount += 1Iftheglobal value ismutable, you can modifyit without declaring it:known = {0:0, 1:1}def example4():known[2] = 1Soyoucanadd,removeandreplaceelementsofagloballistordictionary,butifyouwanttoreassignthevariable, you have todeclare it:def example5():global knownknown = dict()11.7 Long integersIfyou computefibonacci(50),you get:>>> fibonacci(50)12586269025LTheLat the end indicates that theresult isalong integer 2 , or typelong.Valueswithtypeinthavealimitedrange;longintegerscanbearbitrarilybig,butastheygetbiggerthey consume more space and time.Themathematical operators workonlong integers,and thefunctions inthemathmodule, too, soingeneral any code that works withintwillalsowork withlong.Any time the result of a computation is too big to be represented with an integer, Python convertstheresult as along integer:>>> 1000 * 10001000000>>> 100000 * 10000010000000000L2 InPython3.0, typelongis gone;all integers, evenreally bigones, are typeint.

112 Chapter 11. DictionariesInthefirstcase the resulthas typeint;inthe second case itislong.Exercise 11.7 Exponentiation of large integers is the basis of common algorithms for public-keyencryption. Read the Wikipedia page on the RSA algorithm 3 and write functions to encode anddecode messages.11.8 DebuggingAs you work with bigger datasets it can become unwieldy to debug by printing and checking databy hand. Herearesome suggestions fordebugging large datasets:Scale down theinput: Ifpossible,reducethesizeofthedataset. Forexampleiftheprogramreadsatextfile,startwithjustthefirst10lines,orwiththesmallestexampleyoucanfind. Youcaneithereditthefilesthemselves,or(better)modifytheprogramsoitreadsonlythefirstnlines.If there is an error, you can reduce n to the smallest value that manifests the error, and thenincrease it gradually as you find and correct errors.Check summaries and types: Insteadofprintingandcheckingtheentiredataset,considerprintingsummaries of the data: for example, the number of items in a dictionary or the total of a listof numbers.A common cause of runtime errors is a value that is not the right type. For debugging thiskind of error,itisoften enough toprint the type ofavalue.Writeself-checks: Sometimes you can write code to check for errors automatically. For example,if you are computing the average of a list of numbers, you could check that the result is notgreater than the largest element in the list or less than the smallest. This is called a “sanitycheck” because itdetects resultsthat are “insane.”Another kind of check compares the results of two different computations to see if they areconsistent. This iscalled a“consistency check.”Pretty print the output: Formatting debugging output can make it easier to spot an error. We sawan example in Section 6.9. The pprint module provides a pprint function that displaysbuilt-intypes inamorehuman-readable format.Again, timeyou spend building scaffolding can reduce thetimeyou spend debugging.11.9 Glossarydictionary: A mapping fromaset of keys totheir corresponding values.key-value pair: The representation of themapping from akey toavalue.item: Another name forakey-value pair.key: An object that appears inadictionary as thefirstpart ofakey-value pair.value: An object that appears in a dictionary as the second part of a key-value pair. This is morespecific than our previous use of theword “value.”3 wikipedia.org/wiki/RSA.

11.10. Exercises 113implementation: A way of performing acomputation.hashtable: The algorithm usedtoimplement Python dictionaries.hash function: A function used by ahashtable tocompute thelocation for akey.hashable: A type that has a hash function. Immutable types like integers, floats and strings arehashable; mutable types likelistsand dictionaries arenot.lookup: A dictionary operation that takes akey and finds the corresponding value.reverse lookup: A dictionary operation that takes a value and finds one or more keys that map toit.singleton: A list(orother sequence) withasingleelement.call graph: A diagram that shows every frame created during the execution of a program, with anarrow from each caller toeach callee.histogram: Aset of counters.memo: A computed value stored toavoid unnecessary futurecomputation.global variable: A variable defined outside a function. Global variables can be accessed from anyfunction.flag: Aboolean variable used toindicate whether acondition istrue.declaration: A statement likeglobalthat tellstheinterpreter something about avariable.11.10 ExercisesExercise 11.8 If you did Exercise 10.5, you already have a function named has_duplicates thattakes a list as a parameter and returns True if there is any object that appears more than once in thelist.Useadictionary towriteafaster,simpler version ofhas_duplicates.Exercise 11.9 Two words are “rotate pairs” if you can rotate one of them and get the other (seerotate_wordinExercise 8.12).Writeaprogram that reads awordlist and finds allthe rotatepairs.Exercise 11.10 Here’s another Puzzler from Car Talk 4 :This was sent in by a fellow named Dan O’Leary. He came upon a common onesyllable,five-letter word recently that has the following unique property. When youremove the first letter, the remaining letters form a homophone of the original word,that is a word that sounds exactly the same. Replace the first letter, that is, put it backand remove the second letter and the result is yet another homophone of the originalword. And thequestion is,what’s the word?Now I’m going to give you an example that doesn’t work. Let’s look at the five-letterword, ‘wrack.’ W-R-A-C-K, you know like to ‘wrack with pain.’ If I remove the first4 www.cartalk.com/content/puzzler/transcripts/200717.

114 Chapter 11. Dictionariesletter, I am left with a four-letter word, ’R-A-C-K.’ As in, ‘Holy cow, did you see therack on that buck! It must have been a nine-pointer!’ It’s a perfect homophone. If youput the ‘w’ back, and remove the ‘r,’ instead, you’re left with the word, ‘wack,’ whichisareal word, it’sjust not ahomophone of theother twowords.Butthereis,however, atleastonewordthatDanandweknowof,whichwillyieldtwohomophones if you remove either of the first two letters to make two, new four-letterwords. The question is,what’s theword?You can use thedictionary from Exercise 11.1 tocheck whether astringisinthe wordlist.To check whether two words are homophones, you can use the CMU Pronouncing Dictionary. Youcan download it from www.speech.cs.cmu.edu/cgi-bin/cmudict or from thinkpython.com/code/c06d and you can also download thinkpython.com/code/pronounce.py, which providesa function named read_dictionary that reads the pronouncing dictionary and returns a Pythondictionary that maps from each word toastringthat describes itsprimarypronunciation.Write a program that lists all the words that solve the Puzzler. You can see my solution atthinkpython.com/code/homophone.py.

Chapter 12Tuples12.1 Tuples areimmutableA tuple is a sequence of values. The values can be any type, and they are indexed by integers, so inthat respect tuples arealotlikelists. The important difference isthat tuples are immutable.Syntactically, atuple isacomma-separated listofvalues:>>> t = 'a', 'b', 'c', 'd', 'e'Although itisnot necessary, itiscommon toenclose tuples inparentheses:>>> t = ('a', 'b', 'c', 'd', 'e')To create atuple withasingleelement, you have toinclude afinal comma:>>> t1 = 'a',>>> type(t1)A value inparentheses isnot atuple:>>> t2 = ('a')>>> type(t2)Another way to create a tuple is the built-in function tuple. With no argument, it creates an emptytuple:>>> t = tuple()>>> print t()If the argument is a sequence (string, list or tuple), the result is a tuple with the elements of thesequence:>>> t = tuple('lupins')>>> print t('l', 'u', 'p', 'i', 'n', 's')

116 Chapter 12. TuplesBecausetupleisthename of abuilt-infunction, you should avoid using itas avariable name.Most listoperators alsoworkon tuples. The bracket operator indexes an element:>>> t = ('a', 'b', 'c', 'd', 'e')>>> print t[0]'a'And thesliceoperator selects arange ofelements.>>> print t[1:3]('b', 'c')But ifyou trytomodify one of theelements of thetuple, you get an error:>>> t[0] = 'A'TypeError: object doesn't support item assignmentYou can’t modifythe elements of atuple, but you can replace one tuplewithanother:>>> t = ('A',) + t[1:]>>> print t('A', 'b', 'c', 'd', 'e')12.2 Tuple assignmentIt is often useful to swap the values of two variables. With conventional assignments, you have touseatemporary variable. For example, toswapaandb:>>> temp = a>>> a = b>>> b = tempThis solutioniscumbersome; tuple assignment ismoreelegant:>>> a, b = b, aThe left side is a tuple of variables; the right side is a tuple of expressions. Each value is assignedto its respective variable. All the expressions on the right side are evaluated before any of theassignments.The number ofvariables onthe leftand the number of values on theright have tobe thesame:>>> a, b = 1, 2, 3ValueError: too many values to unpackMore generally, the right side can be any kind of sequence (string, list or tuple). For example, tosplitan email address intoauser name and a domain, you could write:>>> addr = 'monty@python.org'>>> uname, domain = addr.split('@')The return value from split is a list with two elements; the first element is assigned to uname, thesecond todomain.

12.3. Tuples as return values 117>>> print unamemonty>>> print domainpython.org12.3 Tuples as returnvaluesStrictly speaking, a function can only return one value, but if the value is a tuple, the effect is thesameasreturningmultiplevalues. Forexample, ifyouwanttodividetwointegersandcomputethequotient and remainder, it is inefficient to compute x/y and then x%y. It is better to compute themboth at thesame time.The built-in function divmod takes two arguments and returns a tuple of two values, the quotientand remainder. You can storetheresult asatuple:>>> t = divmod(7, 3)>>> print t(2, 1)Or usetuple assignment tostoretheelements separately:>>> quot, rem = divmod(7, 3)>>> print quot2>>> print rem1Here isanexample of afunction that returns atuple:def min_max(t):return min(t), max(t)maxandminarebuilt-infunctionsthatfindthelargestandsmallestelementsofasequence. min_maxcomputes both and returnsatupleof twovalues.12.4 Variable-lengthargument tuplesFunctions can take a variable number of arguments. A parameter name that begins with * gathersarguments into atuple. For example,printalltakes any number of arguments and prints them:def printall(*args):print argsThegatherparametercanhaveanynameyoulike,butargsisconventional. Here’showthefunctionworks:>>> printall(1, 2.0, '3')(1, 2.0, '3')The complement of gather is scatter. If you have a sequence of values and you want to pass it to afunction as multiple arguments, you can use the * operator. For example, divmod takes exactly twoarguments; itdoesn’t workwithatuple:

118 Chapter 12. Tuples>>> t = (7, 3)>>> divmod(t)TypeError: divmod expected 2 arguments, got 1But ifyou scatterthe tuple, itworks:>>> divmod(*t)(2, 1)Exercise 12.1 Many of the built-in functions use variable-length argument tuples. For example,maxandmincan take any number of arguments:>>> max(1,2,3)3Butsumdoes not.>>> sum(1,2,3)TypeError: sum expected at most 2 arguments, got 3Writeafunction calledsumallthat takes any number of arguments and returns theirsum.12.5 Listsand tupleszip is a built-in function that takes two or more sequences and “zips” them into a list 1 of tupleswhere each tuplecontains one element from each sequence.This example zips a stringand alist:>>> s = 'abc'>>> t = [0, 1, 2]>>> zip(s, t)[('a', 0), ('b', 1), ('c', 2)]Theresultisalistoftupleswhereeachtuplecontainsacharacterfromthestringandthecorrespondingelementfromthe list.Ifthesequences arenot the samelength, the resulthas the length of theshorter one.>>> zip('Anne', 'Elk')[('A', 'E'), ('n', 'l'), ('n', 'k')]You can use tupleassignment inaforloop totraversealistof tuples:t = [('a', 0), ('b', 1), ('c', 2)]for letter, number in t:print number, letterEach time through the loop, Python selects the next tuple in the list and assigns the elements toletterandnumber. The output ofthis loop is:0 a1 b2 c1 InPython3.0,zipreturns aniterator oftuples, but formost purposes, aniterator behaves like alist.

12.6. Dictionaries and tuples 119If you combine zip, for and tuple assignment, you get a useful idiom for traversing two (or more)sequences at the same time. For example, has_match takes two sequences, t1 and t2, and returnsTrueifthere isanindexisuch thatt1[i] == t2[i]:def has_match(t1, t2):for x, y in zip(t1, t2):if x == y:return Truereturn FalseIfyouneedtotraversetheelementsofasequenceandtheirindices,youcanusethebuilt-infunctionenumerate:for index, element in enumerate('abc'):print index, elementThe output of thisloop is:0 a1 b2 cAgain.12.6 Dictionariesand tuplesDictionarieshaveamethodcalleditemsthatreturnsalistoftuples,whereeachtupleisakey-valuepair 2 .>>> d = {'a':0, 'b':1, 'c':2}>>> t = d.items()>>> print t[('a', 0), ('c', 2), ('b', 1)]As you should expect from adictionary, the itemsareinno particular order.Conversely, you can usealistof tuples toinitializeanew dictionary:>>> t = [('a', 0), ('c', 2), ('b', 1)]>>> d = dict(t)>>> print d{'a': 0, 'c': 2, 'b': 1}Combiningdictwithzipyields aconcise way tocreate adictionary:>>> d = dict(zip('abc', range(3)))>>> print d{'a': 0, 'c': 2, 'b': 1}The dictionary method update also takes a list of tuples and adds them, as key-value pairs, to anexisting dictionary.Combining items, tuple assignment and for, you get the idiom for traversing the keys and valuesof adictionary:2 This behavioris slightly differentin Python3.0.

120 Chapter 12. Tuplesfor key, val in d.items():print val, keyThe output of thisloop is:0 a2 c1 bAgain.It is common to use tuples as keys in dictionaries (primarily because you can’t use lists). For example,a telephone directory might map from last-name, first-name pairs to telephone numbers.Assuming that wehave definedlast,firstandnumber,wecould write:directory[last,first] = numberThe expression inbrackets isatuple. Wecould usetuple assignment totraversethisdictionary.for last, first in directory:print first, last, directory[last,first]This loop traverses the keys in directory, which are tuples. It assigns the elements of each tupletolastandfirst,then prints thename and corresponding telephone number.There are two ways to represent tuples in a state diagram. The more detailed version shows theindices and elements just as they appear in a list. For example, the tuple ('Cleese', 'John')would appear:tuple01’Cleese’’John’But in a larger diagram you might want to leave out the details. For example, a diagram of thetelephone directorymight appear:dict(’Cleese’, ’John’) ’08700 100 222’(’Chapman’, ’Graham’)(’Idle’, ’Eric’)(’Gilliam’, ’Terry’)(’Jones’, ’Terry’)’08700 100 222’’08700 100 222’’08700 100 222’’08700 100 222’(’Palin’, ’Michael’) ’08700 100 222’Here thetuples are shown usingPython syntax as agraphical shorthand.The telephone number inthediagram isthecomplaints linefor theBBC, soplease don’t call it.

12.7. Comparing tuples 12112.7 ComparingtuplesThe relational operators work with tuples and other sequences; Python starts by comparing the firstelement from each sequence. If they are equal, it goes on to the next elements, and so on, until itfinds elements that differ. Subsequent elements arenot considered (even ifthey arereallybig).>>> (0, 1, 2) < (0, 3, 4)True>>> (0, 1, 2000000) < (0, 3, 4)TrueThesortfunctionworksthesameway. Itsortsprimarilybyfirstelement,butinthecaseofatie,itsortsbysecond element, and soon.This feature lends itselftoapattern called DSU forDecorate asequence bybuildingalistoftupleswithoneormoresortkeyspreceding theelementsfrom thesequence,Sort thelistof tuples, andUndecorate by extracting thesortedelements of thesequence.For example, suppose you have a listof words and you want tosortthem fromlongest toshortest:def sort_by_length(words):t = []for word in words:t.append((len(word), word))t.sort(reverse=True)res = []for length, word in t:res.append(word)return resThe firstloop builds alistof tuples, where each tuple isaword preceded byitslength.sort compares the first element, length, first, and only considers the second element to break ties.The keyword argumentreverse=Truetellssorttogo indecreasing order.The second loop traverses thelistof tuples and builds alistof words indescending order of length.Exercise 12.2 In this example, ties are broken by comparing words, so words with the same lengthappear in reverse alphabetical order. For other applications you might want to break ties at random.Modify this example so that words with the same length appear in random order. Hint: see therandomfunction intherandommodule.12.8 SequencesofsequencesI have focused on lists of tuples, but almost all of the examples in this chapter also work with listsof lists, tuples of tuples, and tuples of lists. To avoid enumerating the possible combinations, it issometimes easier totalkabout sequences of sequences.

122 Chapter 12. TuplesInmanycontexts,thedifferentkindsofsequences(strings,listsandtuples)canbeusedinterchangeably.So how and why doyou choose one over theothers?To start with the obvious, strings are more limited than other sequences because the elements havetobecharacters. Theyarealsoimmutable. Ifyouneedtheabilitytochangethecharactersinastring(asopposed tocreating anew string),you might want tousealistof characters instead.Lists are more common than tuples, mostly because they are mutable. But there are a few caseswhere you might prefer tuples:1. In some contexts, like a return statement, it is syntactically simpler to create a tuple than alist. Inother contexts, you might prefer a list.2. If you want to use a sequence as a dictionary key, you have to use an immutable type like atuple or string.3. If you are passing a sequence as an argument to a function, using tuples reduces the potentialfor unexpected behavior due toaliasing.Because tuples are immutable, they don’t provide methods like sort and reverse, which modifyexisting lists. But Python provides the built-in functions sorted and reversed, which take anysequence as aparameter and returnanew listwiththe sameelements inadifferent order.12.9 DebuggingLists, dictionaries and tuples are known generically as data structures; in this chapter we are startingto see compound data structures, like lists of tuples, and dictionaries that contain tuples as keysand lists as values. Compound data structures are useful, but they are prone to what I call shapeerrors; that is, errors caused when a data structure has the wrong type, size or composition. Forexample, ifyouareexpectingalistwithoneintegerandIgiveyouaplainoldinteger(notinalist),itwon’t work.To help debug these kinds of errors, I have written a module called structshape that provides afunction, also called structshape, that takes any kind of data structure as an argument and returnsa string that summarizes its shape. You can download it from thinkpython.com/code/structshape.pyHere’s theresult forasimplelist:>>> from structshape import structshape>>> t = [1,2,3]>>> print structshape(t)list of 3 intAfancierprogrammightwrite“listof3ints,”butitwaseasiernottodealwithplurals. Here’salistof lists:>>> t2 = [[1,2], [3,4], [5,6]]>>> print structshape(t2)list of 3 list of 2 intIftheelements of the listarenot thesame type,structshapegroups them, inorder, by type:

12.10. Glossary 123>>> t3 = [1, 2, 3, 4.0, '5', '6', [7], [8], 9]>>> print structshape(t3)list of (3 int, float, 2 str, 2 list of int, int)Here’s alistoftuples:>>> s = 'abc'>>> lt = zip(t, s)>>> print structshape(lt)list of 3 tuple of (int, str)And here’s adictionary with3itemsthat map integers tostrings.>>> d = dict(lt)>>> print structshape(d)dict of 3 int->strIfyou arehaving trouble keeping track of your data structures,structshapecan help.12.10 Glossarytuple: Animmutable sequence of elements.tupleassignment: An assignment with a sequence on the right side and a tuple of variables on theleft. Therightsideisevaluatedandthenitselementsareassignedtothevariablesontheleft.gather: The operation of assembling avariable-length argument tuple.scatter: The operation oftreating asequence as alistof arguments.DSU: Abbreviation of “decorate-sort-undecorate,” a pattern that involves building a list of tuples,sorting, and extracting part of theresult.data structure: A collection of related values, oftenorganized inlists,dictionaries, tuples,etc.shape (of adata structure): A summary of thetype, sizeand composition ofadata structure.12.11 ExercisesExercise 12.3 Write a function called most_frequent that takes a string and prints the letters indecreasingorderoffrequency. Findtextsamplesfromseveraldifferentlanguagesandseehowletterfrequency varies between languages. Compare your results with the tables at wikipedia.org/wiki/Letter_frequencies.Exercise 12.4 Moreanagrams!1. Write a program that reads a word list from a file (see Section 9.1) and prints all the sets ofwords that areanagrams.Here isan example of what theoutput might looklike:

124 Chapter 12. Tuples['deltas', 'desalt', 'lasted', 'salted', 'slated', 'staled']['retainers', 'ternaries']['generating', 'greatening']['resmelts', 'smelters', 'termless']Hint: you might want to build a dictionary that maps from a set of letters to a list of wordsthatcanbespelledwiththoseletters. Thequestionis,howcanyourepresentthesetoflettersinawaythat can beused as akey?2. Modifythepreviousprogramsothatitprintsthelargestsetofanagramsfirst,followedbythesecond largest set,and soon.3. In Scrabble a “bingo” is when you play all seven tiles in your rack, along with a letter on theboard, to form an eight-letter word. What set of 8 letters forms the most possible bingos?Hint: there areseven.4. Two words form a “metathesis pair” if you can transform one into the other by swappingtwo letters 3 ; for example, “converse” and “conserve.” Write a program that finds all of themetathesispairsinthedictionary. Hint: don’ttestallpairsofwords,anddon’ttestallpossibleswaps.You can download asolutionfromthinkpython.com/code/anagram_sets.py.Exercise 12.5 Here’sanother Car Talk Puzzler 4 :What is the longest English word, that remains a valid English word, as you remove itslettersone at atime?Now,letterscanberemovedfromeitherend,orthemiddle,butyoucan’trearrangeanyof the letters. Every time you drop a letter, you wind up with another English word.If you do that, you’re eventually going to wind up with one letter and that too is goingto be an English word—one that’s found in the dictionary. I want to know what’s thelongest word and how many lettersdoes ithave?I’m going to give you a little modest example: Sprite. Ok? You start off with sprite,you take a letter off, one from the interior of the word, take the r away, and we’re leftwith the word spite, then we take the e off the end, we’re left with spit, we take the soff, we’releftwithpit,it,and I.Writeaprogram tofind allwords that can bereduced inthisway, and then find thelongest one.This exercise isalittlemorechallenging than most, sohere are somesuggestions:1. You might want to write a function that takes a word and computes a list of all the words thatcan beformed by removing one letter. These arethe “children” of theword.2. Recursively, a word is reducible if any of its children are reducible. As a base case, you canconsider the empty stringreducible.3. The wordlist I provided, words.txt, doesn’t contain single letter words. So you might wanttoadd “I”, “a”, and theempty string.4. To improve theperformance of your program, you might want tomemoize thewords thatareknown tobereducible.You can see mysolutionatthinkpython.com/code/reducible.py.3 This exercise is inspired byanexampleatpuzzlers.org.4 www.cartalk.com/content/puzzler/transcripts/200651.

Chapter 13Case study: data structure selection13.1 Word frequencyanalysisAs usual, you should at least attempt the following exercises before you read mysolutions.Exercise 13.1 Write a program that reads a file, breaks each line into words, strips whitespace andpunctuation fromthe words, and converts them tolowercase.Hint: Thestringmoduleprovidesstringsnamedwhitespace,whichcontainsspace,tab,newline,etc., andpunctuationwhich contains the punctuation characters. Let’s see if we can make Pythonswear:>>> import string>>> print string.punctuation!"#$%&'()*+,-./:;?@[\]ˆ_`{|}˜Also, you might consider using thestringmethodsstrip,replaceandtranslate.Exercise 13.2 Go to Project Gutenberg (gutenberg.org) and download your favorite out-ofcopyrightbook inplain text format.Modify your program from the previous exercise to read the book you downloaded, skip over theheader information atthe beginning of thefile, and process therestof the words as before.Then modify the program to count the total number of words in the book, and the number of timeseach wordisused.Printthenumberofdifferentwordsusedinthebook. Comparedifferentbooksbydifferentauthors,writtenindifferent eras. Which author uses themost extensive vocabulary?Exercise 13.3 Modify the program from the previous exercise to print the 20 most frequently-usedwords inthebook.Exercise 13.4 Modify the previous program to read a word list (see Section 9.1) and then print allthewordsinthebookthatarenotinthewordlist. Howmanyofthemaretypos? Howmanyofthemarecommon words that should beinthe wordlist,and how many ofthem arereally obscure?

126 Chapter 13. Casestudy: datastructure selection13.2 RandomnumbersGiven the same inputs, most computer programs generate the same outputs every time, so they aresaidtobedeterministic. Determinismisusuallyagoodthing,sinceweexpectthesamecalculationto yield the same result. For some applications, though, we want the computer to be unpredictable.Games arean obvious example, but there aremore.Making a program truly nondeterministic turns out to be not so easy, but there are ways to makeit at least seem nondeterministic. One of them is to use algorithms that generate pseudorandomnumbers. Pseudorandomnumbersarenottrulyrandombecausetheyaregeneratedbyadeterministiccomputation, but just by looking at the numbers it is all but impossible to distinguish them fromrandom.The random module provides functions that generate pseudorandom numbers (which I will simplycall “random” fromhere on).The function random returns a random float between 0.0 and 1.0 (including 0.0 but not 1.0). Eachtimeyou callrandom,you get thenext number inalong series. To see asample, run thisloop:import randomfor i in range(10):x = random.random()print xThefunctionrandinttakesparameterslowandhighandreturnsanintegerbetweenlowandhigh(including both).>>> random.randint(5, 10)5>>> random.randint(5, 10)9To choose anelement fromasequence at random, you can usechoice:>>> t = [1, 2, 3]>>> random.choice(t)2>>> random.choice(t)3Therandommodulealsoprovidesfunctionstogeneraterandomvaluesfromcontinuousdistributionsincluding Gaussian, exponential, gamma, and afew more.Exercise 13.5 Write a function named choose_from_hist that takes a histogram as defined inSection 11.1 and returns a random value from the histogram, chosen with probability in proportiontofrequency. For example, forthis histogram:>>> t = ['a', 'a', 'b']>>> h = histogram(t)>>> print h{'a': 2, 'b': 1}your function should’a’withprobability 2/3 and'b'withprobability 1/3.

13.3. Word histogram 12713.3 Word histogramHere isaprogram that reads a fileand builds a histogram of thewords inthe file:import stringdef process_file(filename):h = dict()fp = open(filename)for line in fp:process_line(line, h)return hdef process_line(line, h):line = line.replace('-', ' ')for word in line.split():word = word.strip(string.punctuation + string.whitespace)word = word.lower()h[word] = h.get(word, 0) + 1hist = process_file('emma.txt')This program readsemma.txt,which contains thetext ofEmma by Jane Austen.process_fileloopsthroughthelinesofthefile,passingthemoneatatimetoprocess_line. Thehistogramhisbeing used as an accumulator.process_lineusesthestringmethodreplacetoreplacehyphenswithspacesbeforeusingsplitto break the line into a list of strings. It traverses the list of words and uses strip and lower toremove punctuation and convert to lower case. (It is a shorthand to say that strings are “converted;”remember that stringareimmutable, somethods likestripandlowerreturnnew strings.)Finally, process_line updates the histogram by creating a new item or incrementing an existingone.To count the total number of words inthefile, wecan add up the frequencies inthe histogram:def total_words(h):return sum(h.values())The number ofdifferent words isjustthenumber of itemsinthe dictionary:def different_words(h):return len(h)Here issomecode toprintthe results:print 'Total number of words:', total_words(hist)print 'Number of different words:', different_words(hist)And theresults:Total number of words: 161073Number of different words: 7212

128 Chapter 13. Casestudy: datastructure selection13.4 MostcommonwordsTo find the most common words, we can apply the DSU pattern; most_common takes a histogramand returns alistofword-frequency tuples, sortedinreverse order by frequency:def most_common(h):t = []for key, value in h.items():t.append((value, key))t.sort(reverse=True)return tHere isaloop that printsthe tenmost common words:t = most_common(hist)print 'The most common words are:'for freq, word in t[0:10]:print word, '\t', freqAnd here aretheresultsfrom Emma:The most common words are:to 5242the 5204and 4897of 4293i 3191a 3130it 2529her 2483was 2400she 236413.5 Optional parametersWehaveseenbuilt-infunctionsandmethodsthattakeavariablenumberofarguments. Itispossibleto write user-defined functions with optional arguments, too. For example, here is a function thatprintsthe most common words inahistogramdef print_most_common(hist, num=10):t = most_common(hist)print 'The most common words are:'for freq, word in t[0:num]:print word, '\t', freqThe firstparameter is required; the second isoptional. The default value ofnumis10.Ifyou only provide one argument:print_most_common(hist)

13.6. Dictionary subtraction 129numgets the default value. Ifyou provide twoarguments:print_most_common(hist, 20)num gets the value of the argument instead. In other words, the optional argument overrides thedefault value.If a function has both required and optional parameters, all the required parameters have to comefirst,followed by theoptional ones.13.6 DictionarysubtractionFinding the words from the book that are not in the word list from words.txt is a problem youmight recognize as set subtraction; that is, we want to find all the words from one set (the words inthebook) that arenot inanother set (thewords inthelist).subtract takes dictionaries d1 and d2 and returns a new dictionary that contains all the keys fromd1that arenot ind2. Since wedon’t reallycare about thevalues, weset them alltoNone.def subtract(d1, d2):res = dict()for key in d1:if key not in d2:res[key] = Nonereturn resTo find the words in the book that are not in words.txt, we can use process_file to build ahistogram forwords.txt,and thensubtract:words = process_file('words.txt')diff = subtract(hist, words)print "The words in the book that aren't in the word list are:"for word in diff.keys():print word,Here aresomeof the resultsfromEmma:The words in the book that aren't in the word list are:rencontre jane's blanche woodhouses disingenuousnessfriend's venice apartment ...Some ofthesewords arenames and possessives. Others, like“rencontre,” areno longer incommonuse. But afew are common words that should reallybe inthelist!Exercise 13.6 Python provides a data structure called set that provides many common set operations.Read the documentation at docs.python.org/lib/types-set.html and write a programthat uses set subtraction tofind words inthebook that arenot intheword list.13.7 RandomwordsTo choose a random word from the histogram, the simplest algorithm is to build a list with multiplecopies of each word, according tothe observed frequency, and then choose from thelist:

130 Chapter 13. Casestudy: datastructure selectiondef random_word(h):t = []for word, freq in h.items():t.extend([word] * freq)return random.choice(t)The expression [word] * freq creates a list with freq copies of the string word. The extendmethod issimilartoappendexcept that theargument isasequence.Exercise 13.7 This algorithm works, but it is not very efficient; each time you choose a randomword, it rebuilds the list, which is as big as the original book. An obvious improvement is to buildthelistonce and then make multipleselections, but thelistisstillbig.Analternative is:1. Usekeystoget alistof the words inthebook.2. Buildalistthatcontainsthecumulativesumofthewordfrequencies(seeExercise10.1). Thelast item inthis lististhe total number of words inthebook, n.3. Choose a random number from 1 to n. Use a bisection search (See Exercise 10.8) to find theindex where the random number would beinserted inthecumulative sum.4. Usethe index tofind thecorresponding wordinthe wordlist.Writeaprogram that uses thisalgorithm tochoose arandom wordfrom thebook.13.8 MarkovanalysisIf you choose words from the book at random, you can get a sense of the vocabulary, you probablywon’t get asentence:this the small regard harriet which knightley's it most thingsA series of random words seldom makes sense because there is no relationship between successivewords. For example, in a real sentence you would expect an article like “the” to be followed by anadjective oranoun, and probably not averb or adverb.One way to measure these kinds of relationships is Markov analysis 1 , which characterizes, for agiven sequence of words, the probability of the word that comes next. For example, the song Eric,theHalf a Bee begins:Half abee, philosophically,Must, ipsofacto, half not be.But half thebee has got tobeVisavis, itsentity. D’you see?But can abee be saidtobeOr not tobe an entirebeeWhen half thebee isnot abeeDue tosome ancient injury?1 This case study is based onanexamplefromKernighanand Pike, The Practice of Programming, 1999.

13.9. Datastructures 131In this text, the phrase “half the” is always followed by the word “bee,” but the phrase “the bee”might be followed by either “has” or“is”.The result of Markov analysis is a mapping from each prefix (like “half the” and “the bee”) to allpossiblesuffixes (like“has” and “is”).Given this mapping, you can generate a random text by starting with any prefix and choosing atrandom from the possible suffixes. Next, you can combine the end of the prefix and the new suffixtoform thenext prefix, and repeat.For example, if you start with the prefix “Half a,” then the next word has to be “bee,” becausethe prefix only appears once in the text. The next prefix is “a bee,” so the next suffix might be“philosophically,” “be” or “due.”In this example the length of the prefix is always two, but you can do Markov analysis with anyprefix length. The length of theprefix iscalled the “order” of theanalysis.Exercise 13.8 Markov analysis:1. Write a program to read a text from a file and perform Markov analysis. The result should bea dictionary that maps from prefixes to a collection of possible suffixes. The collection mightbe a list, tuple, or dictionary; it is up to you to make an appropriate choice. You can test yourprogramwithprefixlengthtwo,butyoushouldwritetheprograminawaythatmakesiteasytotryother lengths.2. AddafunctiontothepreviousprogramtogeneraterandomtextbasedontheMarkovanalysis.Here isan example from Emma withprefix length 2:He was very clever, be it sweetness or be angry, ashamed or only amused, at sucha stroke. She had never thought of Hannah till you were never meant for me?” ”Icannot make speeches, Emma:” hesoon cut itallhimself.Forthisexample,Ileftthepunctuationattachedtothewords. Theresultisalmostsyntacticallycorrect, but not quite. Semantically, italmost makes sense, but not quite.What happens ifyou increase the prefix length? Does therandom text make more sense?3. Once your program is working, you might want to try a mash-up: if you analyze text fromtwo or more books, the random text you generate will blend the vocabulary and phrases fromthe sources ininterestingways.13.9 DatastructuresUsing Markov analysis to generate random text is fun, but there is also a point to this exercise: datastructureselection. Inyour solutiontotheprevious exercises, you had tochoose:• How torepresent theprefixes.• How torepresent thecollection of possiblesuffixes.• How torepresent themapping fromeach prefix tothecollection of possiblesuffixes.

132 Chapter 13. Casestudy: datastructure selectionOk, the last one is the easy; the only mapping type we have seen is a dictionary, so it is the naturalchoice.For the prefixes, the most obvious options are string, list of strings, or tuple of strings. For thesuffixes, one option isalist;another isahistogram (dictionary).How should you choose? The first step is to think about the operations you will need to implementforeachdatastructure. Fortheprefixes,weneedtobeabletoremovewordsfromthebeginningandadd to the end. For example, if the current prefix is “Half a,” and the next word is “bee,” you needtobe able toformthe next prefix, “a bee.”Your first choice might be a list, since it is easy to add and remove elements, but we also need to beable to use the prefixes as keys in a dictionary, so that rules out lists. With tuples, you can’t appendor remove, but you can usetheaddition operator toformanew tuple:def shift(prefix, word):return prefix[1:] + (word,)shift takes a tuple of words, prefix, and a string, word, and forms a new tuple that has all thewords inprefixexcept the first,andwordadded totheend.For the collection of suffixes, the operations we need to perform include adding a new suffix (orincreasing the frequency of an existing one), and choosing a random suffix.Addinganewsuffixisequallyeasyforthelistimplementationorthehistogram. Choosingarandomelementfromalistiseasy;choosingfromahistogramishardertodoefficiently(seeExercise13.7).So far we have been talking mostly about ease of implementation, but there are other factors toconsider in choosing data structures. One is run time. Sometimes there is a theoretical reason toexpect one data structure to be faster than other; for example, I mentioned that the in operator isfasterfor dictionaries than for lists,at leastwhen thenumber ofelements islarge.But often you don’t know ahead of time which implementation will be faster. One option is toimplementbothofthemandseewhichisbetter. Thisapproachiscalledbenchmarking. Apracticalalternativeistochoosethedatastructurethatiseasiesttoimplement,andthenseeifitisfastenoughfortheintendedapplication. Ifso,thereisnoneedtogoon. Ifnot,therearetools,liketheprofilemodule, that can identifythe places inaprogram that take themost time.The other factor to consider is storage space. For example, using a histogram for the collection ofsuffixes might take less space because you only have to store each word once, no matter how manytimes it appears in the text. In some cases, saving space can also make your program run faster,and in the extreme, your program might not run at all if you run out of memory. But for manyapplications, space isasecondary consideration after runtime.One final thought: in this discussion, I have implied that we should use one data structure for bothanalysis and generation. But since these are separate phases, it would also be possible to use onestructure for analysis and then convert to another structure for generation. This would be a net winifthe timesaved during generation exceeded the timespent inconversion.13.10 DebuggingWhenyouaredebuggingaprogram,andespeciallyifyouareworkingonahardbug,therearefourthings totry:

13.11. Glossary 133reading: Examineyourcode,readitbacktoyourself,andcheckthatitsayswhatyoumeanttosay.running: Experiment by making changes and running different versions. Often if you display theright thing at the right place in the program, the problem becomes obvious, but sometimesyou have tospend sometimetobuild scaffolding.ruminating: Take some time to think! What kind of error is it: syntax, runtime, semantic? Whatinformation can you get from the error messages, or from the output of the program? Whatkind of error could cause the problem you’re seeing? What did you change last, before theproblem appeared?retreating: At some point, the best thing to do is back off, undoing recent changes, until you getback toaprogram that works and that you understand. Then you can startrebuilding.Beginning programmers sometimes get stuck on one of these activities and forget the others. Eachactivity comes withitsown failuremode.For example, reading your code might help if the problem is a typographical error, but not if theproblem is a conceptual misunderstanding. If you don’t understand what your program does, youcan read it100 times and never seethe error,because theerror isinyour head.Running experiments can help, especially if you run small, simple tests. But if you run experimentswithout thinking or reading your code, you might fall into a pattern I call “random walkprogramming,” which is the process of making random changes until the program does the rightthing. Needless tosay, random walk programming can take along time.You have totake time tothink. Debugging islike an experimental science. You should have at leastonehypothesisaboutwhattheproblemis. Iftherearetwoormorepossibilities,trytothinkofatestthat would eliminate one of them.Takingabreakhelpswiththethinking. Sodoestalking. Ifyouexplaintheproblemtosomeoneelse(oreven yourself),you willsometimes find the answer before you finish asking thequestion.But even the best debugging techniques will fail if there are too many errors, or if the code you aretrying to fix is too big and complicated. Sometimes the best option is to retreat, simplifying theprogram until you get tosomething that works and that you understand.Beginningprogrammersareoftenreluctanttoretreatbecausetheycan’tstandtodeletealineofcode(even if it’s wrong). If it makes you feel better, copy your program into another file before you startstrippingitdown. Then you can paste thepieces back inalittlebitat atime.Findingahardbugrequiresreading,running,ruminating,andsometimesretreating. Ifyougetstuckon one of theseactivities, trytheothers.13.11 Glossarydeterministic: Pertaining to a program that does the same thing each time it runs, given the sameinputs.pseudorandom: Pertaining to a sequence of numbers that appear to be random, but are generatedby adeterministic program.default value: The value given toan optional parameter ifno argument isprovided.

134 Chapter 13. Casestudy: datastructure selectionoverride: To replace adefault value withan argument.benchmarking: Theprocessofchoosingbetweendatastructuresbyimplementingalternativesandtestingthem on asample ofthe possibleinputs.13.12 ExercisesExercise 13.9 The “rank” of a word is its position in a list of words sorted by frequency: the mostcommon word has rank 1, thesecond most common has rank 2, etc.Zipf’slawdescribesarelationshipbetweentheranksandfrequenciesofwordsinnaturallanguages 2 .Specifically, itpredicts that the frequency, f,of theword withrankris:f =cr −swhere s and c are parameters that depend on the language and the text. If you take the logarithm ofboth sides ofthis equation, you get:log f =logc−slogrSo ifyou plot log f versus logr,you should get astraight linewithslope−sand intercept logc.Write a program that reads a text from a file, counts word frequencies, and prints one line for eachword, in descending order of frequency, with log f and logr. Use the graphing program of yourchoicetoplottheresultsandcheckwhethertheyformastraightline. Canyouestimatethevalueofs?2 Seewikipedia.org/wiki/Zipf’s_law.

Chapter 14Files14.1 PersistenceMost of the programs we have seen so far are transient in the sense that they run for a short timeandproduce someoutput, butwhen theyend, theirdatadisappears. Ifyouruntheprogram again, itstartswithaclean slate.Other programs are persistent: they run for a long time (or all the time); they keep at least some oftheir data in permanent storage (a hard drive, for example); and if they shut down and restart, theypick up where they leftoff.Examplesofpersistentprogramsareoperatingsystems,whichrunprettymuchwheneveracomputerison, and web servers,which run allthe time, waitingforrequests tocome inon thenetwork.Oneofthesimplestwaysforprogramstomaintaintheirdataisbyreadingandwritingtextfiles. Wehavealreadyseenprogramsthatreadtextfiles;inthischapterwewillseeprogramsthatwritethem.Analternativeistostorethestateoftheprograminadatabase. InthischapterIwillpresentasimpledatabase and amodule,pickle,that makes iteasytostoreprogram data.14.2 Readingand writingAtextfileisasequenceofcharactersstoredonapermanentmediumlikeaharddrive,flashmemory,or CD-ROM. Wesaw how toopen and read afileinSection 9.1.To writeafile, you have toopen itwithmode'w' as asecond parameter:>>> fout = open('output.txt', 'w')>>> print foutIf the file already exists, opening it in write mode clears out the old data and starts fresh, so becareful! Ifthefiledoesn’t exist, anew one iscreated.Thewritemethod puts data intothe file.

136 Chapter 14. Files>>> line1 = "This here's the wattle,\n">>> fout.write(line1)Again, the file object keeps track of where it is, so if you call write again, it adds the new data totheend.>>> line2 = "the emblem of our land.\n">>> fout.write(line2)When you are done writing, you have toclosethe file.>>> fout.close()14.3 FormatoperatorThe argument of write has to be a string, so if we want to put other values in a file, we have toconvert them tostrings. The easiest way todo that iswithstr:>>> x = 52>>> f.write(str(x))Analternativeistousetheformatoperator,%. Whenappliedtointegers,%isthemodulusoperator.But when thefirstoperand is astring,%isthe formatoperator.Thefirstoperandistheformatstring,whichcontainsoneormoreformatsequences,whichspecifyhow the second operand isformatted. The result isastring.For example, the format sequence'%d' means that the second operand should be formatted as aninteger (dstands for “decimal”):>>> camels = 42>>> '%d' % camels'42'The resultisthe string'42',which isnot tobeconfused withthe integer value42.A format sequence can appear anywhere inthe string,soyou can embed avalue inasentence:>>> camels = 42>>> 'I have spotted %d camels.' % camels'I have spotted 42 camels.'If there is more than one format sequence in the string, the second argument has to be a tuple. Eachformat sequence ismatched withanelement ofthe tuple, inorder.The following example uses '%d' to format an integer, '%g' to format a floating-point number(don’t ask why), and'%s' toformatastring:>>> 'In %d years I have spotted %g %s.' % (3, 0.1, 'camels')'In 3 years I have spotted 0.1 camels.'The number of elements in the tuple has to match the number of format sequences in the string.Also, thetypes of the elements have tomatch theformat sequences:

14.4. Filenames and paths 137>>> '%d %d %d' % (1, 2)TypeError: not enough arguments for format string>>> '%d' % 'dollars'TypeError: illegal argument type for built-in operationInthefirstexample, therearen’t enough elements; inthesecond, the element isthe wrong type.The format operator is powerful, but it can be difficult to use. You can read more about it at docs.python.org/lib/typesseq-strings.html.14.4 Filenamesand pathsFiles are organized into directories (also called “folders”). Every running program has a “currentdirectory,”whichisthedefaultdirectoryformostoperations. Forexample,whenyouopenafileforreading, Python looks foritinthe current directory.Theosmoduleprovidesfunctionsforworkingwithfilesanddirectories(“os”standsfor“operatingsystem”). os.getcwdreturnsthe name of the current directory:>>> import os>>> cwd = os.getcwd()>>> print cwd/home/dinsdalecwd stands for “current working directory.” The result in this example is /home/dinsdale, whichisthehome directory of auser nameddinsdale.A string like cwd that identifies a file is called a path. A relative path starts from the currentdirectory; anabsolute path startsfromthe topmost directory inthefile system.The paths we have seen so far are simple filenames, so they are relative to the current directory. Tofind the absolute path toafile, you can useos.path.abspath:>>> os.path.abspath('memo.txt')'/home/dinsdale/memo.txt'os.path.existschecks whether a fileor directory exists:>>> os.path.exists('memo.txt')TrueIfitexists,os.path.isdirchecks whether it’sadirectory:>>> os.path.isdir('memo.txt')False>>> os.path.isdir('music')TrueSimilarly,os.path.isfilechecks whether it’safile.os.listdirreturns alistofthe files (and other directories) inthegiven directory:>>> os.listdir(cwd)['music', 'photos', 'memo.txt']

138 Chapter 14. FilesTodemonstratethesefunctions,thefollowingexample“walks”throughadirectory,printsthenamesof all thefiles, and calls itselfrecursively on allthe directories.def walk(dir):for name in os.listdir(dir):path = os.path.join(dir, name)if os.path.isfile(path):print pathelse:walk(path)os.path.jointakes adirectory and afile name and joins them intoacomplete path.Exercise 14.1 Modify walk so that instead of printing the names of the files, it returns a list ofnames.Exercise 14.2 The os module provides a function called walk that is similar to this one but moreversatile. Read the documentation and use it to print the names of the files in a given directory anditssubdirectories.14.5 CatchingexceptionsA lot of things can go wrong when you try to read and write files. If you try to open a file thatdoesn’t exist, you get anIOError:>>> fin = open('bad_file')IOError: [Errno 2] No such file or directory: 'bad_file'Ifyou don’t have permissiontoaccess afile:>>> fout = open('/etc/passwd', 'w')IOError: [Errno 13] Permission denied: '/etc/passwd'And ifyou trytoopen a directoryfor reading, you get>>> fin = open('/home')IOError: [Errno 21] Is a directoryTo avoid these errors, you could use functions like os.path.exists and os.path.isfile, but itwould take a lot of time and code to check all the possibilities (if “Errno 21” is any indication,there areat least 21things that can go wrong).Itisbettertogoaheadandtry,anddealwithproblemsiftheyhappen,whichisexactlywhatthetrystatement does. The syntax issimilartoanifstatement:try:fin = open('bad_file')for line in fin:print linefin.close()except:print 'Something went wrong.'

14.6. Databases 139Python starts by executing thetry clause. If all goes well, it skips theexceptclause and proceeds.Ifan exception occurs, itjumps out of thetryclause and executes theexceptclause.Handling an exception with a try statement is called catching an exception. In this example, theexcept clause prints an error message that is not very helpful. In general, catching an exceptiongives you a chance tofix theproblem, or tryagain, or at least end theprogram gracefully.14.6 DatabasesAdatabaseisafilethatisorganizedforstoringdata. Mostdatabasesareorganizedlikeadictionaryinthesensethattheymapfromkeystovalues. Thebiggestdifferenceisthatthedatabaseisondisk(orother permanent storage), soitpersistsafterthe program ends.The module anydbm provides an interface for creating and updating database files. As an example,I’llcreate a database that contains captions for image files.Opening adatabase issimilartoopening other files:>>> import anydbm>>> db = anydbm.open('captions.db', 'c')The mode'c' means that the database should be created if it doesn’t already exist. The result is adatabase object that can be used (for most operations) like a dictionary. If you create a new item,anydbmupdates the database file.>>> db['cleese.png'] = 'Photo of John Cleese.'When you access one of the items,anydbmreads the file:>>> print db['cleese.png']Photo of John Cleese.Ifyou make another assignment toan existingkey,anydbmreplaces theold value:>>> db['cleese.png'] = 'Photo of John Cleese doing a silly walk.'>>> print db['cleese.png']Photo of John Cleese doing a silly walk.Many dictionary methods, like keys and items, also work with database objects. So does iterationwithaforstatement.for key in db:print keyAs withother files, you should closethe database when you are done:>>> db.close()14.7 PicklingAlimitationofanydbmisthatthekeysandvalueshavetobestrings. Ifyoutrytouseanyothertype,you get anerror.

140 Chapter 14. FilesThepicklemodulecanhelp. Ittranslatesalmostanytypeofobjectintoastringsuitableforstorageinadatabase, and then translates stringsback intoobjects.pickle.dumpstakesanobjectasaparameterandreturnsastringrepresentation(dumpsisshortfor“dump string”):>>> import pickle>>> t = [1, 2, 3]>>> pickle.dumps(t)'(lp0\nI1\naI2\naI3\na.'The format isn’t obvious to human readers; it is meant to be easy for pickle to interpret.pickle.loads(“load string”) reconstitutes the object:>>> t1 = [1, 2, 3]>>> s = pickle.dumps(t1)>>> t2 = pickle.loads(s)>>> print t2[1, 2, 3]Although thenew object has thesame value asthe old, itisnot (ingeneral) the sameobject:>>> t1 == t2True>>> t1 is t2FalseInother words, pickling and then unpickling has the sameeffect ascopying theobject.You can use pickle to store non-strings in a database. In fact, this combination is so common thatithas been encapsulated inamodule calledshelve.Exercise14.3 IfyoudidExercise12.4,modifyyoursolutionsothatitcreatesadatabasethatmapsfrom each word inthelisttoalistof words that use thesame setof letters.Writeadifferentprogramthatopensthedatabaseandprintsthecontentsinahuman-readableformat.14.8 PipesMost operating systems provide a command-line interface, also known as a shell. Shells usuallyprovide commands to navigate the file system and launch applications. For example, in Unix, youcanchangedirectorieswithcd,displaythecontentsofadirectorywithls,andlaunchawebbrowserby typing (forexample)firefox.Any program that you can launch from the shell can also be launched from Python using a pipe. Apipe isan object that represents arunning process.For example, the Unix command ls -l normally displays the contents of the current directory (inlong format). You can launchlswithos.popen:>>> cmd = 'ls -l'>>> fp = os.popen(cmd)

14.9. Writingmodules 141The argument is a string that contains a shell command. The return value is an object that behavesjustlikeanopenfile. Youcanreadtheoutputfromthelsprocessonelineatatimewithreadlineor get the whole thingat once withread:>>> res = fp.read()When you are done, you close thepipe likeafile:>>> stat = fp.close()>>> print statNoneThe return value is the final status of the ls process; None means that it ended normally (with noerrors).A common use of pipes is to read a compressed file incrementally; that is, without uncompressingthe whole thing at once. The following function takes the name of a compressed file as a parameterand returns apipe that usesgunziptodecompress thecontents:def open_gunzip(filename):cmd = 'gunzip -c ' + filenamefp = os.popen(cmd)return fpIfyoureadlinesfromfponeatatime,youneverhavetostoretheuncompressedfileinmemoryoron disk.14.9 WritingmodulesAny file that contains Python code can be imported as a module. For example, suppose you have afilenamedwc.pywiththefollowing code:def linecount(filename):count = 0for line in open(filename):count += 1return countprint linecount('wc.py')If you run this program, it reads itself and prints the number of lines in the file, which is 7. You canalsoimport itlikethis:>>> import wc7Now you have amodule objectwc:>>> print wcThat provides afunction calledlinecount:

142 Chapter 14. Files>>> wc.linecount('wc.py')7So that’show you writemodules inPython.The only problem with this example is that when you import the module it executes the test codeat the bottom. Normally when you import a module, it defines new functions but it doesn’t executethem.Programs that willbe imported asmodules oftenusethe following idiom:if __name__ == '__main__':print linecount('wc.py')__name__ is a built-in variable that is set when the program starts. If the program is running as ascript, __name__ has the value __main__; in that case, the test code is executed. Otherwise, if themodule isbeing imported, thetestcode isskipped.Exercise14.4 Typethisexampleintoafilenamedwc.pyandrunitasascript. ThenrunthePythoninterpreter andimport wc. What isthevalue of__name__when the module isbeing imported?Warning: If you import a module that has already been imported, Python does nothing. It does notre-read thefile, even if ithas changed.Ifyouwanttoreloadamodule,youcanusethebuilt-infunctionreload,butitcanbetricky,sothesafestthing todo isrestarttheinterpreter and then import the module again.14.10 DebuggingWhenyouarereadingandwritingfiles,youmightrunintoproblemswithwhitespace. Theseerrorscan be hard todebug because spaces, tabs and newlines arenormally invisible:>>> s = '1 2\t 3\n 4'>>> print s1 2 34The built-in function repr can help. It takes any object as an argument and returns a string representationof theobject. For strings,itrepresents whitespace characters withbackslash sequences:>>> print repr(s)'1 2\t 3\n 4'This can be helpful fordebugging.Oneotherproblemyoumightrunintoisthatdifferentsystemsusedifferentcharacterstoindicatetheendofaline. Somesystemsuseanewline,represented\n. Othersuseareturncharacter,represented\r. Some use both. If you move files between different systems, these inconsistencies might causeproblems.For most systems, there are applications to convert from one format to another. You can find them(andreadmoreaboutthisissue)atwikipedia.org/wiki/Newline. Or,ofcourse,youcouldwriteone yourself.

14.11. Glossary 14314.11 Glossarypersistent: Pertaining to a program that runs indefinitely and keeps at least some of its data inpermanent storage.format operator: An operator, %, that takes a format string and a tuple and generates a string thatincludes theelements of thetuple formattedas specified by theformat string.format string: A string,used withtheformat operator, that contains format sequences.format sequence: A sequence of characters in a format string, like %d, that specifies how a valueshould be formatted.text file: A sequence of characters storedinpermanent storagelikeaharddrive.directory: A named collection of files, alsocalled afolder.path: A stringthat identifies a file.relative path: A path that startsfromthe current directory.absolute path: A path that startsfromthe topmost directory inthefile system.catch: Toprevent anexception fromterminatingaprogram usingthetryandexceptstatements.database: Afilewhosecontentsareorganizedlikeadictionarywithkeysthatcorrespondtovalues.14.12 ExercisesExercise 14.5 The urllib module provides methods for manipulating URLs and downloadinginformation from the web. The following example downloads and prints a secret message fromthinkpython.com:import urllibconn = urllib.urlopen('http://thinkpython.com/secret.html')for line in conn.fp:print line.strip()Run thiscode and follow the instructions you seethere.Exercise14.6 InalargecollectionofMP3files,theremaybemorethanonecopyofthesamesong,stored in different directories or with different file names. The goal of this exercise is to search forthese duplicates.1. Writeaprogramthatsearchesadirectoryandallofitssubdirectories,recursively,andreturnsa list of complete paths for all files with a given suffix (like .mp3). Hint: os.path providesseveral useful functions formanipulating file and path names.2. To recognize duplicates, you can use a hash function that reads the file and generates ashort summary of the contents. For example, MD5 (Message-Digest algorithm 5) takes anarbitrarily-long “message” and returns a 128-bit “checksum.” The probability is very smallthat twofiles withdifferent contents willreturnthe samechecksum.You can read about MD5 at wikipedia.org/wiki/Md5. On a Unix system you can use theprogrammd5sumand apipe tocompute checksums from Python.

144 Chapter 14. FilesExercise 14.7 The Internet Movie Database (IMDb) is an online collection of information aboutmovies. Theirdatabaseisavailableinplaintextformat,soitisreasonablyeasytoreadfromPython.Forthisexercise,thefilesyouneedareactors.list.gzandactresses.list.gz;youcandownloadthem fromwww.imdb.com/interfaces#plain.I have written a program that parses these files and splits them into actor names, movie titles, etc.You can download itfromthinkpython.com/code/imdb.py.If you run imdb.py as a script, it reads actors.list.gz and prints one actor-movie pair per line.Or, if you import imdb you can use the function process_file to, well, process the file. Thearguments are a filename, a function object and an optional number of lines to process. Here is anexample:import imdbdef print_info(actor, date, title, role):print actor, date, title, roleimdb.process_file('actors.list.gz', print_info)When you call process_file, it opens filename, reads the contents, and calls print_info oncefor each line in the file. print_info takes an actor, date, movie title and role as arguments andprintsthem.1. Write a program that reads actors.list.gz and actresses.list.gz and uses shelve tobuild adatabase that maps fromeach actor toalistof his orher films.2. Twoactorsare“costars”iftheyhavebeeninatleastonemovietogether. Processthedatabaseyou built in the previous step and build a second database that maps from each actor to a listof his or her costars.3. Write a program that can play the “Six Degrees of Kevin Bacon,” which you can read aboutat wikipedia.org/wiki/Six_Degrees_of_Kevin_Bacon. This problem is challenging becauseit requires you to find the shortest path in a graph. You can read about shortest pathalgorithms atwikipedia.org/wiki/Shortest_path_problem.

Chapter 15Classes and objects15.1 User-definedtypesWe have used many of Python’s built-in types; now we are going to define a new type. As anexample, we willcreate atype calledPointthat represents apoint intwo-dimensional space.Inmathematicalnotation,pointsareoftenwritteninparentheseswithacommaseparatingthecoordinates.For example, (0,0) represents the origin, and (x,y) represents the point x units to the rightand yunits up fromthe origin.There areseveral ways we might represent points inPython:• We could storethecoordinates separately intwo variables,xandy.• We could storethecoordinates as elements inalistortuple.• We could create a new type torepresent points as objects.Creating a new type is (a little) more complicated than the other options, but it has advantages thatwillbe apparent soon.A user-defined type isalsocalled a class. A class definition looks likethis:class Point(object):"""represents a point in 2-D space"""This header indicates that the new class is a Point, which is a kind of object, which is a built-intype.The body is a docstring that explains what the class is for. You can define variables and functionsinsideaclass definition, but wewillget back tothat later.Defining aclass namedPointcreates aclass object.>>> print Point

146 Chapter 15. Classesand objectsBecausePointisdefined at the toplevel, its“full name” is__main__.Point.The class object is like a factory for creating objects. To create a Point, you call Point as if it wereafunction.>>> blank = Point()>>> print blankThe return value is a reference to a Point object, which we assign to blank. Creating a new objectiscalled instantiation, and the object isan instance ofthe class.When you print an instance, Python tells you what class it belongs to and where it is stored inmemory (theprefix0xmeans that the following number isinhexadecimal).15.2 AttributesYou can assignvalues toaninstance usingdot notation:>>> blank.x = 3.0>>> blank.y = 4.0This syntax is similar to the syntax for selecting a variable from a module, such as math.pi orstring.whitespace. Inthiscase,though,weareassigningvaluestonamedelementsofanobject.These elements arecalled attributes.As a noun, “AT-trib-ute” is pronounced with emphasis on the first syllable, as opposed to “a-TRIBute,”whichisaverb.The following diagram shows the result of these assignments. A state diagram that shows an objectand itsattributes iscalled anobject diagram:blankPointxy3.04.0The variableblank refers to a Point object, which contains two attributes. Each attribute refers to afloating-point number.You can read the value of an attributeusingthe samesyntax:>>> print blank.y4.0>>> x = blank.x>>> print x3.0The expression blank.x means, “Go to the object blank refers to and get the value of x.” In thiscase,weassignthatvaluetoavariablenamedx. Thereisnoconflictbetweenthevariablexandtheattributex.You can use dot notation as part of any expression. For example:

15.3. Rectangles 147>>> print '(%g, %g)' % (blank.x, blank.y)(3.0, 4.0)>>> distance = math.sqrt(blank.x**2 + blank.y**2)>>> print distance5.0You can pass an instance as an argument inthe usual way. For example:def print_point(p):print '(%g, %g)' % (p.x, p.y)print_point takes a point as an argument and displays it in mathematical notation. To invoke it,you can passblankas anargument:>>> print_point(blank)(3.0, 4.0)Insidethe function,pisan aliasforblank,soifthefunction modifiesp,blankchanges.Exercise15.1 WriteafunctioncalleddistancethattakestwoPointsasargumentsandreturnsthedistance between them.15.3 RectanglesSometimesitisobviouswhattheattributesofanobjectshouldbe,butothertimesyouhavetomakedecisions. For example, imagine you are designing a class to represent rectangles. What attributeswould you use to specify the location and size of a rectangle? You can ignore angle; to keep thingssimple, assumethat the rectangle iseither vertical or horizontal.There areat least twopossibilities:• You could specify one corner ofthe rectangle (orthecenter), thewidth, and theheight.• You could specify twoopposing corners.Atthispointitishardtosaywhethereitherisbetterthantheother,sowe’llimplementthefirstone,justas an example.Here istheclass definition:class Rectangle(object):"""represent a rectangle.attributes: width, height, corner."""The docstring lists the attributes: width and height are numbers; corner is a Point object thatspecifies thelower-left corner.Torepresentarectangle,youhavetoinstantiateaRectangleobjectandassignvaluestotheattributes:box = Rectangle()box.width = 100.0box.height = 200.0box.corner = Point()box.corner.x = 0.0box.corner.y = 0.0

148 Chapter 15. Classesand objectsTheexpressionbox.corner.xmeans,“Gototheobjectboxreferstoandselecttheattributenamedcorner;then gotothat object and select theattributenamedx.”The figure shows thestateof thisobject:Rectangleboxwidthheightcorner100.0200.0Pointxy0.00.0Anobject that isanattribute ofanother object isembedded.15.4 Instancesas returnvaluesFunctions can return instances. For example, find_center takes a Rectangle as an argument andreturns aPointthat contains thecoordinates of thecenter of theRectangle:def find_center(box):p = Point()p.x = box.corner.x + box.width/2.0p.y = box.corner.y + box.height/2.0return pHere isanexample that passesboxas an argument and assignsthe resultingPoint tocenter:>>> center = find_center(box)>>> print_point(center)(50.0, 100.0)15.5 ObjectsaremutableYoucanchangethestateofanobjectbymakinganassignmenttooneofitsattributes. Forexample,to change the size of a rectangle without changing its position, you can modify the values of widthandheight:box.width = box.width + 50box.height = box.width + 100Youcanalsowritefunctionsthatmodifyobjects. Forexample,grow_rectangletakesaRectangleobjectandtwonumbers,dwidthanddheight,andaddsthenumberstothewidthandheightoftherectangle:def grow_rectangle(rect, dwidth, dheight) :rect.width += dwidthrect.height += dheightHere isanexample that demonstrates theeffect:

15.6. Copying 149>>> print box.width100.0>>> print box.height200.0>>> grow_rectangle(box, 50, 100)>>> print box.width150.0>>> print box.height300.0Insidethe function,rectisan alias forbox,soifthe function modifiesrect,boxchanges.Exercise 15.2 Write a function named move_rectangle that takes a Rectangle and two numbersnameddxanddy. Itshouldchangethelocationoftherectanglebyaddingdxtothexcoordinateofcornerand addingdytotheycoordinate ofcorner.15.6 CopyingAliasing can make a program difficult to read because changes in one place might have unexpectedeffectsinanotherplace. Itishardtokeeptrackofallthevariablesthatmightrefertoagivenobject.Copying an object is often an alternative to aliasing. The copy module contains a function calledcopythat can duplicate any object:>>> p1 = Point()>>> p1.x = 3.0>>> p1.y = 4.0>>> import copy>>> p2 = copy.copy(p1)p1andp2contain the samedata, but they arenot the samePoint.>>> print_point(p1)(3.0, 4.0)>>> print_point(p2)(3.0, 4.0)>>> p1 is p2False>>> p1 == p2FalseThe is operator indicates that p1 and p2 are not the same object, which is what we expected. Butyou might have expected == to yield True because these points contain the same data. In that case,you will be disappointed to learn that for instances, the default behavior of the == operator is thesame as the is operator; it checks object identity, not object equivalence. This behavior can bechanged—we’ll seehow later.If you use copy.copy to duplicate a Rectangle, you will find that it copies the Rectangle object butnot the embedded Point.

150 Chapter 15. Classesand objects>>> box2 = copy.copy(box)>>> box2 is boxFalse>>> box2.corner is box.cornerTrueHere iswhat the object diagram looks like:boxwidth100.0100.0widthbox2heightcorner200.0xy0.00.0200.0heightcornerThis operation is called a shallow copy because it copies the object and any references it contains,but not theembedded objects.Formostapplications,thisisnotwhatyouwant. Inthisexample,invokinggrow_rectangleononeof the Rectangles would not affect the other, but invoking move_rectangle on either would affectboth! This behavior isconfusing and error-prone.Fortunately, the copy module contains a method named deepcopy that copies not only the objectbut also the objects it refers to, and the objects they refer to, and so on. You will not be surprised tolearn that thisoperation iscalled adeep copy.>>> box3 = copy.deepcopy(box)>>> box3 is boxFalse>>> box3.corner is box.cornerFalsebox3andboxare completely separate objects.Exercise15.3 Writeaversionofmove_rectanglethatcreatesandreturnsanewRectangleinsteadof modifying the oldone.15.7 DebuggingWhen you start working with objects, you are likely to encounter some new exceptions. If you trytoaccess an attributethat doesn’t exist, you get anAttributeError:>>> p = Point()>>> print p.zAttributeError: Point instance has no attribute 'z'Ifyou arenot surewhat type an object is,you can ask:>>> type(p)If you are not sure whether an object has a particular attribute, you can use the built-in functionhasattr:

15.8. Glossary 151>>> hasattr(p, 'x')True>>> hasattr(p, 'z')FalseThe first argument can be any object; the second argument is a string that contains the name of theattribute.15.8 Glossaryclass: A user-defined type. A class definition creates anew classobject.class object: Anobjectthatcontainsinformationaboutauser-definedtype. Theclassobjectcanbeused tocreate instances of thetype.instance: An object that belongs toaclass.attribute: One of thenamed values associated withan object.embedded (object): Anobject that isstoredas an attributeof another object.shallow copy: To copy the contents of an object, including any references to embedded objects;implemented bythecopyfunction inthecopymodule.deep copy: To copy the contents of an object as well as any embedded objects, and any objectsembedded inthem, and soon; implemented bythedeepcopyfunction inthecopymodule.object diagram: A diagram that shows objects, their attributes, and thevalues of the attributes.15.9 ExercisesExercise15.4 World.py,whichispartofSwampy(seeChapter4),containsaclassdefinitionforauser-defined type calledWorld. You can import itlikethis:from World import WorldThis version of theimport statement imports theWorld class from theWorld module. The followingcodecreates aWorldobject and callsthemainloopmethod, which waits forthe user.world = World()world.mainloop()A window should appear with a title bar and an empty square. We will use this window to drawPoints, Rectangles and other shapes. Add the following lines before calling mainloop and run theprogram again.canvas = world.ca(width=500, height=500, background='white')bbox = [[-150,-100], [150, 100]]canvas.rectangle(bbox, outline='black', width=2, fill='green4')

152 Chapter 15. Classesand objectsYoushouldseeagreenrectanglewithablackoutline. ThefirstlinecreatesaCanvas,whichappearsin the window as a white square. The Canvas object provides methods like rectangle for drawingvarious shapes.bboxisalistofliststhatrepresentsthe“boundingbox”oftherectangle. Thefirstpairofcoordinatesisthelower-left corner of therectangle; thesecond pair istheupper-right corner.You can draw a circlelikethis:canvas.circle([-25,0], 70, outline=None, fill='red')The first parameter is the coordinate pair for the center of the circle; the second parameter is theradius.If you add this line to the program, the result should resemble the national flag of Bangladesh (seewikipedia.org/wiki/Gallery_of_sovereign-state_flags).1. Write a function called draw_rectangle that takes a Canvas and a Rectangle as argumentsand draws arepresentation of theRectangle onthe Canvas.2. AddanattributenamedcolortoyourRectangleobjectsandmodifydraw_rectanglesothatit usesthe color attributeas the fillcolor.3. Write a function called draw_point that takes a Canvas and a Point as arguments and drawsa representation of thePoint on theCanvas.4. DefineanewclasscalledCirclewithappropriateattributesandinstantiateafewCircleobjects.Writeafunction calleddraw_circlethat draws circleson the canvas.5. Write a program that draws the national flag of the Czech Republic. Hint: you can draw apolygon likethis:points = [[-150,-100], [150, 100], [150, -100]]canvas.polygon(points, fill='blue')I have written a small program that lists the available colors; you can download it fromthinkpython.com/code/color_list.py.

Chapter 16Classes and functions16.1 TimeAs another example of a user-defined type, we’ll define a class called Time that records the time ofday. The class definition looks likethis:class Time(object):"""represents the time of day.attributes: hour, minute, second"""We can create anewTimeobject and assignattributesfor hours, minutes, and seconds:time = Time()time.hour = 11time.minute = 59time.second = 30The statediagram fortheTimeobject looks like this:timeTimehourminutesecond115930Exercise16.1 Writeafunctioncalledprint_timethattakesaTimeobjectandprintsitintheformhour:minute:second. Hint: theformatsequence'%.2d'printsanintegerusingatleasttwodigits,including aleading zeroifnecessary.Exercise 16.2 Write a boolean function called is_after that takes two Time objects, t1 and t2,andreturnsTrueift1followst2chronologicallyandFalseotherwise. Challenge: don’tuseanifstatement.

154 Chapter 16. Classesand functions16.2 PurefunctionsIn the next few sections, we’ll write two functions that add time values. They demonstrate twokinds of functions: pure functions and modifiers. They also demonstrate a development plan I’llcall prototype and patch, which is a way of tackling a complex problem by starting with a simpleprototype and incrementally dealing withthe complications.Here isasimpleprototype ofadd_time:def add_time(t1, t2):sum = Time()sum.hour = t1.hour + t2.hoursum.minute = t1.minute + t2.minutesum.second = t1.second + t2.secondreturn sumThe function creates a new Time object, initializes its attributes, and returns a reference to the newobject. This is called a pure function because it does not modify any of the objects passed to it asarguments and it has no effect, like displaying a value or getting user input, other than returning avalue.To test this function, I’ll create two Time objects: start contains the start time of a movie, likeMonty Python and the Holy Grail, and duration contains the run time of the movie, which is onehour 35minutes.add_timefigures out when themovie willbe done.>>> start = Time()>>> start.hour = 9>>> start.minute = 45>>> start.second = 0>>> duration = Time()>>> duration.hour = 1>>> duration.minute = 35>>> duration.second = 0>>> done = add_time(start, duration)>>> print_time(done)10:80:00Theresult,10:80:00mightnotbewhatyouwerehopingfor. Theproblemisthatthisfunctiondoesnot deal with cases where the number of seconds or minutes adds up to more than sixty. When thathappens, we have to “carry” the extra seconds into the minute column or the extra minutes into thehour column.Here’s an improved version:def add_time(t1, t2):sum = Time()sum.hour = t1.hour + t2.hoursum.minute = t1.minute + t2.minutesum.second = t1.second + t2.second

16.3. Modifiers 155if sum.second >= 60:sum.second -= 60sum.minute += 1if sum.minute >= 60:sum.minute -= 60sum.hour += 1return sumAlthough thisfunction iscorrect, itisstartingtoget big. We willsee ashorteralternative later.16.3 ModifiersSometimes it is useful for a function to modify the objects it gets as parameters. In that case, thechanges are visibletothe caller. Functions that work thisway arecalled modifiers.increment, which adds a given number of seconds to a Time object, can be written naturally as amodifier. Here isarough draft:def increment(time, seconds):time.second += secondsif time.second >= 60:time.second -= 60time.minute += 1if time.minute >= 60:time.minute -= 60time.hour += 1Thefirstlineperformsthebasicoperation;theremainderdealswiththespecialcaseswesawbefore.Isthisfunction correct? What happens iftheparametersecondsismuch greater than sixty?In that case, it is not enough to carry once; we have to keep doing it until time.second is less thansixty. One solution is to replace the if statements with while statements. That would make thefunction correct, but not very efficient.Exercise 16.3 Writeacorrect version ofincrementthat doesn’t contain any loops.Anything that can be done with modifiers can also be done with pure functions. In fact, someprogramming languages only allow pure functions. There is some evidence that programs that usepure functions are faster to develop and less error-prone than programs that use modifiers. Butmodifiers areconvenient at times,and functional programs tend tobelessefficient.Ingeneral,Irecommendthatyouwritepurefunctionswheneveritisreasonableandresorttomodifiersonlyifthereisacompellingadvantage.Thisapproachmightbecalledafunctionalprogrammingstyle.Exercise 16.4 Write a “pure” version of increment that creates and returns a new Time objectrather than modifying the parameter.

156 Chapter 16. Classesand functions16.4 Prototypingversus planningThe development plan I am demonstrating is called “prototype and patch.” For each function, Iwrote a prototype that performed the basic calculation and then tested it, patching errors along theway.Thisapproachcanbeeffective,especiallyifyoudon’tyethaveadeepunderstandingoftheproblem.Butincrementalcorrectionscangeneratecodethatisunnecessarilycomplicated—sinceitdealswithmany special cases—and unreliable—since it ishardtoknow ifyou have found allthe errors.An alternative is planned development, in which high-level insight into the problem can make theprogrammingmucheasier. Inthiscase,theinsightisthataTimeobjectisreallyathree-digitnumberinbase60(seewikipedia.org/wiki/Sexagesimal.)! Thesecondattributeisthe“onescolumn,”the minute attribute is the “sixties column,” and the hour attribute is the “thirty-six hundreds column.”When we wroteadd_timeandincrement,we were effectively doing addition in base 60, which iswhy we had tocarryfrom one column tothenext.This observation suggests another approach to the whole problem—we can convert Time objects tointegers and take advantage of the fact that thecomputer knows how todo integer arithmetic.Here isafunction that converts Times tointegers:def time_to_int(time):minutes = time.hour * 60 + time.minuteseconds = minutes * 60 + time.secondreturn secondsAndhereisthefunctionthatconvertsintegerstoTimes(recallthatdivmoddividesthefirstargumentby thesecond and returns thequotient and remainder as atuple).def int_to_time(seconds):time = Time()minutes, time.second = divmod(seconds, 60)time.hour, time.minute = divmod(minutes, 60)return timeYou might have to think a bit, and run some tests, to convince yourself that these functions arecorrect. One way to test them is to check that time_to_int(int_to_time(x)) == x for manyvalues ofx. Thisis anexample of aconsistency check.Once you areconvinced they are correct, you can use them torewriteadd_time:def add_time(t1, t2):seconds = time_to_int(t1) + time_to_int(t2)return int_to_time(seconds)This version isshorter than theoriginal, and easier toverify.Exercise 16.5 Rewriteincrementusingtime_to_intandint_to_time.In some ways, converting from base 60 to base 10 and back is harder than just dealing with times.Base conversion ismoreabstract; our intuitionfordealing withtimevalues isbetter.

16.5. Debugging 157But if we have the insight to treat times as base 60 numbers and make the investment of writing theconversion functions (time_to_int and int_to_time), we get a program that is shorter, easier toread and debug, and morereliable.Itisalsoeasiertoaddfeatureslater. Forexample,imaginesubtractingtwoTimestofindthedurationbetween them. The naïve approach would be to implement subtraction with borrowing. Using theconversion functions would be easier and more likelytobecorrect.Ironically,sometimesmakingaproblemharder(ormoregeneral)makesiteasier(becausetherearefewer special cases and fewer opportunities for error).16.5 DebuggingATimeobjectiswell-formedifthevaluesofminutesandsecondsarebetween0and60(including0 but not 60) and if hours is positive. hours and minutes should be integral values, but we mightallowsecondstohave afraction part.Requirementslikethesearecalledinvariantsbecausetheyshouldalwaysbetrue. Toputitadifferentway, ifthey are not true, then something has gone wrong.Writingcodetocheckyourinvariantscanhelpyoudetecterrorsandfindtheircauses. Forexample,youmighthaveafunctionlikevalid_timethattakesaTimeobjectandreturnsFalseifitviolatesan invariant:def valid_time(time):if time.hours < 0 or time.minutes < 0 or time.seconds < 0:return Falseif time.minutes >= 60 or time.seconds >= 60:return Falsereturn TrueThen atthe beginning of each function you could check the arguments tomake surethey arevalid:def add_time(t1, t2):if not valid_time(t1) or not valid_time(t2):raise ValueError, 'invalid Time object in add_time'seconds = time_to_int(t1) + time_to_int(t2)return int_to_time(seconds)Or you could use an assert statement, which checks a given invariant and raises an exception if itfails:def add_time(t1, t2):assert valid_time(t1) and valid_time(t2)seconds = time_to_int(t1) + time_to_int(t2)return int_to_time(seconds)assert statements are useful because they distinguish code that deals with normal conditions fromcode that checks forerrors.

158 Chapter 16. Classesand functions16.6 Glossaryprototype and patch: Adevelopmentplanthatinvolveswritingaroughdraftofaprogram,testing,and correcting errorsas they arefound.planned development: A development plan that involves high-level insight into the problem andmore planning than incremental development or prototype development.pure function: A function that does not modify any of the objects it receives as arguments. Mostpure functions arefruitful.modifier: A function that changes one or more of the objects it receives as arguments. Most modifiersare fruitless.functional programming style: A style of program design in which the majority of functions arepure.invariant: A condition that should always be trueduring theexecution of aprogram.16.7 ExercisesExercise16.6 Writeafunctioncalledmul_timethattakesaTimeobjectandanumberandreturnsanew Time object that contains theproduct ofthe original Time and the number.Then use mul_time to write a function that takes a Time object that represents the finishing timein a race, and a number that represents the distance, and returns a Time object that represents theaverage pace (timeper mile).Exercise 16.7 Write a class definition for a Date object that has attributes day, month and year.Writeafunctioncalledincrement_datethattakesaDateobject,dateandaninteger,n,andreturnsa new Date object that represents the day n days after date. Hint: “Thirty days hath September...”Challenge: does your function deal with leap years correctly? See wikipedia.org/wiki/Leap_year.Exercise 16.8 The datetime module provides date and time objects that are similar to the Dateand Time objects in this chapter, but they provide a rich set of methods and operators. Read thedocumentation atdocs.python.org/lib/datetime-date.html.1. Use the datetime module to write a program that gets the current date and prints the day ofthe week.2. Write a program that takes a birthday as input and prints the user’s age and the number ofdays, hours, minutes and seconds until their next birthday.

Chapter 17Classes and methods17.1 Object-orientedfeaturesPython is an object-oriented programming language, which means that it provides features thatsupport object-oriented programming.It is not easy to define object-oriented programming, but we have already seen some of its characteristics:• Programs are made up of object definitions and function definitions, and most of the computationisexpressed intermsof operations on objects.• Each object definition corresponds to some object or concept in the real world, and the functionsthat operate onthat object correspond totheways real-world objects interact.For example, the Time class defined in Chapter 16 corresponds to the way people record the timeof day, and the functions we defined correspond to the kinds of things people do with times. Similarly,the Point and Rectangle classes correspond to the mathematical concepts of a point and arectangle.So far, we have not taken advantage of the features Python provides to support object-orientedprogramming. Thesefeaturesarenotstrictlynecessary; mostofthemprovidealternativesyntaxforthingswehavealreadydone. Butinmanycases,thealternativeismoreconciseandmoreaccuratelyconveys thestructureof theprogram.For example, in the Time program, there is no obvious connection between the class definition andthe function definitions that follow. With some examination, it is apparent that every function takesat least oneTimeobject as anargument.This observation is the motivation for methods; a method is a function that is associated with aparticular class. We have seen methods for strings, lists, dictionaries and tuples. In this chapter, wewilldefine methods for user-defined types.Methods aresemantically thesame asfunctions, but there aretwosyntactic differences:• Methods are defined inside a class definition in order to make the relationship between theclass and the method explicit.

160 Chapter 17. Classes and methods• The syntax for invoking amethod isdifferent fromthe syntax forcalling afunction.In the next few sections, we will take the functions from the previous two chapters and transformthem into methods. This transformation is purely mechanical; you can do it simply by following asequence of steps. If you are comfortable converting from one form to another, you will be able tochoose thebest form forwhatever you aredoing.17.2 PrintingobjectsIn Chapter 16, we defined a class named Time and in Exercise 16.1, you wrote a function namedprint_time:class Time(object):"""represents the time of day.attributes: hour, minute, second"""def print_time(time):print '%.2d:%.2d:%.2d' % (time.hour, time.minute, time.second)To call thisfunction, you have topass aTimeobject asan argument:>>> start = Time()>>> start.hour = 9>>> start.minute = 45>>> start.second = 00>>> print_time(start)09:45:00To make print_time a method, all we have to do is move the function definition inside the classdefinition. Notice thechange inindentation.class Time(object):def print_time(time):print '%.2d:%.2d:%.2d' % (time.hour, time.minute, time.second)Now there are two ways to call print_time. The first (and less common) way is to use functionsyntax:>>> Time.print_time(start)09:45:00Inthisuseofdotnotation,Timeisthenameoftheclass,andprint_timeisthenameofthemethod.startis passedas aparameter.The second (and moreconcise) way istousemethod syntax:>>> start.print_time()09:45:00In this use of dot notation, print_time is the name of the method (again), and start is the objectthe method is invoked on, which is called the subject. Just as the subject of a sentence is what thesentence isabout, the subject of amethod invocation iswhat themethod isabout.

17.3. Another example 161Inside the method, the subject is assigned to the first parameter, so in this case start is assigned totime.Byconvention,thefirstparameterofamethodiscalledself,soitwouldbemorecommontowriteprint_timelikethis:class Time(object):def print_time(self):print '%.2d:%.2d:%.2d' % (self.hour, self.minute, self.second)The reason forthis convention isan implicitmetaphor:• The syntax for a function call, print_time(start), suggests that the function is the activeagent. Itsays something like, “Heyprint_time! Here’s an object foryou toprint.”• In object-oriented programming, the objects are the active agents. A method invocation likestart.print_time()says “Heystart! Please print yourself.”Thischangeinperspectivemightbemorepolite,butitisnotobviousthatitisuseful. Intheexampleswe have seen so far, it may not be. But sometimes shifting responsibility from the functions ontothe objects makes it possible to write more versatile functions, and makes it easier to maintain andreusecode.Exercise17.1 Rewritetime_to_int(fromSection16.4)asamethod. Itisprobablynotappropriatetorewriteint_to_timeasamethod; it’snot clear what object you would invoke iton!17.3 AnotherexampleHere’s aversion ofincrement(fromSection 16.3) rewrittenas amethod:# inside class Time:def increment(self, seconds):seconds += self.time_to_int()return int_to_time(seconds)This version assumes that time_to_int is written as a method, as in Exercise 17.1. Also, note thatitisapure function, not amodifier.Here’s how you would invokeincrement:>>> start.print_time()09:45:00>>> end = start.increment(1337)>>> end.print_time()10:07:17The subject, start, gets assigned to the first parameter, self. The argument, 1337, gets assignedtothesecond parameter,seconds.This mechanism can be confusing, especially if you make an error. For example, if you invokeincrementwithtwoarguments, you get:

162 Chapter 17. Classes and methods>>> end = start.increment(1337, 460)TypeError: increment() takes exactly 2 arguments (3 given)The error message is initially confusing, because there are only two arguments in parentheses. Butthesubject isalsoconsidered an argument, soall together that’s three.17.4 Amorecomplicatedexampleis_after (from Exercise 16.2) is slightly more complicated because it takes two Time objects asparameters. Inthiscaseitisconventionaltonamethefirstparameterselfandthesecondparameterother:# inside class Time:def is_after(self, other):return self.time_to_int() > other.time_to_int()To usethis method, you have toinvoke it onone object and pass theother asan argument:>>> end.is_after(start)TrueOne nice thingabout thissyntax isthat italmost reads likeEnglish: “end isafter start?”17.5 Theinit methodThe init method (short for “initialization”) is a special method that gets invoked when an object isinstantiated. Its full name is__init__(two underscore characters, followed byinit, and then twomore underscores). Aninit method for theTimeclass might look likethis:# inside class Time:def __init__(self, hour=0, minute=0, second=0):self.hour = hourself.minute = minuteself.second = secondItiscommonfortheparametersof__init__tohavethesamenamesastheattributes. Thestatementself.hour = hourstoresthe value of the parameterhouras anattributeofself.The parameters areoptional, soifyou callTimewithno arguments, you get thedefault values.>>> time = Time()>>> time.print_time()00:00:00Ifyou provide one argument, itoverrideshour:

17.6. The str method 163>>> time = Time (9)>>> time.print_time()09:00:00Ifyou provide twoarguments, they overridehourandminute.>>> time = Time(9, 45)>>> time.print_time()09:45:00And ifyou provide three arguments, they override all threedefault values.Exercise 17.2 Write an init method for the Point class that takes x and y as optional parametersand assigns them tothe corresponding attributes.17.6 The str method__str__isaspecial method, like__init__,that issupposed toreturn astringrepresentation of anobject.For example, here isastrmethod forTime objects:# inside class Time:def __str__(self):return '%.2d:%.2d:%.2d' % (self.hour, self.minute, self.second)When youprintan object, Python invokes thestrmethod:>>> time = Time(9, 45)>>> print time09:45:00When I write a new class, I almost always start by writing __init__, which makes it easier toinstantiateobjects, and__str__,which isuseful fordebugging.Exercise 17.3 Writeastrmethod forthePointclass. Create aPoint object and print it.17.7 OperatoroverloadingBy defining other special methods, you can specify the behavior of operators on user-defined types.For example, if you define a method named __add__ for the Time class, you can use the + operatoron Timeobjects.Here iswhat the definition might look like:# inside class Time:def __add__(self, other):seconds = self.time_to_int() + other.time_to_int()return int_to_time(seconds)

164 Chapter 17. Classes and methodsAnd here ishow you could useit:>>> start = Time(9, 45)>>> duration = Time(1, 35)>>> print start + duration11:20:00Whenyouapplythe+operatortoTimeobjects,Pythoninvokes__add__. Whenyouprinttheresult,Python invokes__str__. Sothere isquitealothappening behind thescenes!Changing the behavior of an operator so that it works with user-defined types is called operatoroverloading. For every operator in Python there is a corresponding special method, like __add__.For moredetails, seedocs.python.org/ref/specialnames.html.Exercise 17.4 Writeanaddmethod for thePoint class.17.8 Type-baseddispatchIn the previous section we added two Time objects, but you also might want to add an integer to aTimeobject. Thefollowingisaversionof__add__thatchecksthetypeofotherandinvokeseitheradd_timeorincrement:# inside class Time:def __add__(self, other):if isinstance(other, Time):return self.add_time(other)else:return self.increment(other)def add_time(self, other):seconds = self.time_to_int() + other.time_to_int()return int_to_time(seconds)def increment(self, seconds):seconds += self.time_to_int()return int_to_time(seconds)The built-in function isinstance takes a value and a class object, and returns True if the value isan instance of theclass.If other is a Time object, __add__ invokes add_time. Otherwise it assumes that the parameteris a number and invokes increment. This operation is called a type-based dispatch because itdispatches the computation todifferent methods based on thetype of thearguments.Here areexamples that usethe+operator withdifferent types:>>> start = Time(9, 45)>>> duration = Time(1, 35)>>> print start + duration11:20:00>>> print start + 133710:07:17

17.9. Polymorphism 165Unfortunately,thisimplementationofadditionisnotcommutative. Iftheintegeristhefirstoperand,you get>>> print 1337 + startTypeError: unsupported operand type(s) for +: 'int' and 'instance'The problem is, instead of asking the Time object to add an integer, Python is asking an integer toaddaTimeobject,anditdoesn’tknowhowtodothat. Butthereisacleversolutionforthisproblem:the special method __radd__, which stands for “right-side add.” This method is invoked when aTime object appears on theright sideof the+operator. Here’s thedefinition:# inside class Time:def __radd__(self, other):return self.__add__(other)And here’s how it’sused:>>> print 1337 + start10:07:17Exercise 17.5 Writeanaddmethod for Points that works witheither a Point object or atuple:• If the second operand is a Point, the method should return a new Point whose x coordinate isthe sum of thexcoordinates of the operands, and likewise forthe ycoordinates.• If the second operand is a tuple, the method should add the first element of the tuple to the xcoordinate and thesecond element tothe ycoordinate, and returnanew Point withtheresult.17.9 PolymorphismType-baseddispatchisusefulwhenitisnecessary,but(fortunately)itisnotalwaysnecessary. Oftenyou can avoid it bywritingfunctions that workcorrectly for arguments withdifferent types.Manyofthefunctionswewroteforstringswillactuallyworkforanykindofsequence. Forexample,inSection 11.1we usedhistogramtocount thenumber oftimes each letterappears inaword.def histogram(s):d = dict()for c in s:if c not in d:d[c] = 1else:d[c] = d[c]+1return dThis function also works for lists, tuples, and even dictionaries, as long as the elements of s arehashable, sothey can be usedas keys ind.>>> t = ['spam', 'egg', 'spam', 'spam', 'bacon', 'spam']>>> histogram(t){'bacon': 1, 'egg': 1, 'spam': 4}

166 Chapter 17. Classes and methodsFunctions that can work with several types are called polymorphic. Polymorphism can facilitatecode reuse. For example, the built-in function sum, which adds the elements of a sequence, worksas long as theelements of thesequence support addition.Since Time objects provide anaddmethod, they work withsum:>>> t1 = Time(7, 43)>>> t2 = Time(7, 41)>>> t3 = Time(7, 37)>>> total = sum([t1, t2, t3])>>> print total23:01:00In general, if all of the operations inside a function work with a given type, then the function workswiththat type.The best kind of polymorphism is the unintentional kind, where you discover that a function youalready wrote can be applied toatype you never planned for.17.10 DebuggingIt is legal to add attributes to objects at any point in the execution of a program, but if you area stickler for type theory, it is a dubious practice to have objects of the same type with differentattributesets. Itisusually agood idea toinitializeall ofan objects attributesinthe initmethod.If you are not sure whether an object has a particular attribute, you can use the built-in functionhasattr(seeSection 15.7).Anotherwaytoaccesstheattributesofanobjectisthroughthespecialattribute__dict__,whichisadictionary that maps attributenames (as strings)and values:>>> p = Point(3, 4)>>> print p.__dict__{'y': 4, 'x': 3}For purposes ofdebugging, you might find ituseful tokeep thisfunction handy:def print_attributes(obj):for attr in obj.__dict__:print attr, getattr(obj, attr)print_attributestraversestheitemsintheobject’sdictionaryandprintseachattributenameanditscorresponding value.The built-in function getattr takes an object and an attribute name (as a string) and returns theattribute’svalue.17.11 Glossaryobject-oriented language: A language that provides features, such as user-defined classes andmethod syntax, that facilitateobject-oriented programming.

17.12. Exercises 167object-oriented programming: Astyleofprogramminginwhichdataandtheoperationsthatmanipulateitareorganized intoclasses and methods.method: Afunctionthatisdefinedinsideaclassdefinitionandisinvokedoninstancesofthatclass.subject: The object amethod isinvoked on.operator overloading: Changingthebehaviorofanoperatorlike+soitworkswithauser-definedtype.type-based dispatch: A programming pattern that checks the type of an operand and invokes differentfunctions for different types.polymorphic: Pertaining toafunction that can work withmorethan one type.17.12 ExercisesExercise17.6 Thisexerciseisacautionarytaleaboutoneofthemostcommon,anddifficulttofind,errorsinPython.1. Writeadefinition foraclass namedKangaroowiththefollowing methods:(a) An __init__ method that initializes an attribute named pouch_contents to an emptylist.(b) A method named put_in_pouch that takes an object of any type and adds it topouch_contents.(c) A __str__ method that returns a string representation of the Kangaroo object and thecontents of thepouch.Test your code by creating two Kangaroo objects, assigning them to variables named kangaandroo,and then addingrootothecontents ofkanga’spouch.2. Downloadthinkpython.com/code/BadKangaroo.py. Itcontainsasolutiontothepreviousproblem withone big, nastybug. Findand fixthe bug.If you get stuck, you can download thinkpython.com/code/GoodKangaroo.py, which explainstheproblem and demonstrates asolution.Exercise 17.7 Visual is a Python module that provides 3-D graphics. It is not always included in aPythoninstallation,soyoumighthavetoinstallitfromyoursoftwarerepositoryor,ifit’snotthere,fromvpython.org.The following example creates a 3-D space that is 256 units wide, long and high, and sets the“center” tobe thepoint (128,128,128). Then itdraws a bluesphere.from visual import *scene.range = (256, 256, 256)scene.center = (128, 128, 128)color = (0.1, 0.1, 0.9) # mostly bluesphere(pos=scene.center, radius=128, color=color)

168 Chapter 17. Classes and methodscolor is an RGB tuple; that is, the elements are Red-Green-Blue levels between 0.0 and 1.0 (seewikipedia.org/wiki/RGB_color_model).If you run this code, you should see a window with a black background and a blue sphere. If youdrag the middle button up and down, you can zoom in and out. You can also rotate the scene bydragging theright button, but withonly one sphere intheworld, itis hardtotell thedifference.The following loop creates acube of spheres:t = range(0, 256, 51)for x in t:for y in t:for z in t:pos = x, y, zsphere(pos=pos, radius=10, color=color)1. Put thiscode inascriptand make sureitworks foryou.2. Modify the program so that each sphere in the cube has the color that corresponds to itspositioninRGBspace. Noticethatthecoordinatesareintherange0–255,buttheRGBtuplesare intherange 0.0–1.0.3. Download thinkpython.com/code/color_list.py and use the function read_colors togenerate a list of the available colors on your system, their names and RGB values. For eachnamed color draw asphere intheposition that corresponds toitsRGB values.You can see mysolutionatthinkpython.com/code/color_space.py.

Chapter 18InheritanceIn this chapter we will develop classes to represent playing cards, decks of cards, and poker hands.If you don’t play poker, you can read about it at wikipedia.org/wiki/Poker, but you don’t haveto; I’lltellyou what you need toknow forthe exercises.IfyouarenotfamiliarwithAnglo-Americanplayingcards,youcanreadaboutthematwikipedia.org/wiki/Playing_cards.18.1 CardobjectsThere are fifty-two cards in a deck, each of which belongs to one of four suits and one of thirteenranks. The suits are Spades, Hearts, Diamonds, and Clubs (in descending order in bridge). Theranks are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. Depending on the game that you areplaying, an Ace may be higher thanKing or lower than2.Ifwewanttodefineanewobjecttorepresentaplayingcard,itisobviouswhattheattributesshouldbe: rank and suit. It is not as obvious what type the attributes should be. One possibility is touse strings containing words like'Spade' for suits and'Queen' for ranks. One problem with thisimplementationisthatitwouldnotbeeasytocomparecardstoseewhichhadahigherrankorsuit.An alternative is to use integers to encode the ranks and suits. In this context, “encode” means thatwe are going to define a mapping between numbers and suits, or between numbers and ranks. Thiskind of encoding isnot meant tobe asecret (that would be “encryption”).For example, thistable shows the suitsand thecorresponding integer codes:Spades ↦→ 3Hearts ↦→ 2Diamonds ↦→ 1Clubs ↦→ 0This code makes it easy to compare cards; because higher suits map to higher numbers, we cancompare suitsby comparing theircodes.The mapping for ranks is fairly obvious; each of the numerical ranks maps to the correspondinginteger, and forface cards:

170 Chapter 18. InheritanceJack ↦→ 11Queen ↦→ 12King ↦→ 13I am using the ↦→ symbol to make it clear that these mappings are not part of the Python program.They arepart of the program design, but they don’t appear explicitly inthe code.The class definition forCardlooks likethis:class Card(object):"""represents a standard playing card."""def __init__(self, suit=0, rank=2):self.suit = suitself.rank = rankAs usual, the init method takes an optional parameter for each attribute. The default card is the 2 ofClubs.To create aCard, you callCardwiththesuitand rankof the card you want.queen_of_diamonds = Card(1, 12)18.2 ClassattributesIn order to print Card objects in a way that people can easily read, we need a mapping from theinteger codes to the corresponding ranks and suits. A natural way to do that is with lists of strings.We assigntheseliststoclass attributes:# inside class Card:suit_names = ['Clubs', 'Diamonds', 'Hearts', 'Spades']rank_names = [None, 'Ace', '2', '3', '4', '5', '6', '7','8', '9', '10', 'Jack', 'Queen', 'King']def __str__(self):return '%s of %s' % (Card.rank_names[self.rank],Card.suit_names[self.suit])Variables like suit_names and rank_names, which are defined inside a class but outside of anymethod, are called classattributes because they areassociated withtheclass objectCard.This term distinguishes them from variables like suit and rank, which are called instance attributesbecause they areassociated withaparticular instance.Both kinds of attribute are accessed using dot notation. For example, in __str__, self is a Cardobject, and self.rank is its rank. Similarly, Card is a class object, and Card.rank_names is a listof stringsassociated withtheclass.Everycardhasitsownsuitandrank,butthereisonlyonecopyofsuit_namesandrank_names.Puttingitalltogether,theexpressionCard.rank_names[self.rank]means“usetheattributerankfrom the object self as an index into the list rank_names from the class Card, and select theappropriate string.”

18.3. Comparing cards 171Thefirstelementofrank_namesisNonebecausethereisnocardwithrankzero. ByincludingNoneas a place-keeper, we get a mapping with the nice property that the index 2 maps to the string'2',and soon. To avoid thistweak, we could have used adictionary instead of alist.Withthe methods wehave sofar,wecan create and print cards:>>> card1 = Card(2, 11)>>> print card1Jack of HeartsHere isadiagram that shows theCardclass object and one Card instance:Cardtypesuit_namesrank_nameslistlistcard1Cardsuitrank111Card is a class object, so it has type type. card1 has type Card. (To save space, I didn’t draw thecontents ofsuit_namesandrank_names).18.3 ComparingcardsFor built-in types, there are relational operators (, ==, etc.) that compare values and determinewhen one is greater than, less than, or equal to another. For user-defined types, we can override thebehavior of thebuilt-inoperators by providing amethod named__cmp__.__cmp__ takes two parameters, self and other, and returns a positive number if the first object isgreater, anegative number if thesecond object isgreater, and 0ifthey areequal toeach other.The correct ordering for cards is not obvious. For example, which is better, the 3 of Clubs or the 2ofDiamonds? Onehasahigherrank,buttheotherhasahighersuit. Inordertocomparecards,youhave todecide whether rank or suitismoreimportant.The answer might depend on what game you are playing, but to keep things simple, we’ll make thearbitrarychoicethatsuitismoreimportant,soalloftheSpadesoutrankalloftheDiamonds,andsoon.Withthat decided, wecan write__cmp__:# inside class Card:def __cmp__(self, other):# check the suitsif self.suit > other.suit: return 1

172 Chapter 18. Inheritanceif self.suit < other.suit: return -1# suits are the same... check ranksif self.rank > other.rank: return 1if self.rank < other.rank: return -1# ranks are the same... it's a tiereturn 0You can writethismore concisely using tuplecomparison:# inside class Card:def __cmp__(self, other):t1 = self.suit, self.rankt2 = other.suit, other.rankreturn cmp(t1, t2)The built-in function cmp has the same interface as the method __cmp__: it takes two values andreturnsapositivenumberifthefirstislarger,anegativenumberifthesecondislarger,and0iftheyareequal.Exercise 18.1 Write a __cmp__ method for Time objects. Hint: you can use tuple comparison, butyou alsomight consider usinginteger subtraction.18.4 DecksNow that we have Cards, the next step is to define Decks. Since a deck is made up of cards, it isnatural foreach Deck tocontain alistofcards as anattribute.The following is a class definition for Deck. The init method creates the attribute cards and generatesthestandard setof fifty-twocards:class Deck(object):def __init__(self):self.cards = []for suit in range(4):for rank in range(1, 14):card = Card(suit, rank)self.cards.append(card)Theeasiestwaytopopulatethedeckiswithanestedloop. Theouterloopenumeratesthesuitsfrom0to3. Theinnerloopenumeratestheranksfrom1to13. EachiterationcreatesanewCardwiththecurrent suitand rank, and appends ittoself.cards.18.5 Printingthe deckHere isa__str__method forDeck:

18.6. Add, remove, shuffle and sort 173#inside class Deck:def __str__(self):res = []for card in self.cards:res.append(str(card))return '\n'.join(res)Thismethoddemonstratesanefficientwaytoaccumulatealargestring: buildingalistofstringsandthen using join. The built-in function str invokes the __str__ method on each card and returnsthestringrepresentation.Since we invoke join on a newline character, the cards are separated by newlines. Here’s what theresultlooks like:>>> deck = Deck()>>> print deckAce of Clubs2 of Clubs3 of Clubs...10 of SpadesJack of SpadesQueen of SpadesKing of SpadesEven though theresult appears on 52lines, itisone long stringthat contains newlines.18.6 Add,remove,shuffle and sortTo deal cards, we would like a method that removes a card from the deck and returns it. The listmethodpopprovides a convenient way todothat:#inside class Deck:def pop_card(self):return self.cards.pop()Since pop removes the last card in the list, we are dealing from the bottom of the deck. In real lifebottom dealing isfrowned upon 1 ,but inthis context it’sok.To add acard, wecan usethelistmethodappend:#inside class Deck:def add_card(self, card):self.cards.append(card)A method like this that uses another function without doing much real work is sometimes called aveneer. The metaphor comes from woodworking, where it is common to glue a thin layer of goodquality wood tothe surfaceof acheaper piece ofwood.1 Seewikipedia.org/wiki/Bottom_dealing

174 Chapter 18. InheritanceIn this case we are defining a “thin” method that expresses a list operation in terms that are appropriatefordecks.Asanotherexample,wecanwriteaDeckmethodnamedshuffleusingthefunctionshufflefromtherandommodule:# inside class Deck:def shuffle(self):random.shuffle(self.cards)Don’t forget toimportrandom.Exercise 18.2 Write a Deck method namedsortthat uses the list methodsortto sort the cards inaDeck. sortuses the__cmp__method wedefined todetermine sortorder.18.7 InheritanceThe language feature most often associated with object-oriented programming is inheritance. Inheritanceistheabilitytodefine a new classthat isamodified version of anexisting class.Itiscalled“inheritance”becausethenewclassinheritsthemethodsoftheexistingclass. Extendingthismetaphor, the existing classiscalled the parent and thenew classiscalled the child.As an example, let’s say we want a class to represent a “hand,” that is, the set of cards held by oneplayer. A hand is similar to a deck: both are made up of a set of cards, and both require operationslikeadding and removing cards.A hand is also different from a deck; there are operations we want for hands that don’t make sensefor a deck. For example, in poker we might compare two hands to see which one wins. In bridge,wemight compute ascorefor ahand inorder tomake a bid.This relationship between classes—similar,but different—lends itselftoinheritance.Thedefinitionofachildclassislikeotherclassdefinitions,butthenameoftheparentclassappearsinparentheses:class Hand(Deck):"""represents a hand of playing cards"""ThisdefinitionindicatesthatHandinheritsfromDeck;thatmeanswecanusemethodslikepop_cardandadd_cardfor Hands as wellas Decks.Handalsoinherits__init__fromDeck,butitdoesn’treallydowhatwewant: insteadofpopulatingthehand with52 new cards, theinit method for Hands should initializecardswithan empty list.Ifweprovide an initmethod intheHandclass, itoverrides the one intheDeckclass:# inside class Hand:def __init__(self, label=''):self.cards = []self.label = label

18.8. Classdiagrams 175So when you create a Hand, Python invokes this initmethod:>>> hand = Hand('new hand')>>> print hand.cards[]>>> print hand.labelnew handBut the other methods are inherited from Deck, so we can use pop_card and add_card to deal acard:>>> deck = Deck()>>> card = deck.pop_card()>>> hand.add_card(card)>>> print handKing of SpadesA natural next stepistoencapsulate thiscode inamethod calledmove_cards:#inside class Deck:def move_cards(self, hand, num):for i in range(num):hand.add_card(self.pop_card())move_cards takes two arguments, a Hand object and the number of cards to deal. It modifies bothselfandhand,and returnsNone.In some games, cards are moved from one hand to another, or from a hand back to the deck. Youcan use move_cards for any of these operations: self can be either a Deck or a Hand, and hand,despite thename, can alsobe aDeck.Exercise 18.3 Write a Deck method called deal_hands that takes two parameters, the number ofhands and the number of cards per hand, and that creates new Hand objects, deals the appropriatenumber of cards per hand, and returnsalistof Hand objects.Inheritance is a useful feature. Some programs that would be repetitive without inheritance can bewritten more elegantly with it. Inheritance can facilitate code reuse, since you can customize thebehavior of parent classes without having to modify them. In some cases, the inheritance structurereflects thenatural structureof theproblem, which makes theprogram easier tounderstand.Ontheotherhand, inheritancecanmakeprogramsdifficulttoread. Whenamethodisinvoked, itissometimes not clear where to find its definition. The relevant code may be scattered among severalmodules. Also, many of the things that can be done using inheritance can be done as well or betterwithout it.18.8 ClassdiagramsSofarwehaveseenstackdiagrams,whichshowthestateofaprogram,andobjectdiagrams,whichshow the attributes of an object and their values. These diagrams represent a snapshot in the executionofaprogram, sothey change as theprogram runs.

176 Chapter 18. InheritanceThey are also highly detailed; for some purposes, too detailed. A class diagram is a more abstractrepresentation of the structure of a program. Instead of showing individual objects, it shows classesand the relationships between them.There areseveral kinds of relationship between classes:• Objects in one class might contain references to objects in another class. For example, eachRectangle contains a reference to a Point, and each Deck contains references to many Cards.This kind of relationship iscalled HAS-A, as in, “aRectangle has aPoint.”• Oneclassmightinheritfromanother. ThisrelationshipiscalledIS-A,asin,“aHandisakindof aDeck.”• One class might depend on another in the sense that changes in one class would requirechanges intheother.A class diagram is a graphical representation of these relationships 2 . For example, this diagramshows the relationships betweenCard,DeckandHand.Deck*CardHandThe arrow with a hollow triangle head represents an IS-A relationship; in this case it indicates thatHand inherits from Deck.ThestandardarrowheadrepresentsaHAS-Arelationship;inthiscaseaDeckhasreferencestoCardobjects.The star (*) near the arrow head is a multiplicity; it indicates how many Cards a Deck has. Amultiplicity can be a simple number, like 52, a range, like 5..7 or a star, which indicates that aDeck can have any number ofCards.AmoredetaileddiagrammightshowthataDeckactuallycontainsalistofCards,butbuilt-intypeslikelistand dict areusually not included inclass diagrams.Exercise18.4 ReadTurtleWorld.py,World.pyandGui.pyanddrawaclassdiagramthatshowstherelationships among theclasses defined there.18.9 DebuggingInheritance can make debugging a challenge because when you invoke a method on an object, youmight not know which method willbe invoked.Suppose you are writing a function that works with Hand objects. You would like it to work withall kinds of Hands, like PokerHands, BridgeHands, etc. If you invoke a method like shuffle, you2 The diagrams I am using here are similar to UML (see wikipedia.org/wiki/Unified_Modeling_Language),with afew simplifications.

18.10. Glossary 177might get the one defined in Deck, but if any of the subclasses override this method, you’ll get thatversion instead.Anytimeyouareunsureabouttheflowofexecutionthroughyourprogram,thesimplestsolutionistoaddprintstatementsatthebeginningoftherelevantmethods. IfDeck.shuffleprintsamessagethat says something like Running Deck.shuffle, then as the program runs it traces the flow ofexecution.Asanalternative,youcouldusethisfunction,whichtakesanobjectandamethodname(asastring)and returns theclass that provides thedefinition of themethod:def find_defining_class(obj, meth_name):for ty in type(obj).mro():if meth_name in ty.__dict__:return tyHere’s an example:>>> hand = Hand()>>> print find_defining_class(hand, 'shuffle')So theshufflemethod for thisHand isthe one inDeck.find_defining_class uses the mro method to get the list of class objects (types) that will besearched formethods. “MRO” stands for“method resolution order.”Here’s a program design suggestion: whenever you override a method, the interface of the newmethod should be the same as the old. It should take the same parameters, return the same type,and obey the same preconditions and postconditions. If you obey this rule, you will find that anyfunctiondesignedtoworkwithaninstanceofasuperclass,likeaDeck,willalsoworkwithinstancesof subclasses likeaHand or PokerHand.Ifyou violate thisrule, your code will collapse like(sorry)ahouse of cards.18.10 Glossaryencode: To represent one set of values using another set of values by constructing a mapping betweenthem.class attribute: An attribute associated with a class object. Class attributes are defined inside aclass definition but outside any method.instance attribute: Anattributeassociated withaninstance of a class.veneer: A method or function that provides a different interface to another function without doingmuch computation.inheritance: The ability to define a new class that is a modified version of a previously definedclass.parent class: The classfrom which achild class inherits.child class: A new classcreated by inheritingfrom an existingclass; alsocalled a“subclass.”

178 Chapter 18. InheritanceIS-A relationship: The relationshipbetween a childclass and itsparent class.HAS-A relationship: The relationship between two classes where instances of one class containreferences toinstances of theother.class diagram: Adiagramthatshowstheclassesinaprogramandtherelationshipsbetweenthem.multiplicity: A notation in a class diagram that shows, for a HAS-A relationship, how many referencesthereare toinstances of another class.18.11 ExercisesExercise 18.5 The following are the possible hands in poker, in increasing order of value (anddecreasing order of probability):pair: twocards withthesame ranktwopair: twopairs of cards withthe samerankthree of akind: threecards withthe samerankstraight: five cards with ranks in sequence (aces can be high or low, so Ace-2-3-4-5 is a straightand sois10-Jack-Queen-King-Ace,butQueen-King-Ace-2-3isnot.)flush: five cards withthe samesuitfullhouse: threecards withone rank, twocards withanotherfour of akind: four cards withthesame rankstraight flush: five cards insequence (as defined above) and withthesame suitThe goal of theseexercises istoestimatetheprobability ofdrawing thesevarious hands.1. Download thefollowing files fromthinkpython.com/code:Card.py : A complete version of theCard,DeckandHandclasses inthischapter.PokerHand.py : An incomplete implementation of a class that represents a poker hand, andsomecode that testsit.2. If you runPokerHand.py,it deals seven 7-card poker hands and checks to see if any of themcontains aflush. Read this code carefully before you go on.3. Add methods to PokerHand.py named has_pair, has_twopair, etc. that return True orFalseaccordingtowhetherornotthehandmeetstherelevantcriteria. Yourcodeshouldworkcorrectlyfor“hands”thatcontainanynumberofcards(although5and7arethemostcommonsizes).4. Write a method named classify that figures out the highest-value classification for a handand sets the label attribute accordingly. For example, a 7-card hand might contain a flushand apair; itshould belabeled “flush”.5. When you are convinced that your classification methods are working, the next step is toestimatetheprobabilitiesofthevarioushands. WriteafunctioninPokerHand.pythatshufflesa deck of cards, divides it into hands, classifies the hands, and counts the number of timesvarious classifications appear.

18.11. Exercises 1796. Print a table of the classifications and their probabilities. Run your program with larger andlarger numbers of hands until the output values converge to a reasonable degree of accuracy.Compare your resultstothevalues atwikipedia.org/wiki/Hand_rankings.Exercise 18.6 This exercise uses TurtleWorld from Chapter 4. You will write code that makesTurtles play tag. If you are not familiar with the rules of tag, see wikipedia.org/wiki/Tag_(game).1. Download thinkpython.com/code/Wobbler.py and run it. You should see a TurtleWorldwiththree Turtles. Ifyou press the Run button, theTurtles wander at random.2. Read the code and make sure you understand how it works. The Wobbler class inherits fromTurtle,which means that theTurtlemethodslt,rt,fdandbkwork onWobblers.The step method gets invoked by TurtleWorld. It invokes steer, which turns the Turtlein the desired direction, wobble, which makes a random turn in proportion to the Turtle’sclumsiness, andmove,which moves forwardafew pixels, depending on the Turtle’sspeed.3. Create a file named Tagger.py. Import everything from Wobbler, then define a class namedTagger that inherits from Wobbler. Call make_world passing the Tagger class object as anargument.4. Add a steer method to Tagger to override the one in Wobbler. As a starting place, writea version that always points the Turtle toward the origin. Hint: use the math function atan2and theTurtleattributesx,yandheading.5. Modify steer so that the Turtles stay in bounds. For debugging, you might want to use theStep button, which invokessteponce on each Turtle.6. Modify steer so that each Turtle points toward its nearest neighbor. Hint: Turtles have anattribute,world,thatisareferencetotheTurtleWorldtheylivein,andtheTurtleWorldhasanattribute,animals,that isalistof all Turtles intheworld.7. Modify steer so the Turtles play tag. You can add methods to Tagger and you can overridesteer and __init__, but you may not modify or override step, wobble or move. Also,steerisallowed tochange the heading of theTurtle but not the position.Adjust the rules and your steer method for good quality play; for example, it should bepossible forthe slow Turtletotagthe fasterTurtles eventually.You can get mysolution fromthinkpython.com/code/Tagger.py.

180 Chapter 18. Inheritance

Chapter 19Case study: Tkinter19.1 GUIMost of the programs we have seen so far are text-based, but many programs use graphical userinterfaces, alsoknown as GUIs.PythonprovidesseveralchoicesforwritingGUI-basedprograms,includingwxPython,Tkinter,andQt. Each has pros and cons, which iswhy Python has not converged on astandard.The one I will present in this chapter is Tkinter because I think it is the easiest to get started with.Most ofthe concepts inthischapter apply totheother GUI modules, too.There are several books and web pages about Tkinter. One of the best online resources is An IntroductiontoTkinter by Fredrik Lundh.I have written a module called Gui.py that comes with Swampy. It provides a simplified interfacetothefunctions and classes inTkinter. The examples inthischapter arebased on thismodule.Here isasimpleexample that creates and displays a Gui:To create aGUI, you have toimportGuiand instantiate aGui object:from Gui import *g = Gui()g.title('Gui')g.mainloop()When you run this code, a window should appear with an empty gray square and the title Gui.mainloop runs the event loop, which waits for the user to do something and responds accordingly.Itisaninfiniteloop;itrunsuntiltheuserclosesthewindow,orpressesControl-C,ordoessomethingthat causes theprogram toquit.ThisGuidoesn’tdomuchbecauseitdoesn’thaveanywidgets. Widgetsaretheelementsthatmakeup aGUI;they include:Button: A widget, containing text or an image, that performs an action when pressed.Canvas: A region that can display lines,rectangles, circles and other shapes.

182 Chapter 19. Casestudy: TkinterEntry: A region where userscan typetext.Scrollbar: A widget that controls the visiblepart ofanother widget.Frame: A container, often invisible,that contains other widgets.The empty gray square you see when you create a Gui is a Frame. When you create a new widget,itisadded tothis Frame.19.2 Buttonsand callbacksThe methodbucreates aButton widget:button = g.bu(text='Press me.')The return value from bu is a Button object. The button that appears in the Frame is a graphicalrepresentation ofthis object; you can control thebutton by invoking methods onit.bu takes up to 32 parameters that control the appearance and function of the button. These parametersare called options. Instead of providing values for all 32 options, you can use keywordarguments, like text='Press me.', to specify only the options you need and use the default valuesfor therest.WhenyouaddawidgettotheFrame,itgets“shrink-wrapped;”thatis,theFrameshrinkstothesizeof theButton. Ifyou add morewidgets, the Frame grows toaccommodate them.The methodlacreates aLabel widget:label = g.la(text='Press the button.')By default, Tkinter stacks the widgets top-to-bottom and centers them. We’ll see how to overridethat behavior soon.If you press the button, you will see that it doesn’t do much. That’s because you haven’t “wired itup;” that is,you haven’t tolditwhat todo!The option that controls the behavior of a button is command. The value of command is a functionthat gets executed when the button is pressed. For example, here is a function that creates a newLabel:def make_label():g.la(text='Thank you.')Now wecan create abutton withthisfunction as itscommand:button2 = g.bu(text='No, press me!', command=make_label)When you press thisbutton, itshould executemake_labeland anew label should appear.The value of the command option is a function object, which is known as a callback because afteryoucallbutocreatethebutton,theflowofexecution“callsback”whentheuserpressesthebutton.This kind of flow is characteristic of event-driven programming. User actions, like button pressesandkeystrokes,arecalledevents. Inevent-drivenprogramming,theflowofexecutionisdeterminedby user actions rather than by theprogrammer.The challenge of event-driven programming is to construct a set of widgets and callbacks that workcorrectly (orat least generate appropriate errormessages) forany sequence of user actions.

19.3. Canvas widgets 183Exercise 19.1 Write a program that creates a GUI with a single button. When the button is presseditshouldcreateasecondbutton. Whenthatbuttonispressed,itshouldcreatealabelthatsays,“Nicejob!”.What happens if you press the buttons more than once? You can see my solution at thinkpython.com/code/button_demo.py19.3 Canvas widgetsOne of the most versatile widgets is the Canvas, which creates a region for drawing lines, circlesand other shapes. Ifyou didExercise 15.4 you arealready familiarwithcanvases.The methodcacreates anew Canvas:canvas = g.ca(width=500, height=500)widthandheightarethedimensions of the canvas inpixels.After you create a widget, you can still change the values of the options with the config method.For example, thebgoption changes thebackground color:canvas.config(bg='white')The value of bg is a string that names a color. The set of legal color names is different for differentimplementations of Python, but all implementations provide at least:white blackred green bluecyan yellow magentaShapes on a Canvas are called items. For example, the Canvas method circle draws (you guessedit)acircle:item = canvas.circle([0,0], 100, fill='red')Thefirstargumentisacoordinatepairthatspecifiesthecenterofthecircle;thesecondistheradius.Gui.py provides a standard Cartesian coordinate system with the origin at the center of the Canvasand the positive y axis pointing up. This is different from some other graphics systems where theoriginisinthe upper leftcorner, withthe yaxis pointing down.Thefilloption specifies that the circleshould be filledinwithred.ThereturnvaluefromcircleisanItemobjectthatprovidesmethodsformodifyingtheitemonthecanvas. For example, you can useconfigtochange any of thecircle’s options:item.config(fill='yellow', outline='orange', width=10)widthis thethickness of theoutline inpixels;outlineisthecolor.Exercise 19.2 Write a program that creates a Canvas and a Button. When the user presses theButton, itshould draw acircleon thecanvas.

184 Chapter 19. Casestudy: Tkinter19.4 CoordinatesequencesTherectanglemethodtakesasequenceofcoordinatesthatspecifyoppositecornersoftherectangle.Thisexampledrawsagreenrectanglewiththelowerleftcornerattheoriginandtheupperrightcorner at (200,100):canvas.rectangle([[0, 0], [200, 100]],fill='blue', outline='orange', width=10)Thiswayofspecifyingcornersiscalledaboundingboxbecausethetwopointsboundtherectangle.ovaltakes a bounding box and draws an oval withinthespecified rectangle:canvas.oval([[0, 0], [200, 100]], outline='orange', width=10)linetakesasequenceofcoordinatesanddrawsalinethatconnectsthepoints. Thisexampledrawstwolegs ofatriangle:canvas.line([[0, 100], [100, 200], [200, 100]], width=10)polygontakesthesamearguments,butitdrawsthelastlegofthepolygon(ifnecessary)andfillsitin:canvas.polygon([[0, 100], [100, 200], [200, 100]],fill='red', outline='orange', width=10)19.5 MorewidgetsTkinter provides two widgets that let users type text: an Entry, which is a single line, and a Textwidget, which has multiplelines.encreates a new Entry:entry = g.en(text='Default text.')Thetextoptionallowsyoutoputtextintotheentrywhenitiscreated. Thegetmethodreturnsthecontents of theEntry (which mayhave been changed by theuser):>>> entry.get()'Default text.'tecreates a Text widget:text = g.te(width=100, height=5)widthandheightarethedimensions of the widget incharacters and lines.insertputs text intotheText widget:text.insert(END, 'A line of text.')ENDisaspecial index that indicates the lastcharacter inthe Text widget.You can also specify a character using a dotted index, like 1.1, which has the line number beforethe dot and the column number after. The following example adds the letters 'nother' after thefirstcharacter of thefirstline.

19.6. Packing widgets 185>>> text.insert(1.1, 'nother')The get method reads the text in the widget; it takes a start and end index as arguments. Thefollowing example returns all thetext inthewidget, including thenewline character:>>> text.get(0.0, END)'Another line of text.\n'The delete method removes text from the widget; the following example deletes all but the firsttwocharacters:>>> text.delete(1.2, END)>>> text.get(0.0, END)'An\n'Exercise 19.3 Modify your solution to Exercise 19.2 by adding an Entry widget and a second button.When the user presses the second button, it should read a color name from the Entry and use itto change the fill color of the circle. Use config to modify the existing circle; don’t create a newone.Your program should handle the case where the user tries to change the color of a circle that hasn’tbeen created, and the casewhere the color name isinvalid.You can see mysolutionatthinkpython.com/code/circle_demo.py.19.6 PackingwidgetsSo far we have been stacking widgets in a single column, but in most GUIs the layout is morecomplicated. For example, hereisaslightlysimplified version of TurtleWorld (seeChapter 4).

186 Chapter 19. Casestudy: TkinterThissectionpresentsthecodethatcreatesthisGUI,brokenintoaseriesofsteps. Youcandownloadthecomplete example fromthinkpython.com/code/SimpleTurtleWorld.py.At the top level, this GUI contains two widgets—a Canvas and a Frame—arranged in a row. So thefirststepistocreate the row.class SimpleTurtleWorld(TurtleWorld):"""This class is identical to TurtleWorld, but the code thatlays out the GUI is simplified for explanatory purposes."""def setup(self):self.row()...setup is the function that creates and arranges the widgets. Arranging widgets in a GUI is calledpacking.row creates a row Frame and makes it the “current Frame.” Until this Frame is closed or anotherFrame iscreated, all subsequent widgets are packed inarow.Here isthecode that creates the Canvas and thecolumn Frame that hold theother widgets:self.canvas = self.ca(width=400, height=400, bg='white')self.col()The firstwidget inthecolumn isagridFrame, which contains four buttons arranged two-by-two:self.gr(cols=2)self.bu(text='Print canvas', command=self.canvas.dump)

19.6. Packing widgets 187self.bu(text='Quit', command=self.quit)self.bu(text='Make Turtle', command=self.make_turtle)self.bu(text='Clear', command=self.clear)self.endgr()gr creates the grid; the argument is the number of columns. Widgets in the grid are laid out left-toright,top-to-bottom.The first button uses self.canvas.dump as a callback; the second uses self.quit. These arebound methods, which means they are associated with a particular object. When they are invoked,they are invoked onthe object.The next widget inthe column isarow Frame that contains aButton and anEntry:self.row([0,1], pady=30)self.bu(text='Run file', command=self.run_file)self.en_file = self.en(text='snowflake.py', width=5)self.endrow()The first argument to row is a list of weights that determines how extra space is allocated betweenwidgets. The list [0,1] means that all extra space is allocated to the second widget, which is theEntry. If you run this code and resize the window, you will see that the Entry grows and the Buttondoesn’t.The optionpady“pads” thisrow inthe ydirection, adding 30pixels of space above and below.endrow ends this row of widgets, so subsequent widgets are packed in the column Frame. Gui.pykeeps astack of Frames:• When you use row, col or gr to create a Frame, it goes on top of the stack and becomes thecurrent Frame.• When you use endrow, endcol or endgr to close a Frame, it gets popped off the stack andthe previous Frame on thestack becomes thecurrent Frame.The method run_file reads the contents of the Entry, uses it as a filename, reads the contents andpasses it to run_code. self.inter is an Interpreter object that knows how to take a string andexecute itas Python code.def run_file(self):filename = self.en_file.get()fp = open(filename)source = fp.read()self.inter.run_code(source, filename)The lasttwowidgets areaText widget and aButton:self.te_code = self.te(width=25, height=10)self.te_code.insert(END, 'world.clear()\n')self.te_code.insert(END, 'bob = Turtle(world)\n')self.bu(text='Run code', command=self.run_text)run_text is similar torun_file except that it takes the code from the Text widget instead of fromafile:

188 Chapter 19. Casestudy: Tkinterdef run_text(self):source = self.te_code.get(1.0, END)self.inter.run_code(source, '')Unfortunately, the details of widget layout are different in other languages, and in different Pythonmodules. Tkinter alone provides three different mechanisms for arranging widgets. These mechanismsarecalledgeometrymanagers.TheoneIdemonstratedinthissectionisthe“grid”geometrymanager; theothers are called “pack” and “place”.Fortunately, most of theconcepts inthissection apply toother GUI modules and other languages.19.7 Menusand CallablesA Menubutton is a widget that looks like a button, but when pressed it pops up a menu. After theuser selects anitem, themenu disappears.Here is code that creates a color selection Menubutton (you can download it from thinkpython.com/code/menubutton_demo.py):g = Gui()g.la('Select a color:')colors = ['red', 'green', 'blue']mb = g.mb(text=colors[0])mb creates the Menubutton. Initially, the text on the button is the name of the default color. Thefollowing loop creates one menu item foreach color:for color in colors:g.mi(mb, text=color, command=Callable(set_color, color))The firstargument ofmiistheMenubutton theseitems areassociated with.The command option is a Callable object, which is something new. So far we have seen functionsand bound methods used as callbacks, which works fine if you don’t have to pass any argumentsto the function. Otherwise you have to construct a Callable object that contains a function, likeset_color,and itsarguments, likecolor.The Callable object stores a reference to the function and the arguments as attributes. Later, whentheuser clicks onamenu item,the callback calls thefunction and passes thestoredarguments.Here iswhatset_colormight look like:def set_color(color):mb.config(text=color)print colorWhentheuserselectsamenuitemandset_coloriscalled,itconfigurestheMenubuttontodisplaythe newly-selected color. It also print the color; if you try this example, you can confirm thatset_coloriscalled when you select anitem (and not called when you create the Callable object).

19.8. Binding 18919.8 BindingAbindingisanassociationbetweenawidget,aneventandacallback: whenanevent(likeabuttonpress)happens on awidget, thecallback isinvoked.Many widgets have default bindings. For example, when you press a button, the default bindingchangesthereliefofthebuttontomakeitlookdepressed. Whenyoureleasethebutton,thebindingrestoresthe appearance of the button and invokes thecallback specified withthecommandoption.Youcanusethebindmethodtooverridethesedefaultbindingsortoaddnewones. Forexample,thiscodecreatesabindingforacanvas(youcandownloadthecodeinthissectionfromthinkpython.com/code/draggable_demo.py):ca.bind('', make_circle)The first argument is an event string; this event is triggered when the user presses the left mousebutton. Other mouse events includeButtonMotion,ButtonReleaseandDouble-Button.The second argument is an event handler. An event handler is a function or bound method, like acallback, but an important difference is that an event handler takes an Event object as a parameter.Here isanexample:def make_circle(event):pos = ca.canvas_coords([event.x, event.y])item = ca.circle(pos, 5, fill='red')The Event object contains information about the type of event and details like the coordinates ofthe mouse pointer. In this example the information we need is the location of the mouse click.These values are in “pixel coordinates,” which are defined by the underlying graphical system. Themethodcanvas_coordstranslatesthemto“Canvascoordinates,”whicharecompatiblewithCanvasmethods likecircle.For Entry widgets, it is common to bind the event, which is triggered when the userpresses the Returnor Enter key. For example, thefollowing code creates a Button and anEntry.bu = g.bu('Make text item:', make_text)en = g.en()en.bind('', make_text)make_text is called when the Button is pressed or when the user hits Return while typing in theEntry. To make thiswork, weneed afunctionthat canbecalled asacommand (withnoarguments)or as anevent handler (withan Event as anargument):def make_text(event=None):text = en.get()item = ca.text([0,0], text)make_textgets thecontents of the Entryand displays it asaText item inthe Canvas.It is also possible to create bindings for Canvas items. The following is a class definition forDraggable, which is a child class of Item that provides bindings that implement drag-and-dropcapability.class Draggable(Item):

190 Chapter 19. Casestudy: Tkinterdef __init__(self, item):self.canvas = item.canvasself.tag = item.tagself.bind('', self.select)self.bind('', self.drag)self.bind('', self.drop)The init method takes an Item as a parameter. It copies the attributes of the Item and then createsbindings for threeevents: abutton press,button motion, and button release.The event handler select stores the coordinates of the current event and the original color of theitem, then changes thecolor toyellow:def select(self, event):self.dragx = event.xself.dragy = event.yself.fill = self.cget('fill')self.config(fill='yellow')cgetstandsfor“getconfiguration;”ittakesthenameofanoptionasastringandreturnsthecurrentvalue of that option.drag computes how far the object has moved relative to the starting place, updates the stored coordinates,and then moves the item.def drag(self, event):dx = event.x - self.dragxdy = event.y - self.dragyself.dragx = event.xself.dragy = event.yself.move(dx, dy)This computation isdone inpixel coordinates; thereisno need toconvert toCanvas coordinates.Finally,droprestorestheoriginal color of the item:def drop(self, event):self.config(fill=self.fill)You can use theDraggable class to add drag-and-drop capability to an existing item. For example,here is a modified version of make_circle that uses circle to create an Item and Draggable tomake it draggable:def make_circle(event):pos = ca.canvas_coords([event.x, event.y])item = ca.circle(pos, 5, fill='red')item = Draggable(item)This example demonstrates one of the benefits of inheritance: you can modify the capabilities ofa parent class without modifying its definition. This is particularly useful if you want to changebehavior defined inamodule you did not write.

19.9. Debugging 19119.9 DebuggingOne of the challenges of GUI programming is keeping track of which things happen while the GUIisbeing built and which things happen later inresponse touser events.Forexample,whenyouaresettingupacallback,itisacommonerrortocallthefunctionratherthanpassing areference toit:def the_callback():print 'Called.'g.bu(text='This is wrong!', command=the_callback())If you run this code, you will see that it calls the_callback immediately, and then creates thebutton. When you press the button, it does nothing because the return value from the_callback isNone. UsuallyyoudonotwanttoinvokeacallbackwhileyouaresettinguptheGUI;itshouldonlybe invoked laterinresponse toauser event.Another challenge of GUI programming is that you don’t have control of the flow of execution.Whichpartsoftheprogramexecuteandtheirorderaredeterminedbyuseractions. Thatmeansthatyou have todesign your program toworkcorrectly for any possiblesequence of events.For example, the GUI in Exercise 19.3 has two widgets: one creates a Circle item and the otherchanges the color of the Circle. If the user creates the circle and then changes its color, there’s noproblem. But what if the user changes the color of a circle that doesn’t exist yet? Or creates morethan one circle?As the number of widgets grows, it is increasingly difficult to imagine all possible sequences ofevents. Onewaytomanagethiscomplexityistoencapsulatethestateofthesysteminanobjectandthen consider:• Whatarethepossiblestates? IntheCircleexample,wemightconsidertwostates: beforeandafter theuser creates thefirst circle.• In each state, what events can occur? In the example, the user can press either of the buttons,or quit.• For each state-event pair, what is the desired outcome? Since there are two states and twobuttons, thereare fourstate-event pairs toconsider.• What can cause a transition from one state to another? In this case, there is a transition whenthe user creates the firstcircle.You might also find it useful to define, and check, invariants that should hold regardless of thesequence of events.This approach to GUI programming can help you write correct code without taking the time to testevery possiblesequence of user events!19.10 GlossaryGUI: A graphical user interface.widget: One of theelements that makes up aGUI, including buttons, menus, text entry fields, etc.

192 Chapter 19. Casestudy: Tkinteroption: A value that controls the appearance orfunction ofawidget.keyword argument: An argument that indicates theparameter name aspart ofthe function call.callback: A function associated withawidget that iscalled when theuser performs anaction.bound method: A method associated withaparticular instance.event-driven programming: Astyleofprogramminginwhichtheflowofexecutionisdeterminedby user actions.event: A user action, likeamouse click orkey press,that causes aGUI torespond.event loop: Aninfinite loop that waits foruser actions and responds.item: A graphical element on aCanvas widget.bounding box: Arectanglethatenclosesasetofitems,usuallyspecifiedbytwoopposingcorners.pack: To arrange and displaythe elements ofaGUI.geometry manager: A system for packing widgets.binding: An association between a widget, an event, and an event handler. The event handler iscalled when theevent occurs inthe widget.19.11 ExercisesExercise 19.4 For this exercise, you willwritean image viewer. Here isasimpleexample:g = Gui()canvas = g.ca(width=300)photo = PhotoImage(file='danger.gif')canvas.image([0,0], image=photo)g.mainloop()PhotoImage reads a file and returns a PhotoImage object that Tkinter can display. Canvas.imageputs the image on the canvas, centered on the given coordinates. You can also put images on labels,buttons, and some other widgets:g.la(image=photo)g.bu(image=photo)PhotoImage can only handle a few image formats, like GIF and PPM, but we can use the PythonImaging Library (PIL)toread other files.The name of the PIL module is Image, but Tkinter defines an object with the same name. To avoidtheconflict, you can useimport...aslikethis:import Image as PILimport ImageTkThe first line imports Image and gives it the local name PIL. The second line imports ImageTk,which can translateaPILimage intoaTkinter PhotoImage. Here’san example:

19.11. Exercises 193image = PIL.open('allen.png')photo2 = ImageTk.PhotoImage(image)g.la(image=photo2)1. Download image_demo.py, danger.gif and allen.png from thinkpython.com/code.Runimage_demo.py. YoumighthavetoinstallPILandImageTk. Theyareprobablyinyoursoftwarerepository, but ifnot you can get them frompythonware.com/products/pil/.2. In image_demo.py change the name of the second PhotoImage from photo2 to photo andrun theprogram again. You should see thesecond PhotoImage but not the first.TheproblemisthatwhenyoureassignphotoitoverwritesthereferencetothefirstPhotoImage,which then disappears. The same thing happens if you assign a PhotoImage to a localvariable; itdisappears when the function ends.To avoid this problem, you have to store a reference to each PhotoImage you want to keep.Youcanuseaglobalvariable,orstorePhotoImagesinadatastructureorasanattributeofanobject.Thisbehaviorcanbefrustrating,whichiswhyIamwarningyou(andwhytheexampleimagesays “Danger!”).3. Starting with this example, write a program that takes the name of a directory and loopsthrough all the files, displaying any files that PIL recognizes as images. You can use a trystatement tocatch the files PILdoesn’t recognize.When theuser clicks on theimage, the program should displaythe next one.4. PIL provides a variety of methods for manipulating images. You can read about them atpythonware.com/library/pil/handbook. As a challenge, choose a few of these methodsand provide a GUIfor applying them toimages.You can download asimplesolution fromthinkpython.com/code/ImageBrowser.py.Exercise 19.5 A vector graphics editor is a program that allows users to draw and edit shapes onthescreen and generate output files invector graphics formatslike Postscriptand SVG 1 .Write a simple vector graphics editor using Tkinter. At a minimum, it should allow users to drawlines, circles and rectangles, and it should use Canvas.dump to generate a Postscript description ofthecontents ofthe Canvas.As achallenge, you could allow users toselect and resizeitems on theCanvas.Exercise 19.6 Use Tkinter to write a basic web browser. It should have a Text widget where theuser can enter aURLand aCanvas todisplay the contents of thepage.You can use the urllib module to download files (see Exercise 14.5) and the HTMLParser moduletoparsethe HTML tags (seedocs.python.org/lib/module-HTMLParser.html).At a minimum your browser should handle plain text and hyperlinks. As a challenge you couldhandle background colors,text formattingtags and images.1 Seewikipedia.org/wiki/Vector_graphics_editor.

194 Chapter 19. Casestudy: Tkinter

Appendix ADebuggingDifferentkindsoferrorscanoccurinaprogram,anditisusefultodistinguishamongtheminordertotrackthem down morequickly:• Syntax errors are produced by Python when it is translating the source code into byte code.Theyusuallyindicatethatthereissomethingwrongwiththesyntaxoftheprogram. Example:Omitting the colon at the end of a def statement yields the somewhat redundant messageSyntaxError: invalid syntax.• Runtimeerrorsareproduced bytheinterpreterifsomethinggoeswrongwhiletheprogram isrunning. Mostruntimeerrormessagesincludeinformationaboutwheretheerroroccurredandwhatfunctionswereexecuting. Example: Aninfiniterecursioneventually causestheruntimeerror “maximum recursion depth exceeded.”• Semantic errors are problems with a program that runs without producing error messages butdoesn’t do the right thing. Example: An expression may not be evaluated in the order youexpect, yielding anincorrect result.The first step in debugging is to figure out which kind of error you are dealing with. Although thefollowing sections are organized by error type, some techniques are applicable in more than onesituation.A.1 Syntax errorsSyntax errors are usually easy to fix once you figure out what they are. Unfortunately, the errormessagesareoftennothelpful. ThemostcommonmessagesareSyntaxError: invalid syntaxandSyntaxError: invalid token,neither of which isvery informative.On the other hand, the message does tell you where in the program the problem occurred. Actually,ittellsyouwherePythonnoticedaproblem,whichisnotnecessarilywheretheerroris. Sometimestheerror isprior tothelocation of the errormessage, oftenon the preceding line.If you are building the program incrementally, you should have a good idea about where the erroris. Itwillbe inthelast lineyou added.

196 Appendix A. DebuggingIfyouarecopyingcodefromabook,startbycomparingyourcodetothebook’scodeverycarefully.Check every character. At the same time, remember that the book might be wrong, so if you seesomething that looks likeasyntax error,it might be.Here aresomeways toavoid themost common syntax errors:1. Make sureyou arenot using aPython keyword for avariable name.2. Checkthatyouhaveacolonattheendoftheheaderofeverycompound statement,includingfor,while,if,anddefstatements.3. Make surethat any stringsinthe code have matching quotation marks.4. If you have multiline strings with triple quotes (single or double), make sure you have terminatedthe string properly. An unterminated string may cause an invalid token error atthe end of your program, or it may treat the following part of the program as a string until itcomes tothe next string. Inthe second case, itmight not produce an error message at all!5. An unclosed opening operator—(, {, or [—makes Python continue with the next line as partof the current statement. Generally, an error occurs almost immediately inthenext line.6. Check for theclassic=instead of==insideaconditional.7. Check the indentation to make sure it lines up the way it is supposed to. Python can handlespaceandtabs,butifyoumixthemitcancauseproblems. Thebestwaytoavoidthisproblemistouse atext editor that knows about Python and generates consistent indentation.Ifnothing works,move ontothe next section...A.1.1 I keepmakingchangesand itmakesnodifference.If the interpreter says there is an error and you don’t see it, that might be because you and theinterpreter are not looking at the same code. Check your programming environment to make surethat the program you areediting istheone Python istryingtorun.Ifyouarenotsure,tryputtinganobviousanddeliberatesyntaxerroratthebeginningoftheprogram.Now runitagain. Ifthe interpreter doesn’t find thenew error,you arenot running thenew code.There areafew likelyculprits:• Youeditedthefileandforgottosavethechangesbeforerunningitagain. Someprogrammingenvironments do thisfor you, but somedon’t.• You changed thename of the file, but you are stillrunning the oldname.• Something inyour development environment is configured incorrectly.• If you are writing a module and using import, make sure you don’t give your module thesame name as one of the standard Python modules.• Ifyouareusingimporttoreadamodule,rememberthatyouhavetorestarttheinterpreterorusereloadtoreadamodified file. Ifyou import the module again, itdoesn’t do anything.If you get stuck and you can’t figure out what is going on, one approach is to start again with a newprogram like “Hello, World!,” and make sure you can get a known program to run. Then graduallyadd the pieces ofthe original program tothe new one.

A.2. Runtime errors 197A.2 Runtime errorsOnceyourprogramissyntacticallycorrect,Pythoncancompileitandatleaststartrunningit. Whatcould possibly gowrong?A.2.1 Myprogram doesabsolutelynothing.Thisproblemismostcommonwhenyourfileconsistsoffunctionsandclassesbutdoesnotactuallyinvoke anything to start execution. This may be intentional if you only plan to import this moduletosupply classes and functions.If it is not intentional, make sure that you are invoking a function to start execution, or execute onefrom theinteractive prompt. Alsoseethe“Flow of Execution” section below.A.2.2 Myprogram hangs.Ifaprogramstopsandseemstobedoingnothing,itis“hanging.” Oftenthatmeansthatitiscaughtinan infiniteloop or infinite recursion.• Ifthereisaparticularloopthatyoususpectistheproblem,addaprintstatementimmediatelybefore the loop that says “entering the loop” and another immediately after that says “exitingthe loop.”Run the program. If you get the first message and not the second, you’ve got an infinite loop.Go tothe“Infinite Loop” section below.• Most of the time, an infinite recursion will cause the program to run for a while and thenproduce a “RuntimeError: Maximum recursion depth exceeded” error. If that happens, go tothe “Infinite Recursion” section below.If you are not getting this error but you suspect there is a problem with a recursive method orfunction, you can stillusethe techniques inthe“Infinite Recursion” section.• If neither of those steps works, start testing other loops and other recursive functions andmethods.• Ifthatdoesn’twork,thenitispossiblethatyoudon’tunderstandtheflowofexecutioninyourprogram. Gotothe“Flow of Execution” section below.Infinite LoopIf you think you have an infinite loop and you think you know what loop is causing the problem,add a print statement at the end of the loop that prints the values of the variables in the conditionand the value of the condition.For example:while x > 0 and y < 0 :# do something to x# do something to yprint "x: ", xprint "y: ", yprint "condition: ", (x > 0 and y < 0)

198 Appendix A. DebuggingNow when you run the program, you will see three lines of output for each time through the loop.The last time through the loop, the condition should be false. If the loop keeps going, you will beabletoseethevaluesofxandy,andyoumightfigureoutwhytheyarenotbeingupdatedcorrectly.Infinite RecursionMost of the time, an infinite recursion will cause the program to run for a while and then produce aMaximum recursion depth exceedederror.If you suspect that a function or method is causing an infinite recursion, start by checking to makesure that there is a base case. In other words, there should be some condition that will cause thefunctionormethodtoreturnwithoutmakingarecursiveinvocation. Ifnot,thenyouneedtorethinkthealgorithm and identify abase case.If there is a base case but the program doesn’t seem to be reaching it, add a print statement at thebeginning of the function or method that prints the parameters. Now when you run the program,youwillseeafewlinesofoutputeverytimethefunctionormethodisinvoked,andyouwillseetheparameters. If the parameters are not moving toward the base case, you will get some ideas aboutwhy not.Flow of ExecutionIfyouarenotsurehowtheflowofexecutionismovingthroughyourprogram,addprintstatementstothebeginningofeachfunctionwithamessagelike“enteringfunctionfoo,”wherefooisthenameof thefunction.Now when you runtheprogram, itwillprint atrace of each function as itisinvoked.A.2.3 WhenIrunthe programIgetan exception.If something goes wrong during runtime, Python prints a message that includes the name of theexception, thelineof the program where theproblem occurred, and atraceback.The traceback identifies the function that is currently running, and then the function that invoked it,andthenthefunctionthatinvokedthat,andsoon. Inotherwords,ittracesthesequenceoffunctioninvocations that got you to where you are. It also includes the line number in your file where eachof thesecalls occurs.The first step is to examine the place in the program where the error occurred and see if you canfigure out what happened. These are someof themost common runtime errors:NameError: Youaretryingtouseavariablethatdoesn’texistinthecurrentenvironment. Rememberthat local variables are local. You cannot refer to them from outside the function wherethey aredefined.TypeError: There are several possiblecauses:• You are trying to use a value improperly. Example: indexing a string, list, or tuple withsomething other than aninteger.• There is a mismatch between the items in a format string and the items passed for conversion.This can happen if either the number of items does not match or an invalidconversion iscalled for.

A.3. Semantic errors 199• You are passing the wrong number of arguments to a function or method. For methods,lookatthemethoddefinitionandcheckthatthefirstparameterisself. Thenlookatthemethod invocation; make sure you are invoking the method on an object with the righttype and providing theother arguments correctly.KeyError: You are trying to access an element of a dictionary using a key that the dictionary doesnot contain.AttributeError: You are trying to access an attribute or method that does not exist. Check thespelling! You can usedirtolistthe attributesthat doexist.If an AttributeError indicates that an object has NoneType, that means that it is None. Onecommoncauseisforgettingtoreturnavaluefromafunction;ifyougettotheendofafunctionwithouthittingareturnstatement,itreturnsNone. Anothercommoncauseisusingtheresultfrom alistmethod, likesort,that returnsNone.IndexError: Theindexyouareusingtoaccessalist,string,ortupleisgreaterthanitslengthminusone. Immediately before the site of the error, add a print statement to display the value ofthe index and thelength of the array. Isthe arraytheright size? Isthe index the rightvalue?ThePythondebugger(pdb)isusefulfortrackingdownExceptionsbecauseitallowsyoutoexaminethe state of the program immediately before the error. You can read about pdb at docs.python.org/lib/module-pdb.html.A.2.4 I addedsomanyprint statements Iget inundatedwith output.One of the problems with using print statements for debugging is that you can end up buried inoutput. There are twoways toproceed: simplifytheoutput or simplifytheprogram.To simplify the output, you can remove or comment out print statements that aren’t helping, orcombine them, or format the output soit iseasier tounderstand.To simplify the program, there are several things you can do. First, scale down the problem theprogram is working on. For example, if you are searching a list, search a small list. If the programtakes input from theuser, give itthe simplestinput that causes theproblem.Second, clean up the program. Remove dead code and reorganize the program to make it as easyto read as possible. For example, if you suspect that the problem is in a deeply nested part of theprogram, try rewriting that part with simpler structure. If you suspect a large function, try splittingitintosmaller functions and testingthem separately.Often the process of finding the minimal test case leads you to the bug. If you find that a programworks inone situationbut not inanother, that gives you aclue about what isgoing on.Similarly, rewriting a piece of code can help you find subtle bugs. If you make a change that youthink shouldn’t affect theprogram, and it does, that can tipyou off.A.3 Semantic errorsIn some ways, semantic errors are the hardest to debug, because the interpreter provides no informationabout what iswrong. Only you know what the program issupposed todo.

200 Appendix A. DebuggingThe first step is to make a connection between the program text and the behavior you are seeing.You need a hypothesis about what the program is actually doing. One of the things that makes thathard isthat computers run sofast.Youwilloftenwishthatyoucouldslowtheprogramdowntohumanspeed,andwithsomedebuggersyou can. But the time it takes to insert a few well-placed print statements is often short comparedtosettingupthedebugger,insertingandremovingbreakpoints,and“stepping”theprogramtowheretheerror isoccurring.A.3.1 Myprogram doesn’twork.You should askyourself thesequestions:• Istheresomethingtheprogramwassupposedtodobutwhichdoesn’tseemtobehappening?Find the section of the code that performs that function and make sure it is executing whenyou thinkitshould.• Issomethinghappeningthatshouldn’t? Findcodeinyourprogramthatperformsthatfunctionand seeifitisexecuting when itshouldn’t.• Is a section of code producing an effect that is not what you expected? Make sure that youunderstand the code in question, especially if it involves invocations to functions or methodsinotherPythonmodules. Readthedocumentationforthefunctionsyouinvoke. Trythemoutby writingsimpletestcases and checking the results.Inordertoprogram,youneedtohaveamentalmodelofhowprogramswork. Ifyouwriteaprogramthat doesn’t do what you expect, very often the problem is not in the program; it’s in your mentalmodel.The best way to correct your mental model is to break the program into its components (usuallythe functions and methods) and test each component independently. Once you find the discrepancybetween your model and reality, you can solve the problem.Of course, you should be building and testing components as you develop the program. If youencounter a problem, there should be only a small amount of new code that is not known to becorrect.A.3.2 I’ve got abighairyexpressionandit doesn’tdowhat I expect.Writingcomplexexpressionsisfineaslongastheyarereadable,buttheycanbehardtodebug. Itisoftenagoodideatobreakacomplexexpressionintoaseriesofassignmentstotemporaryvariables.For example:self.hands[i].addCard(self.hands[self.findNeighbor(i)].popCard())This can be rewrittenas:neighbor = self.findNeighbor(i)pickedCard = self.hands[neighbor].popCard()self.hands[i].addCard(pickedCard)

A.3. Semantic errors 201The explicit version is easier to read because the variable names provide additional documentation,and it is easier to debug because you can check the types of the intermediate variables and displaytheir values.Anotherproblemthatcanoccurwithbigexpressionsisthattheorderofevaluationmaynotbewhatyou expect. For example, ifyou aretranslatingthe expression2π x intoPython, you might write:y = x / 2 * math.piThat is not correct because multiplication and division have the same precedence and are evaluatedfrom lefttoright. Sothis expression computes xπ/2.A good waytodebug expressions istoadd parentheses tomake theorder ofevaluation explicit:y = x / (2 * math.pi)Whenever you are not sure of the order of evaluation, use parentheses. Not only will the programbe correct (in the sense of doing what you intended), it will also be more readable for other peoplewho haven’t memorized therules of precedence.A.3.3 I’ve got afunction or methodthatdoesn’treturnwhatIexpect.If you have a return statement with a complex expression, you don’t have a chance to print thereturnvalue before returning. Again, you can use atemporary variable. For example, insteadof:return self.hands[i].removeMatches()you could write:count = self.hands[i].removeMatches()return countNow you have the opportunity todisplay thevalue ofcountbeforereturning.A.3.4 I’m really,really stuckandIneedhelp.First, try getting away from the computer for a few minutes. Computers emit waves that affect thebrain, causing thesesymptoms:• Frustration and rage.• Superstitious beliefs (“the computer hates me”) and magical thinking (“the program onlyworks when Iwear myhat backward”).• Random walk programming (the attempt to program by writing every possible program andchoosing the one that does theright thing).If you find yourself suffering from any of these symptoms, get up and go for a walk. When you arecalm, think about the program. What is it doing? What are some possible causes of that behavior?When was the lasttimeyou had aworking program, and what did you donext?Sometimesitjusttakestimetofindabug. IoftenfindbugswhenIamawayfromthecomputerandletmymindwander. Someofthebestplacestofindbugsaretrains,showers,andinbed,justbeforeyou fallasleep.

202 Appendix A. DebuggingA.3.5 No,Ireally needhelp.It happens. Even the best programmers occasionally get stuck. Sometimes you work on a programsolong that you can’t seetheerror. A freshpair of eyes isjustthe thing.Before you bring someone else in, make sure you are prepared. Your program should be as simpleas possible, and you should be working on the smallest input that causes the error. You should haveprintstatementsintheappropriateplaces(andtheoutputtheyproduceshouldbecomprehensible).You should understand the problem well enough todescribe it concisely.When you bring someone intohelp, be suretogive them the informationthey need:• Ifthere isan errormessage, what isitand what part of theprogram does itindicate?• What was the last thing you did before this error occurred? What were the last lines of codethat you wrote, or what isthe new testcase that fails?• What have you triedsofar,and what have you learned?Whenyoufindthebug,takeasecondtothinkaboutwhatyoucouldhavedonetofinditfaster. Nexttimeyou seesomething similar,you willbe able tofind thebug morequickly.Remember, the goal is not just to make the program work. The goal is to learn how to make theprogram work.

Indexabecedarian, 72, 83abs function, 52absolute path, 137, 143access, 89accumulator, 100histogram, 127list,93string,173sum, 93Ackerman function, 61add method, 163addition withcarrying, 68algorithm, 3, 7, 67, 130Euclid, 62MD5, 143RSA, 112square root, 69aliasing, 96, 100, 147, 149, 167copying toavoid, 99alphabet, 37alternative execution, 41ambiguity, 5anagram, 100anagram set,123, 140and operator, 40anydbm module, 139append method, 92, 98, 101, 172, 173arcfunction, 31argument, 17, 19, 21, 22, 26, 97gather, 117keyword, 33, 36, 121, 182list,97optional, 76, 95, 107variable-length tuple, 117argument scatter,117arithmeticoperator, 12assertstatement, 157assignment, 15, 63, 89augmented, 93, 100item, 74, 90, 116multiple, 68, 110tuple, 116–118, 123assignment statement, 10attributedict ,166class, 170, 177initializing, 166instance, 146, 151, 170, 177AttributeError,150, 199augmented assignment, 93, 100Austin, Jane, 127available colors, 152, 168Bacon, Kevin, 144Bangladesh, national flag, 152base case, 44, 47benchmarking, 132, 134big, hairyexpression, 200binary search, 101binding, 189, 192bingo, 124birthday, 158birthday paradox, 100bisect module, 101bisection search, 101bisection, debugging by, 68bitwiseoperator, 12body, 19, 25, 65bool type, 39boolean expression, 39, 46boolean function, 54, 153boolean operator, 76borrowing, subtraction with,68, 157bound method, 187, 192bounding box, 152, 184, 192bracketsquiggly, 103bracket operator, 71, 89, 116branch, 41, 47break statement, 65bug, 3, 7worst,167

204 Indexworstever, 193Button widget, 182calculator, 8, 16call graph, 109, 113Callable object, 188callback, 182, 187–189, 191, 192Canvas coordinate, 183, 190Canvas item,183Canvas object, 151Canvas widget, 183Car Talk, 86, 113, 124Card class,170card, playing, 169carrying, addition with, 68, 154, 156case-sensitivity, variable names, 15catch, 143chained conditional, 41, 47character, 71checksum, 143child class,174, 177choice function, 126circlefunction, 31circular definition, 56class,145, 151Card, 170child, 174, 177Date, 158Deck, 172Hand, 174Kangaroo, 167parent, 174Point, 145, 163Rectangle, 147SimpleTurtleWorld, 186Time, 153class attribute,170, 177class definition, 145class diagram, 176, 178class object, 146, 151close method, 136, 139, 141cmp function, 172cmp method, 171Collatz conjecture, 65colon, 19, 196color list,152, 168comment, 14, 16commutativity, 14, 165compare function, 52comparisonstring,77tuple, 121, 172compile, 1,7composition, 19, 22, 26, 54, 172compound statement, 40, 47compressionfile, 141concatenation, 14, 16, 23, 72, 74, 95list,91, 98, 101condition, 40, 47, 65, 197conditional, 196chained, 41, 47nested, 42, 47conditional execution, 40conditional statement, 40, 47, 55config method, 183consistency check, 112, 156contributors, viiconversiontype, 17coordinateCanvas, 183, 190pixel, 190coordinate sequence, 184copydeep, 150shallow, 150slice, 74, 92toavoid aliasing, 99copy module, 149copying objects, 149count method, 76counter, 75, 79, 104, 111counting and looping, 75crosswords, 81cummings, e. e., 3cumulative sum, 94Czech Republic, national flag, 152data structure, 122, 123, 131database, 139, 143, 144Date class,158datetime module, 158dead code, 52, 60, 199debugger (pdb), 199debugging, 3, 6, 7, 15, 25, 35, 45, 59, 77, 85,98, 112, 122, 132, 142, 150, 157, 166,176, 191, 195by bisection, 68emotional response, 6, 201

Index 205experimental, 4superstition, 201Deck class, 172deck, playing cards, 172declaration, 110, 113decorate-sort-undecorate pattern, 121decrement, 64, 69deep copy, 150, 151deepcopy function, 150def keyword, 19default value, 128, 133, 162avoiding mutable, 167definitioncircular, 56class,145function, 19recursive, 124del operator, 94deletion, element of list,94delimiter,95, 100deterministic, 126, 133development plan, 36encapsulation and generalization, 35incremental, 52, 195planned, 156problem recognition, 84, 85prototype and patch, 154, 156random walk programming, 133, 201diagramcall graph, 113class,176, 178object, 146, 148, 150, 151, 153, 171stack, 23, 97state, 10, 63, 78, 90, 96, 97, 108, 120, 146,148, 150, 153, 171dict attribute, 166dict function, 103dictionary, 103, 112, 119, 199initialize, 119invert, 107lookup, 106looping with,106reverse lookup, 106subtraction, 129traversal, 119, 166dictionary methodsanydbm module, 139Dijkstra,Edsger, 85directory, 137, 143walk, 138working, 137dispatchtype-based, 165dispatch, type-based, 164divisibility, 39divisionfloating-point, 12floor, 12, 46divmod, 117, 156docstring, 35, 36, 145documentation, 8dot notation, 18, 26, 75, 146, 160, 170double letters,86Doyle, Arthur Conan, 4drag-and-drop, 189DSU pattern, 121, 123, 128duplicate, 100, 101, 113, 143Einstein, Albert,33element, 89, 99element deletion, 94elif keyword, 41ellipses, 20else keyword, 41email address, 116embedded object, 148, 151, 167copying, 149emotional debugging, 6, 201empty list,89empty string,79, 95encapsulation, 32, 36, 54, 67, 75, 175encode, 169, 177encrypt, 169encryption, 112end ofline character, 142Entry widget, 184enumerate function, 119epsilon, 67equality and assignment, 63equivalence, 96equivalent, 100errorcompile-time, 195runtime, 3, 15, 44, 46, 195semantic, 4, 10, 15, 78, 195, 199shape, 122syntax, 3, 15, 195error checking, 58error message, 3, 4, 6, 10, 15, 195Euclid’s algorithm, 62

206 Indexeval function, 69evaluate, 13event, 192event handler, 189event loop, 181, 192Event object, 189event string,189event-driven programming, 182, 191, 192exception, 3, 7, 15, 195, 198AttributeError,150, 199IndexError, 72, 78, 90, 199IOError,138KeyError, 104, 199NameError, 23, 198OverflowError, 46RuntimeError, 44SyntaxError, 19TypeError, 71, 74, 108, 116, 117, 136, 161,198UnboundLocalError, 111ValueError, 45, 107, 116exception, catching, 138executable, 2, 7exercise, secret, 143exists function, 137experimental debugging, 4, 133expression, 12, 13, 16bigand hairy, 200boolean, 39, 46extend method, 92factorial function, 56, 58False special value, 39Fermat’s Last Theorem, 47fibonacci function, 57, 109file, 135compression, 141permission, 138reading and writing,135fileobject, 81, 86filename, 137filter pattern, 93, 100find function, 74flag, 110, 113float function, 17float type, 9floating-point, 15, 67floating-point division, 12floor division, 12, 16, 46flow of execution, 21, 26, 58, 59, 64, 177, 191,198flower, 37folder, 137for loop, 30, 72, 91, 119formal language, 4, 8format operator, 136, 143, 198format sequence, 136, 143format string,136, 143frabjous, 56frame, 23, 26, 43, 57, 109Frame widget, 186Free Documentation License, GNU, v, vifrequency, 105letter,123word, 125, 134fruitfulfunction, 24, 26frustration,201function, 19, 25, 159abs, 52ack, 61arc, 31choice, 126circle, 31cmp, 172compare, 52deepcopy, 150dict, 103enumerate, 119eval, 69exists, 137factorial, 56fibonacci, 57, 109find, 74float, 17getattr, 166getcwd, 137hasattr, 150, 166int, 17isinstance, 58, 164len, 26, 72, 104list,95log, 18max, 117, 118min, 117, 118open, 81, 82, 135, 138, 139polygon, 31popen, 140randint, 100, 126random, 121, 126

Index 207raw input, 45recursive, 43reload, 142, 196repr,142reversed, 122shuffle, 174sorted, 122sqrt,18, 53str,18sum, 118tuple, 115type, 150zip, 118function argument, 21function call, 17, 26function composition, 54function definition, 19, 20, 25function frame, 23, 26, 43, 109function object, 20, 26function parameter, 21function syntax, 160function typemodifier, 155pure, 154function, fruitful,24function, math, 18function, reasons for,25function, trigonometric, 18function, tuple asreturn value, 117function, void, 24functional programming style, 155, 158gamma function, 58gather, 117, 123GCD (greatestcommon divisor),61generalization, 32, 36, 83, 157geometry manager, 188, 192get method, 105getattr function, 166getcwd function, 137global statement, 110global variable, 110, 113update, 110GNU Free Documentation License, v, vigraphical user interface, 181greatest common divisor (GCD),61grid, 27guardian pattern, 59, 60, 77GUI, 181, 191Gui module, 181gunzip (Unix command), 141Hand class,174hanging, 197HAS-A relationship, 176, 178hasattr function, 150, 166hash function, 108, 113hashable, 108, 113, 120hashtable, 104, 113header, 19, 25, 196Hello, World, 6help utility,8hexadecimal, 146high-level language, 1, 7histogram, 105, 113random choice, 126, 129word frequencies, 127Holmes, Sherlock, 4homophone, 114HTMLParser module, 193hyperlink, 193hypotenuse, 54identical, 100identity, 96if statement, 40Image module, 192image viewer, 192IMDb (Internet Movie Database), 144immutability, 74, 79, 97, 108, 115, 122implementation, 105, 113, 132import statement, 26, 29, 142inoperator, 76, 90, 104increment, 64, 68, 155, 161incremental development, 60, 195indentation, 19, 160, 196index, 71, 77, 79, 89, 99, 103, 198looping with, 84, 91negative, 72slice, 73, 92startingat zero, 71, 90IndexError, 72, 78, 90, 199infinite loop, 65, 69, 181, 197infinite recursion, 44, 47, 58, 197, 198inheritance, 174, 177init method, 162, 166, 170, 172, 174initializationvariable, 68initialization (beforeupdate), 64instance, 29, 36, 146, 151

208 Indexas argument, 147as returnvalue, 148instance attribute, 146, 151, 170, 177instantiation, 146int function, 17int type, 9integer, 15long, 111interactive mode, 2, 7, 12, 24interface, 33, 35, 36, 177interlocking words,101Internet Movie Database (IMDb), 144interpret, 1, 7invariant, 157, 158, 191invert dictionary, 107invocation, 75, 79IOError,138isoperator, 96, 149IS-A relationship, 176, 178isinstance function, 58, 164item, 79, 89Canvas, 183, 192dictionary, 112item assignment, 74, 90, 116item update, 91itemsmethod, 119iteration, 63, 64, 69joinmethod, 95, 173Kangaroo class,167Kevin Bacon Game, 144key, 103, 112key-value pair, 103, 112, 119keyboard input, 45KeyError, 104, 199keys method, 106keyword, 11, 15, 196def, 19elif,41else, 41keyword argument, 33, 36, 121, 182, 192Koch curve, 48Label widget, 182languageformal, 4high-level, 1low-level, 1natural, 4programming, 1safe, 3Turing complete, 55leap of faith, 57len function, 26, 72, 104letter frequency, 123letter rotation, 80, 113Linux, 4lipogram, 82list,89, 95, 99, 122as argument, 97comprehension, 94concatenation, 91, 98, 101copy, 92element, 89empty, 89function, 95index, 90membership, 90method, 92nested, 89, 91of objects, 172of tuples, 118operation, 91repetition, 91slice, 92traversal, 91, 100literalness, 5local variable, 22, 26log function, 18logarithm, 134logical operator, 39, 40long integer, 111lookup, 113lookup, dictionary, 106loop, 31, 36, 65, 118condition, 197event, 181for,30, 72, 91infinite, 65, 181, 197nested, 172traversal, 72while, 64loopingwithdictionaries, 106withindices, 84, 91withstrings,75looping and counting, 75low-level language, 1, 7ls (Unixcommand), 140

Index 209map pattern, 93, 100map to, 169mapping, 90, 100, 131Markov analysis, 130mash-up, 131math function, 18max function, 117, 118McCloskey, Robert, 72MD5 algorithm, 143membershipbinary search, 101bisection search, 101dictionary, 104list,90set,104memo, 109, 113mental model, 200Menubutton widget, 188metaphor, method invocation, 161metathesis, 124method, 75, 79, 159, 167cmp , 171str ,163, 172add, 163append, 92, 98, 172, 173close, 136, 139, 141config, 183count, 76extend, 92get, 105init,162, 170, 172, 174items,119join, 95, 173keys, 106mro, 177pop, 94, 173radd, 165read, 141readline, 81, 141remove, 94replace, 125setdefault, 109sort,92, 99, 121, 174split,95, 116string,79strip,82, 125translate, 125update, 119values, 104void, 93method append, 101method resolution order,177method syntax, 160method, bound, 187method, list,92min function, 117, 118model, mental, 200modifier, 155, 158module, 18, 26anydbm, 139bisect, 101copy, 149datetime, 158Gui, 181HTMLParser, 193Image, 192os, 137pickle, 135, 139pprint, 112profile, 132random, 100, 121, 126, 174reload, 142, 196shelve, 140, 144string,125structshape, 122urllib, 143, 193Visual, 167vpython, 167World, 151module object, 18, 141module, writing,141modulus operator, 39, 46Monty Python and the Holy Grail,154MP3, 143mro method, 177multilinestring, 35, 196multiple assignment, 63, 68, 110multiplicity(inclass diagram), 176, 178mutability, 74, 90, 92, 97, 111, 115, 122, 148mutable object, asdefault value, 167NameError, 23, 198natural language, 4, 8negative index, 72nested conditional, 42, 47nested list,89, 91, 100newline, 45, 63, 173Newton’s method, 66None special value, 24, 52, 60, 93, 94not operator, 40

210 Indexnumber, random, 126object, 74, 79, 95, 96, 100, 145Callable, 188Canvas, 151class,146copying, 149embedded, 148, 151, 167Event, 189file, 81, 86function, 20, 26module, 141mutable, 148printing, 160object code, 2,7object diagram, 146, 148, 150, 151, 153, 171object-oriented language, 166object-oriented programming, 159, 167, 174octal, 11odometer, 86open function, 81, 82, 135, 138, 139operand, 12, 16operator, 16and, 40bitwise,12boolean, 76bracket, 71, 89, 116del, 94format, 136, 143, 198in, 76, 90, 104is,96, 149logical, 39, 40modulus, 39, 46not, 40or,40overloading, 167relational, 40, 171slice,73, 79, 92, 98, 116string,14update, 93operator overloading, 164, 171operator, arithmetic, 12option, 182, 192optional argument, 76, 95, 107optional parameter, 128, 162or operator, 40order of operations, 13, 15, 201os module, 137other (parameter name), 162OverflowError, 46overloading, 167override, 129, 134, 162, 171, 174, 177packing widgets, 186, 192palindrome, 61, 79, 84, 86parameter, 21, 23, 25, 97gather, 117optional, 128, 162other, 162self,161parent class, 174, 177parenthesesargument in, 17empty, 19, 75matching, 3overriding precedence, 13parameters in, 22parent class in, 174tuples in,115parse, 5, 8, 144pass statement, 41path, 137, 143absolute, 137relative, 137patterndecorate-sort-undecorate, 121DSU, 121, 128filter, 93, 100guardian, 59, 60, 77map, 93, 100reduce, 93, 100search, 75, 79, 83, 107swap, 116pdb (Python debugger), 199PEMDAS, 13permission, file, 138persistence, 135, 143pi, 18, 69pickle module, 135, 139pickling, 139pie, 37PIL (Python Imaging Library), 192pipe, 140, 143pixel coordinate, 190plain text, 81, 125, 144, 193planned development, 156, 158playing card, Anglo-American, 169poetry, 5Point class,145, 163point, mathematical, 145

Index 211poker, 169, 178polygon function, 31polymorphism, 166, 167, 176pop method, 94, 173popen function, 140portability, 1, 7postcondition, 36, 59, 177pprint module, 112precedence, 16, 201precondition, 36, 59, 100, 177prefix, 131prettyprint, 112print statement, 6, 8, 163, 199problem recognition, 84–86problem solving, 1, 7profile module, 132program, 2, 7program testing, 85programming language, 1Project Gutenberg, 125prompt, 2, 7, 45prose, 5prototype and patch, 154, 156, 158pseudorandom, 126, 133pure function, 154, 158Puzzler, 86, 113, 124Pythagorean theorem, 52Python 3.0, 6, 12, 45, 111, 118Python debugger (pdb), 199Python Imaging Library (PIL),192python.org, 8quotation mark, 6, 9, 35, 74, 196radd method, 165radian, 18rage, 201raisestatement, 107, 157Ramanujan, Srinivasa, 69randint function, 100, 126random function, 121, 126random module, 100, 121, 126, 174random number, 126random text, 131random walk programming, 133, 201rank, 169raw input function, 45read method, 141readline method, 81, 141Rectangle class, 147recursion, 42, 43, 47, 55, 57base case, 44infinite, 44, 58, 198recursive definition, 56, 124reduce pattern, 93, 100reducible word, 114, 124redundancy, 5refactoring, 34, 36reference, 97, 100aliasing, 96relational operator, 40, 171relative path, 137, 143reload function, 142, 196remove method, 94repetition, 30list,91replace method, 125repr function, 142representation, 145, 147, 169return statement, 43, 51, 201return value, 17, 26, 51, 148tuple, 117reverse lookup, dictionary, 106, 113reverse wordpair, 101reversed function, 122rotationletters,113rotation, letter,80RSA algorithm, 112rules of precedence, 13, 16running pace, 8, 16, 158runtime error,3, 15, 44, 46, 195, 198RuntimeError, 44, 58safelanguage, 3sanity check, 112scaffolding, 53, 60, 112scatter, 117, 123Scrabble, 124script, 2, 7script mode, 2, 7, 12, 24search, 107search pattern, 75, 79, 83search, binary, 101search, bisection, 101secret exercise, 143self (parameter name), 161semantic error,4, 8, 10, 15, 78, 195, 199semantics, 4, 8, 159sequence, 71, 79, 89, 95, 115, 121

212 Indexcoordinate, 184set,129anagram, 123, 140set membership, 104setdefault method, 109sexagesimal, 156shallow copy, 150, 151shape, 123shape error,122shell,140shelve module, 140, 144shuffle function, 174SimpleTurtleWorld class,186sinefunction, 18singleton, 108, 113, 115slice,79copy, 74, 92list,92string,73tuple, 116update, 92sliceoperator, 73, 79, 92, 98, 116sortmethod, 92, 99, 121, 174sortedfunction, 122source code, 2, 7special case, 85, 86, 155special valueFalse, 39None, 24, 52, 60, 93, 94True, 39splitmethod, 95, 116sqrt,53sqrtfunction, 18square root, 66squiggly bracket, 103stack diagram, 23, 26, 36, 43, 56, 60, 97state diagram, 10, 15, 63, 78, 90, 96, 97, 108,120, 146, 148, 150, 153, 171statement, 12, 15assert,157assignment, 10, 63break, 65compound, 40conditional, 40, 47, 55for,30, 72, 91global, 110if,40import, 26, 29, 142pass, 41print,6, 8, 163, 199raise, 107, 157return, 43, 51, 201try, 138while, 64step size,79strfunction, 18str method, 163, 172string, 9, 15, 95, 122accumulator, 173comparison, 77empty, 95immutable, 74method, 75multiline, 35, 196operation, 14slice, 73triple-quoted, 35stringmethod, 79stringmodule, 125stringrepresentation, 142, 163stringtype, 9stripmethod, 82, 125structshape module, 122structure, 5subclass, 174subject, 160, 167, 187subtractiondictionary, 129withborrowing, 68subtraction withborrowing, 157suffix, 131suit,169sum function, 118superclass, 174superstitious debugging, 201SVG, 193Swampy, 29, 81, 151, 179, 181swap pattern, 116syntax, 3, 7, 159, 196syntax error,3, 7, 15, 195SyntaxError, 19Tagger, 179temporary variable, 51, 60, 201test case, minimal, 199testingand absence of bugs, 85incremental development, 52interactive mode, 2ishard, 85

Index 213knowing the answer, 53leap of faith,57minimal testcase, 199textplain, 81, 125, 144, 193random, 131text file, 143Text widget, 184Time class,153Tkinter, 181token, 5, 8traceback, 24, 26, 44, 45, 107, 198translatemethod, 125traversal, 72, 75, 77, 79, 83, 93, 100, 105, 106,118, 119, 121, 127dictionary, 166list,91traversedictionary, 119triangle, 47trigonometric function, 18triple-quoted string,35True special value, 39trystatement, 138tuple, 115, 117, 122, 123as key indictionary, 120, 132assignment, 116comparison, 121, 172inbrackets, 120singleton, 115slice,116tuple assignment, 117, 118, 123tuple function, 115Turing complete language, 55Turing Thesis, 55Turing, Alan, 55turtletypewriter, 37TurtleWorld, 29, 48, 179type, 9, 15bool, 39dict, 103file, 135float, 9int,9list,89long, 111set,129str,9tuple, 115user-defined, 145, 153type checking, 58type conversion, 17type function, 150type-based dispatch, 164, 165, 167TypeError, 71, 74, 108, 116, 117, 136, 161, 198typewriter, turtle,37typographical error,133UML, 176UnboundLocalError, 111underscore character, 11uniqueness, 101Unix commandgunzip, 141ls,140update, 64, 66, 68coordinate, 190database, 139global variable, 110histogram, 127item, 91slice, 92update method, 119update operator, 93URL, 143, 193urllibmodule, 143, 193use before def, 15, 21user-defined type, 145, 153value, 9, 15, 95, 96, 112default, 128tuple, 117ValueError, 45, 107, 116values method, 104variable, 10, 15global, 110local, 22temporary, 51, 60, 201updating, 64variable-length argument tuple, 117vector graphics, 193veneer, 173, 177Visual module, 167void function, 24, 26void method, 93vpython module, 167walk, directory, 138while loop, 64whitespace, 25, 46, 82, 142, 196widget, 181, 191

214 IndexButton, 182Canvas, 183Entry, 184Frame, 186Label, 182Menubutton, 188Text, 184widget, packing, 186wordcount, 141wordfrequency, 125, 134word, reducible, 114, 124working directory, 137Worldmodule, 151worstbug, 167ever, 193zero, index startingat, 71, 90zipfunction, 118usewithdict, 119Zipf’slaw, 134