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\title{Think Python}

\author{Allen B. Downey}

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{\Large

Allen Downey\\

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{\Large Green Tea Press}

{\small Needham, Massachusetts}

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{\small

Copyright \copyright ~2015 Allen Downey.

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Green Tea Press \\

9 Washburn Ave \\

Needham MA 02492

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Permission is granted to copy, distribute, and/or modify this document

under the terms of the Creative Commons Attribution-NonCommercial 3.0 Unported

License, which is available at \url{http://creativecommons.org/licenses/by-nc/3.0/}.

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\chapter{Preface}

\section*{The strange history of this book}

In January 1999 I was preparing to teach an introductory programming

class in Java. I had taught it three times and I was getting

frustrated. The failure rate in the class was too high and, even for

students who succeeded, the overall level of achievement was too low.

One of the problems I saw was the books.

They were too big, with too much unnecessary detail about Java, and

not enough high-level guidance about how to program. And they all

suffered from the trap door effect: they would start out easy,

proceed gradually, and then somewhere around Chapter 5 the bottom would

fall out. The students would get too much new material, too fast,

and I would spend the rest of the semester picking up the pieces.

Two weeks before the first day of classes, I decided to write my

own book. My goals were:

\begin{itemize}

\item Keep it short. It is better for students to read 10 pages

than not read 50 pages.

\item Be careful with vocabulary. I tried to minimize jargon

and define each term at first use.

\item Build gradually. To avoid trap doors, I took the most difficult

topics and split them into a series of small steps.

\item Focus on programming, not the programming language. I included

the minimum useful subset of Java and left out the rest.

\end{itemize}

I needed a title, so on a whim I chose {\em How to Think Like

a Computer Scientist}.

My first version was rough, but it worked. Students did the reading,

and they understood enough that I could spend class time on the hard

topics, the interesting topics and (most important) letting the

students practice.

I released the book under the GNU Free Documentation License,

which allows users to copy, modify, and distribute the book.

\index{GNU Free Documentation License}

\index{Free Documentation License, GNU}

What happened next is the cool part. Jeff Elkner, a high school

teacher in Virginia, adopted my book and translated it into

Python. He sent me a copy of his translation, and I had the

unusual experience of learning Python by reading my own book.

As Green Tea Press, I published the first Python version in 2001.

\index{Elkner, Jeff}

In 2003 I started teaching at Olin College and I got to teach

Python for the first time. The contrast with Java was striking.

Students struggled less, learned more, worked on more interesting

projects, and generally had a lot more fun.

\index{Olin College}

Since then I've continued to develop the book,

correcting errors, improving some of the examples and

adding material, especially exercises.

The result is this book, now with the less grandiose title

{\em Think Python}. Some of the changes are:

\begin{itemize}

\item I added a section about debugging at the end of each chapter.

These sections present general techniques for finding and avoiding

bugs, and warnings about Python pitfalls.

\item I added more exercises, ranging from short tests of

understanding to a few substantial projects. Most exercises

include a link to my solution.

\item I added a series of case studies---longer examples with

exercises, solutions, and discussion.

\item I expanded the discussion of program development plans

and basic design patterns.

\item I added appendices about debugging and analysis of algorithms.

\end{itemize}

The second edition of {\em Think Python} has these new features:

\begin{itemize}

\item The book and all supporting code have been updated to Python 3.

\item I added a few sections, and more details on the web, to help

beginners get started running Python in a browser, so you don't have

to deal with installing Python until you want to.

\item For Chapter~\ref{turtle} I switched from my own turtle graphics

package, called Swampy, to a more standard Python module, {\tt

turtle}, which is easier to install and more powerful.

\item I added a new chapter called ``The Goodies'', which introduces

some additional Python features that are not strictly necessary, but

sometimes handy.

\end{itemize}

I hope you enjoy working with this book, and that it helps

you learn to program and think like

a computer scientist, at least a little bit.

Allen B. Downey \\

Olin College \\

\section*{Acknowledgments}

Many thanks to Jeff Elkner, who

translated my Java book into Python, which got this project

started and introduced me to what has turned out to be my

favorite language.

\index{Elkner, Jeff}

Thanks also to Chris Meyers, who contributed several sections

to {\em How to Think Like a Computer Scientist}.

\index{Meyers, Chris}

Thanks to the Free Software Foundation for developing

the GNU Free Documentation License, which helped make

my collaboration with Jeff and Chris possible, and Creative

Commons for the license I am using now.

\index{GNU Free Documentation License}

\index{Free Documentation License, GNU}

\index{Creative Commons}

Thanks to the editors at Lulu who worked on

{\em How to Think Like a Computer Scientist}.

Thanks to the editors at O'Reilly Media who worked on

{\em Think Python}.

Thanks to all the students who worked with earlier

versions of this book and all the contributors (listed

below) who sent in corrections and suggestions.

\section*{Contributor List}

\index{contributors}

More than 100 sharp-eyed and thoughtful readers have sent in

suggestions and corrections over the past few years. Their

contributions, and enthusiasm for this project, have been a

huge help.

If you have a suggestion or correction, please send email to

{\tt feedback@thinkpython.com}. If I make a change based on your

feedback, I will add you to the contributor list

(unless you ask to be omitted).

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 are fine, too, but not quite as easy to work with.

Thanks!

\begin{itemize}

\small

\item Lloyd Hugh Allen sent in a correction to Section 8.4.

\item Yvon Boulianne sent in a correction of a semantic error in

Chapter 5.

\item Fred Bremmer submitted a correction in Section 2.1.

\item Jonah Cohen wrote the Perl scripts to convert the

LaTeX source for this book into beautiful HTML.

\item Michael Conlon sent in a grammar correction in Chapter 2

and an improvement in style in Chapter 1, and he initiated discussion

on the technical aspects of interpreters.

\item Benoit Girard sent in a

correction to a humorous mistake in Section 5.6.

\item Courtney Gleason and Katherine Smith wrote {\tt horsebet.py},

which was used as a case study in an earlier version of the book. Their

program can now be found on the website.

\item Lee Harr submitted more corrections than we have room to list

here, and indeed he should be listed as one of the principal editors

of the text.

\item James Kaylin is a student using the text. He has submitted

numerous corrections.

\item David Kershaw fixed the broken {\tt catTwice} function in Section

3.10.

\item Eddie Lam has sent in numerous corrections to Chapters

1, 2, and 3.

He also fixed the Makefile so that it creates an index the first time it is

run and helped us set up a versioning scheme.

\item Man-Yong Lee sent in a correction to the example code in

Section 2.4.

\item David Mayo pointed out that the word ``unconsciously"

in Chapter 1 needed

to be changed to ``subconsciously".

\item Chris McAloon sent in several corrections to Sections 3.9 and

3.10.

\item Matthew J. Moelter has been a long-time contributor who sent

in numerous corrections and suggestions to the book.

\item Simon Dicon Montford reported a missing function definition and

several typos in Chapter 3. He also found errors in the {\tt increment}

function in Chapter 13.

\item John Ouzts corrected the definition of ``return value"

in Chapter 3.

\item Kevin Parks sent in valuable comments and suggestions as to how

to improve the distribution of the book.

\item David Pool sent in a typo in the glossary of Chapter 1, as well

as kind words of encouragement.

\item Michael Schmitt sent in a correction to the chapter on files

and exceptions.

\item Robin Shaw pointed out an error in Section 13.1, where the

printTime function was used in an example without being defined.

\item Paul Sleigh found an error in Chapter 7 and a bug in Jonah Cohen's

Perl script that generates HTML from LaTeX.

\item Craig T. Snydal is testing the text in a course at Drew

University. He has contributed several valuable suggestions and corrections.

\item Ian Thomas and his students are using the text in a programming

course. They are the first ones to test the chapters in the latter half

of the book, and they have made numerous corrections and suggestions.

\item Keith Verheyden sent in a correction in Chapter 3.

\item Peter Winstanley let us know about a longstanding error in

our Latin in Chapter 3.

\item Chris Wrobel made corrections to the code in the chapter on

file I/O and exceptions.

\item Moshe Zadka has made invaluable contributions to this project.

In addition to writing the first draft of the chapter on Dictionaries, he

provided continual guidance in the early stages of the book.

\item Christoph Zwerschke sent several corrections and

pedagogic suggestions, and explained the difference between {\em gleich}

and {\em selbe}.

\item James Mayer sent us a whole slew of spelling and

typographical errors, including two in the contributor list.

\item Hayden McAfee caught a potentially confusing inconsistency

between two examples.

\item Angel Arnal is part of an international team of translators

working on the Spanish version of the text. He has also found several

errors in the English version.

\item Tauhidul Hoque and Lex Berezhny created the illustrations

in Chapter 1 and improved many of the other illustrations.

\item Dr. Michele Alzetta caught an error in Chapter 8 and sent

some interesting pedagogic comments and suggestions about Fibonacci

and Old Maid.

\item Andy Mitchell caught a typo in Chapter 1 and a broken example

in Chapter 2.

\item Kalin Harvey suggested a clarification in Chapter 7 and

caught some typos.

\item Christopher P. Smith caught several typos and helped us

update the book for Python 2.2.

\item David Hutchins caught a typo in the Foreword.

\item Gregor Lingl is teaching Python at a high school in Vienna,

Austria. He is working on a German translation of the book,

and he caught a couple of bad errors in Chapter 5.

\item Julie Peters caught a typo in the Preface.

\item Florin Oprina sent in an improvement in {\tt makeTime},

a correction in {\tt printTime}, and a nice typo.

\item D.~J.~Webre suggested a clarification in Chapter 3.

\item Ken found a fistful of errors in Chapters 8, 9 and 11.

\item Ivo Wever caught a typo in Chapter 5 and suggested a clarification

in Chapter 3.

\item Curtis Yanko suggested a clarification in Chapter 2.

\item Ben Logan sent in a number of typos and problems with translating

the book into HTML.

\item Jason Armstrong saw the missing word in Chapter 2.

\item Louis Cordier noticed a spot in Chapter 16 where the code

didn't match the text.

\item Brian Cain suggested several clarifications in Chapters 2 and 3.

\item Rob Black sent in a passel of corrections, including some

changes for Python 2.2.

\item Jean-Philippe Rey at Ecole Centrale

Paris sent a number of patches, including some updates for Python 2.2

and other thoughtful improvements.

\item Jason Mader at George Washington University made a number

of useful suggestions and corrections.

\item Jan Gundtofte-Bruun reminded us that ``a error'' is an error.

\item Abel David and Alexis Dinno reminded us that the plural of

``matrix'' is ``matrices'', not ``matrixes''. This error was in the

book for years, but two readers with the same initials reported it on

the same day. Weird.

\item Charles Thayer encouraged us to get rid of the semi-colons

we had put at the ends of some statements and to clean up our

use of ``argument'' and ``parameter''.

\item Roger Sperberg pointed out a twisted piece of logic in Chapter 3.

\item Sam Bull pointed out a confusing paragraph in Chapter 2.

\item Andrew Cheung pointed out two instances of ``use before def''.

\item C. Corey Capel spotted the missing word in the Third Theorem

of Debugging and a typo in Chapter 4.

\item Alessandra helped clear up some Turtle confusion.

\item Wim Champagne found a brain-o in a dictionary example.

\item Douglas Wright pointed out a problem with floor division in

{\tt arc}.

\item Jared Spindor found some jetsam at the end of a sentence.

\item Lin Peiheng sent a number of very helpful suggestions.

\item Ray Hagtvedt sent in two errors and a not-quite-error.

\item Torsten H\"{u}bsch pointed out an inconsistency in Swampy.

\item Inga Petuhhov corrected an example in Chapter 14.

\item Arne Babenhauserheide sent several helpful corrections.

\item Mark E. Casida is is good at spotting repeated words.

\item Scott Tyler filled in a that was missing. And then sent in

a heap of corrections.

\item Gordon Shephard sent in several corrections, all in separate

emails.

\item Andrew Turner {\tt spot}ted an error in Chapter 8.

\item Adam Hobart fixed a problem with floor division in {\tt arc}.

\item Daryl Hammond and Sarah Zimmerman pointed out that I served

up {\tt math.pi} too early. And Zim spotted a typo.

\item George Sass found a bug in a Debugging section.

\item Brian Bingham suggested Exercise~\ref{exrotatepairs}.

\item Leah Engelbert-Fenton pointed out that I used {\tt tuple}

as a variable name, contrary to my own advice. And then found

a bunch of typos and a ``use before def''.

\item Joe Funke spotted a typo.

\item Chao-chao Chen found an inconsistency in the Fibonacci example.

\item Jeff Paine knows the difference between space and spam.

\item Lubos Pintes sent in a typo.

\item Gregg Lind and Abigail Heithoff suggested Exercise~\ref{checksum}.

\item Max Hailperin has sent in a number of corrections and

suggestions. Max is one of the authors of the extraordinary {\em

Concrete Abstractions}, which you might want to read when you are

done with this book.

\item Chotipat Pornavalai found an error in an error message.

\item Stanislaw Antol sent a list of very helpful suggestions.

\item Eric Pashman sent a number of corrections for Chapters 4--11.

\item Miguel Azevedo found some typos.

\item Jianhua Liu sent in a long list of corrections.

\item Nick King found a missing word.

\item Martin Zuther sent a long list of suggestions.

\item Adam Zimmerman found an inconsistency in my instance

of an ``instance'' and several other errors.

\item Ratnakar Tiwari suggested a footnote explaining degenerate

triangles.

\item Anurag Goel suggested another solution for \verb"is_abecedarian"

and sent some additional corrections. And he knows how to

spell Jane Austen.

\item Kelli Kratzer spotted one of the typos.

\item Mark Griffiths pointed out a confusing example in Chapter 3.

\item Roydan Ongie found an error in my Newton's method.

\item Patryk Wolowiec helped me with a problem in the HTML version.

\item Mark Chonofsky told me about a new keyword in Python 3.

\item Russell Coleman helped me with my geometry.

\item Nam Nguyen found a typo and pointed out that I used the Decorator

pattern but didn't mention it by name.

\item St\'{e}phane Morin sent in several corrections and suggestions.

\item Paul Stoop corrected a typo in \verb+uses_only+.

\item Eric Bronner pointed out a confusion in the discussion of the

order of operations.

\item Alexandros Gezerlis set a new standard for the number and

quality of suggestions he submitted. We are deeply grateful!

\item Gray Thomas knows his right from his left.

\item Giovanni Escobar Sosa sent a long list of corrections and

suggestions.

\item Daniel Neilson corrected an error about the order of operations.

\item Will McGinnis pointed out that {\tt polyline} was defined

differently in two places.

\item Frank Hecker pointed out an exercise that was under-specified, and

some broken links.

\item Animesh B helped me clean up a confusing example.

\item Martin Caspersen found two round-off errors.

\item Gregor Ulm sent several corrections and suggestions.

\item Dimitrios Tsirigkas suggested I clarify an exercise.

\item Carlos Tafur sent a page of corrections and suggestions.

\item Martin Nordsletten found a bug in an exercise solution.

\item Sven Hoexter pointed out that a variable named {\tt input}

shadows a build-in function.

\item Stephen Gregory pointed out the problem with {\tt cmp}

in Python 3.

\item Ishwar Bhat corrected my statement of Fermat's last theorem.

\item Andrea Zanella translated the book into Italian, and sent a

number of corrections along the way.

\item Many, many thanks to Melissa Lewis and Luciano Ramalho for

excellent comments and suggestions on the second edition.

\item Thanks to Harry Percival from PythonAnywhere for his help

getting people started running Python in a browser.

\item Xavier Van Aubel made several useful corrections in the second

edition.

\item William Murray corrected my definition of floor division.

\item Per Starb{\"a}ck brought me up to date on universal newlines in Python 3.

% ENDCONTRIB

In addition, people who spotted typos or made corrections include

Czeslaw Czapla, Dale Wilson,

Richard Fursa, Brian McGhie, Lokesh Kumar Makani, Matthew Shultz, Viet

Le, Victor Simeone, Lars O.D. Christensen, Swarup Sahoo, Alix Etienne,

Kuang He, Wei Huang, Karen Barber, and Eric Ransom.

\end{itemize}

\normalsize

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% START THE BOOK

\mainmatter

\chapter{The way of the program}

The goal of this book is to teach you to think like a computer

scientist. This way of thinking combines some of the best features of

mathematics, engineering, and natural science. Like mathematicians,

computer scientists use formal languages to denote ideas (specifically

computations). Like engineers, they design things, assembling

components into systems and evaluating tradeoffs among alternatives.

Like scientists, they observe the behavior of complex systems, form

hypotheses, and test predictions. \index{problem solving}

The single most important skill for a computer scientist is {\bf

problem solving}. Problem solving means the ability to formulate

problems, think creatively about solutions, and express a solution

clearly and accurately. As it turns out, the process of learning to

program is an excellent opportunity to practice problem-solving

skills. That's why this chapter is called, ``The way of the

program''.

On one level, you will be learning to program, a useful skill by

itself. On another level, you will use programming as a means to an

end. As we go along, that end will become clearer.

\section{What is a program?}

A {\bf program} is a sequence of instructions that specifies how to

perform a computation. The computation might be something

mathematical, such as solving a system of equations or finding the

roots of a polynomial, but it can also be a symbolic computation, such

as searching and replacing text in a document or something

graphical, like processing an image or playing a video.

\index{program}

The details look different in different languages, but a few basic

instructions appear in just about every language:

\begin{description}

\item[input:] Get data from the keyboard, a file, the network, or some

other device.

\item[output:] Display data on the screen, save it in a

file, send it over the network, etc.

\item[math:] Perform basic mathematical operations like addition and

multiplication.

\item[conditional execution:] Check for certain conditions and

run the appropriate code.

\item[repetition:] Perform some action repeatedly, usually with

some variation.

\end{description}

Believe it or not, that's pretty much all there is to it. Every

program you've ever used, no matter how complicated, is made up of

instructions that look pretty much like these. So you can think of

programming as the process of breaking a large, complex task

into smaller and smaller subtasks until the subtasks are

simple enough to be performed with one of these basic instructions.

\section{Running Python}

One of the challenges of getting started with Python is that you

might have to install Python and related software on your computer.

If you are familiar with your operating system, and especially

if you are comfortable with the command-line interface, you will

have no trouble installing Python. But for beginners, it can be

painful to learn about system administration and programming at the

same time.

\index{running Python}

\index{Python!running}

To avoid that problem, I recommend that you start out running Python

in a browser. Later, when you are comfortable with Python, I'll

make suggestions for installing Python on your computer.

\index{Python in a browser}

There are a number of web pages you can use to run Python. If you

already have a favorite, go ahead and use it. Otherwise I recommend

PythonAnywhere. I provide detailed instructions for getting started

at \url{http://tinyurl.com/thinkpython2e}.

\index{PythonAnywhere}

There are two versions of Python, called Python 2 and Python 3.

They are very similar, so if you learn one, it is easy to switch

to the other. In fact, there are only a few differences you will

encounter as a beginner.

This book is written for Python 3, but I include some notes

about Python 2.

\index{Python 2}

The Python {\bf interpreter} is a program that reads and executes

Python code. Depending on your environment, you might start the

interpreter by clicking on an icon, or by typing {\tt python} on

a command line.

When it starts, you should see output like this:

\index{interpreter}

\begin{verbatim}

Python 3.4.0 (default, Jun 19 2015, 14:20:21)

[GCC 4.8.2] on linux

Type "help", "copyright", "credits" or "license" for more information.

>>>

\end{verbatim}

%

The first three lines contain information about the interpreter

and the operating system it's running on, so it might be different for

you. But you should check that the version number, which is

{\tt 3.4.0} in this example, begins with 3, which indicates that

you are running Python 3. If it begins with 2, you are running

(you guessed it) Python 2.

The last line is a {\bf prompt} that indicates that the interpreter is

ready for you to enter code.

If you type a line of code and hit Enter, the interpreter displays the

result:

\index{prompt}

\begin{verbatim}

>>> 1 + 1

2

\end{verbatim}

%

Now you're ready to get started.

From here on, I assume that you know how to start the Python

interpreter and run code.

\section{The first program}

\label{hello}

\index{Hello, World}

Traditionally, the first program you write in a new language

is called ``Hello, World!'' because all it does is display the

words ``Hello, World!''. In Python, it looks like this:

\begin{verbatim}

>>> print('Hello, World!')

\end{verbatim}

%

This is an example of a {\bf print statement}, although it

doesn't actually print anything on paper. It displays a result on the

screen. In this case, the result is the words

\begin{verbatim}

Hello, World!

\end{verbatim}

%

The quotation marks in the program mark the beginning and end

of the text to be displayed; they don't appear in the result.

\index{quotation mark}

\index{print statement}

\index{statement!print}

The parentheses indicate that {\tt print} is a function. We'll get

to functions in Chapter~\ref{funcchap}.

\index{function} \index{print function}

In Python 2, the print statement is slightly different; it is not

a function, so it doesn't use parentheses.

\index{Python 2}

\begin{verbatim}

>>> print 'Hello, World!'

\end{verbatim}

%

This distinction will make more sense soon, but that's enough to

get started.

\section{Arithmetic operators}

\index{operator!arithmetic}

\index{arithmetic operator}

After ``Hello, World'', the next step is arithmetic. Python provides

{\bf operators}, which are special symbols that represent computations

like addition and multiplication.

The operators {\tt +}, {\tt -}, and {\tt *} perform addition,

subtraction, and multiplication, as in the following examples:

\begin{verbatim}

>>> 40 + 2

42

>>> 43 - 1

42

>>> 6 * 7

42

\end{verbatim}

%

The operator {\tt /} performs division:

\begin{verbatim}

>>> 84 / 2

42.0

\end{verbatim}

%

You might wonder why the result is {\tt 42.0} instead of {\tt 42}.

I'll explain in the next section.

Finally, the operator {\tt **} performs exponentiation; that is,

it raises a number to a power:

\begin{verbatim}

>>> 6**2 + 6

42

\end{verbatim}

%

In some other languages, \verb"^" is used for exponentiation, but

in Python it is a bitwise operator called XOR. If you are not

familiar with bitwise operators, the result will surprise you:

\begin{verbatim}

>>> 6 ^ 2

4

\end{verbatim}

%

I won't cover

bitwise operators in this book, but you can read about

them at \url{http://wiki.python.org/moin/BitwiseOperators}.

\index{bitwise operator}

\index{operator!bitwise}

\section{Values and types}

\index{value}

\index{type}

\index{string}

A {\bf value} is one of the basic things a program works with, like a

letter or a number. Some values we have seen so far are {\tt 2},

{\tt 42.0}, and \verb"'Hello, World!'".

These values belong to different {\bf types}:

{\tt 2} is an {\bf integer}, {\tt 42.0} is a {\bf floating-point number},

and \verb"'Hello, World!'" is a {\bf string},

so-called because the letters it contains are strung together.

\index{integer}

\index{floating-point}

If you are not sure what type a value has, the interpreter can

tell you:

\begin{verbatim}

>>> type(2)

<class 'int'>