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+## Appendix A Proof of Theorem 1
+
+### 
+
+[MISSING_PAGE_POST]
+
+Proof of Theorem 1
+
+[MISSING_PAGE_EMPTY:2]
+
+## Chapter 1 Introduction
+
+In this thesis we introduce a new class of _finite_Green Tea Press
+
+9 Washburn Ave
+
+Needham MA 02492
+
+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 [http://creativecommons.org/licenses/by-nc/3.0/](http://creativecommons.org/licenses/by-nc/3.0/).
+
+The original form of this book is LaTeX source code. Compiling this LaTeX source has the effect of generating a device-independent representation of a textbook, which can be converted to other formats and printed.
+
+The LaTeX source for this book is available from [http://www.thinkpython.com](http://www.thinkpython.com)
+
+## Preface
+
+### 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:
+
+* Keep it short. It is better for students to read 10 pages than not read 50 pages.
+* Be careful with vocabulary. I tried to minimize the jargon and define each term at first use.
+* Build gradually. To avoid trap doors, I took the most difficult topics and split them into a series of small steps.
+* Focus on programming, not the programming language. I included the minimum useful subset of Java and left out the rest.
+
+I needed a title, so on a whim I chose _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.
+
+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.
+
+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.
+
+Over the last nine years I 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 _Think Python_. Some of the changes are:
+
+* 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.
+* I added more exercises, ranging from short tests of understanding to a few substantial projects. And I wrote solutions for most of them.
+* I added a series of case studies--longer examples with exercises, solutions, and discussion. Some are based on Swampy, a suite of Python programs I wrote for use in my classes. Swampy, code examples, and some solutions are available from [http://thinkpython.com](http://thinkpython.com).
+* I expanded the discussion of program development plans and basic design patterns.
+* I added appendices about debugging, analysis of algorithms, and UML diagrams with Lumpy.
+
+I hope you enjoy working with this book, and that it helps you learn to program and think, at least a little bit, like a computer scientist.
+
+Allen B. Downey
+
+Needham MA
+
+Allen Downey is a Professor of Computer Science at the Franklin W. Olin College of Engineering.
+
+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.
+
+Thanks also to Chris Meyers, who contributed several sections to _How to Think Like a Computer Scientist_.
+
+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.
+
+Thanks to the editors at Lulu who worked on _How to Think Like a Computer Scientist_.
+
+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.
+
+## Contributor List
+
+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 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!
+
+* Lloyd Hugh Allen sent in a correction to Section 8.4.
+* Yvon Boulianne sent in a correction of a semantic error in Chapter 5.
+* Fred Bremmer submitted a correction in Section 2.1.
+* Jonah Cohen wrote the Perl scripts to convert the LaTeX source for this book into beautiful HTML.
+* 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.
+* Benoit Girard sent in a correction to a humorous mistake in Section 5.6.
+* Courtney Gleason and Katherine Smith wrote 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.
+* 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.
+* James Kaylin is a student using the text. He has submitted numerous corrections.
+* David Kershaw fixed the broken catTwice function in Section 3.10.
+* 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.
+* Man-Yong Lee sent in a correction to the example code in Section 2.4.
+* David Mayo pointed out that the word "unconsciously" in Chapter 1 needed to be changed to "subconsciously".
+* Chris McAloon sent in several corrections to Sections 3.9 and 3.10.
+* Matthew J. Moelter has been a long-time contributor who sent in numerous corrections and suggestions to the book.
+* Simon Dicon Montford reported a missing function definition and several typos in Chapter 3. He also found errors in the increment function in Chapter 13.
+* John Ouzts corrected the definition of "return value" in Chapter 3.
+* Kevin Parks sent in valuable comments and suggestions as to how to improve the distribution of the book.
+* David Pool sent in a typo in the glossary of Chapter 1, as well as kind words of encouragement.
+* Michael Schmitt sent in a correction to the chapter on files and exceptions.
+
+* Robin Shaw pointed out an error in Section 13.1, where the printTime function was used in an example without being defined.
+* Paul Sleigh found an error in Chapter 7 and a bug in Jonah Cohen's Perl script that generates HTML from LaTeX.
+* Craig T. Snydal is testing the text in a course at Drew University. He has contributed several valuable suggestions and corrections.
+* 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.
+* Keith Verheyden sent in a correction in Chapter 3.
+* Peter Winstanley let us know about a longstanding error in our Latin in Chapter 3.
+* Chris Wrobel made corrections to the code in the chapter on file I/O and exceptions.
+* 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.
+* Christoph Zwerschke sent several corrections and pedagogic suggestions, and explained the difference between _gleich_ and _selbe_.
+* James Mayer sent us a whole slew of spelling and typographical errors, including two in the contributor list.
+* Hayden McAfee caught a potentially confusing inconsistency between two examples.
+* 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.
+* Tauhidul Hoque and Lex Berezhny created the illustrations in Chapter 1 and improved many of the other illustrations.
+* Dr. Michele Alzetta caught an error in Chapter 8 and sent some interesting pedagogic comments and suggestions about Fibonacci and Old Maid.
+* Andy Mitchell caught a typo in Chapter 1 and a broken example in Chapter 2.
+* Kalin Harvey suggested a clarification in Chapter 7 and caught some typos.
+* Christopher P. Smith caught several typos and helped us update the book for Python 2.2.
+* David Hutchins caught a typo in the Foreword.
+* 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.
+* Julie Peters caught a typo in the Preface.
+* Florin Oprina sent in an improvement in makeTime, a correction in printTime, and a nice typo.
+* D. J. Webre suggested a clarification in Chapter 3.
+* Ken found a fistful of errors in Chapters 8, 9 and 11.
+* Ivo Wever caught a typo in Chapter 5 and suggested a clarification in Chapter 3.
+* Curtis Yanko suggested a clarification in Chapter 2.
+
+* Ben Logan sent in a number of typos and problems with translating the book into HTML.
+* Jason Armstrong saw the missing word in Chapter 2.
+* Louis Cordier noticed a spot in Chapter 16 where the code didn't match the text.
+* Brian Cain suggested several clarifications in Chapters 2 and 3.
+* Rob Black sent in a passel of corrections, including some changes for Python 2.2.
+* Jean-Philippe Rey at Ecole Centrale Paris sent a number of patches, including some updates for Python 2.2 and other thoughtful improvements.
+* Jason Mader at George Washington University made a number of useful suggestions and corrections.
+* Jan Gundtoffe-Bruun reminded us that "a error" is an error.
+* Abel David and Alexis Dinno reminded us that the plural of "matrix" is "matrices", not "matrices". This error was in the book for years, but two readers with the same initials reported it on the same day. Weird.
+* 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".
+* Roger Sperberg pointed out a twisted piece of logic in Chapter 3.
+* Sam Bull pointed out a confusing paragraph in Chapter 2.
+* Andrew Cheung pointed out two instances of "use before def."
+* C. Corey Capel spotted the missing word in the Third Theorem of Debugging and a typo in Chapter 4.
+* Alessandra helped clear up some Turtle confusion.
+* Wim Champagne found a brain-o in a dictionary example.
+* Douglas Wright pointed out a problem with floor division in ar c.
+* Jared Spindor found some jetsam at the end of a sentence.
+* Lin Peiheng sent a number of very helpful suggestions.
+* Ray Hagtvedt sent in two errors and a not-quite-error.
+* Torsten Hubsch pointed out an inconsistency in Swampy.
+* Inga Petuhhov corrected an example in Chapter 14.
+* Arne Babenhauserheide sent several helpful corrections.
+* Mark E. Casida is is good at spotting repeated words.
+* Scott Tyler filled in a that was missing. And then sent in a heap of corrections.
+* Gordon Shephard sent in several corrections, all in separate emails.
+* Andrew Turner spotted an error in Chapter 8.
+* Adam Hobart fixed a problem with floor division in arc.
+
+* Daryl Hammond and Sarah Zimmerman pointed out that I served up math.pi too early. And Zim spotted a typo.
+* George Sass found a bug in a Debugging section.
+* Brian Bingham suggested Exercise 11.10.
+* Leah Engelbert-Fenton pointed out that I used tuple as a variable name, contrary to my own advice. And then found a bunch of typos and a "use before def."
+* Joe Funke spotted a typo.
+* Chao-chao Chen found an inconsistency in the Fibonacci example.
+* Jeff Paine knows the difference between space and spam.
+* Lubos Pintes sent in a typo.
+* Gregg Lind and Abigail Heithoff suggested Exercise 14.4.
+* Max Hailperin has sent in a number of corrections and suggestions. Max is one of the authors of the extraordinary _Concrete Abstractions_, which you might want to read when you are done with this book.
+* Chotipat Pornavalai found an error in an error message.
+* Stanislaw Antol sent a list of very helpful suggestions.
+* Eric Pashman sent a number of corrections for Chapters 4-11.
+* Miguel Azevedo found some typos.
+* Jianhua Liu sent in a long list of corrections.
+* Nick King found a missing word.
+* Martin Zuther sent a long list of suggestions.
+* Adam Zimmerman found an inconsistency in my instance of an "instance" and several other errors.
+* Ratnakar Tiwari suggested a footnote explaining degenerate triangles.
+* Anurag Goel suggested another solution for is_abeedarian and sent some additional corrections. And he knows how to spell Jane Austen.
+* Kelli Kratzer spotted one of the typos.
+* Mark Griffiths pointed out a confusing example in Chapter 3.
+* Roydan Ongie found an error in my Newton's method.
+* Patryk Wolowiec helped me with a problem in the HTML version.
+* Mark Chonofsky told me about a new keyword in Python 3.
+* Russell Coleman helped me with my geometry.
+* Wei Huang spotted several typographical errors.
+* Karen Barber spotted the the oldest typo in the book.
+
+* Nam Nguyen found a typo and pointed out that I used the Decorator pattern but didn't mention it by name.
+* Stephane Morin sent in several corrections and suggestions.
+* Paul Stoop corrected a typo in uses_only.
+* Eric Bronner pointed out a confusion in the discussion of the order of operations.
+* Alexandros Gezerlis set a new standard for the number and quality of suggestions he submitted. We are deeply grateful!
+* Gray Thomas knows his right from his left.
+* Giovanni Escobar Sosa sent a long list of corrections and suggestions.
+* Alix Etienne fixed one of the URLs.
+* Kuang He found a typo.
+* Daniel Neilson corrected an error about the order of operations.
+* Will McGinnis pointed out that polyline was defined differently in two places.
+* Swarup Sahoo spotted a missing semi-colon.
+* Frank Hecker pointed out an exercise that was under-specified, and some broken links.
+* Animesh B helped me clean up a confusing example.
+* Martin Caspersen found two round-off errors.
+* Gregor Ulm sent several corrections and suggestions.
+* Dimitrios Tsirigkas suggested I clarify an exercise.
+* Carlos Tafur sent a page of corrections and suggestions.
+* Martin Nordsletten found a bug in an exercise solution.
+* Lars O.D. Christensen found a broken reference.
+* Victor Simeone found a typo.
+* Sven Hoexter pointed out that a variable named input shadows a built-in function.
+* Viet Le found a typo.
+* Stephen Gregory pointed out the problem with cmp in Python 3.
+* Matthew Shultz let me know about a broken link.
+* Lokesh Kumar Makani let me know about some broken links and some changes in error messages.
+* Ishwar Bhat corrected my statement of Fermat's last theorem.
+* Brian McGhie suggested a clarification.
+* Andrea Zanella translated the book into Italian, and sent a number of corrections along the way.
+
+## Chapter 0 Preface
+
+###### Contents
+
+* 1 The way of the program
+	* 1.1 The Python programming language
+	* 1.2 What is a program?
+	* 1.3 What is debugging?
+	* 1.4 Formal and natural languages
+	* 1.5 The first program
+	* 1.6 Debugging
+	* 1.7 Glossary
+	* 1.8 Exercises
+* 2 Variables, expressions and statements
+	* 2.1 Values and types
+	* 2.2 Variables
+	* 2.3 Variable names and keywords
+	* 2.4 Operators and operands
+	* 2.5 Expressions and statements
+	* 2.6 Interactive mode and script mode
+	* 2.7 Order of operations
+	* 2.8 String operations
+	* 2.9 Comments
+* 2.10 Debugging
+* 2.11 Glossary
+* 2.12 Exercises
+* 3 Functions
+	* 3.1 Function calls
+	* 3.2 Type conversion functions
+	* 3.3 Math functions
+	* 3.4 Composition
+	* 3.5 Adding new functions
+	* 3.6 Definitions and uses
+	* 3.7 Flow of execution
+	* 3.8 Parameters and arguments
+	* 3.9 Variables and parameters are local
+* 3.10 Stack diagrams
+* 3.11 Fruitful functions and void functions
+* 3.12 Why functions?
+* 3.13 Importing with from
+* 3.14 Debugging
+* 3.15 Glossary
+* 3.16 Exercises
+* 4 Case study: interface design
+	* 4.1 TurtleWorld
+	* 4.2 Simple repetition
+	* 4.3 Exercises
+	* 4.4 Encapsulation
+	* 4.5 Generalization
+	* 4.6 Interface design
+	* 4.7 Refactoring
+	* 4.8 A development plan
+	* 4.9 docstring
+* 4.10 Debugging
+* 4.11 Glossary
+* 4.12 Exercises
+* 5 **Conditionally and recursion*
+	* 5.1 Modulus operator
+	* 5.2 Boolean expressions
+	* 5.3 Logical operators
+	* 5.4 Conditional execution
+	* 5.5 Alternative execution
+	* 5.6 Chained conditionals
+	* 5.7 Nested conditionals
+	* 5.8 Recursion
+	* 5.9 Stack diagrams for recursive functions
+* 5.10 Infinite recursion
+* 5.11 Keyboard input
+* 5.12 Debugging
+* 5.13 Glossary
+* 5.14 Exercises
+* 6 **Fruitful functions*
+	* 6.1 Return values
+	* 6.2 Incremental development
+	* 6.3 Composition
+	* 6.4 Boolean functions
+	* 6.5 More recursion
+	* 6.6 Leap of faith
+	* 6.7 One more example
+	* 6.8 Checking types
+	* 6.9 Debugging
+* 6.10 Glossary
+* 6.11 Exercises
+* 7 Iteration
+	* 7.1 Multiple assignment
+	* 7.2 Updating variables
+	* 7.3 The while statement
+	* 7.4 break
+	* 7.5 Square roots
+	* 7.6 Algorithms
+	* 7.7 Debugging
+	* 7.8 Glossary
+	* 7.9 Exercises
+* 8 Strings
+	* 8.1 A string is a sequence
+	* 8.2 len
+	* 8.3 Traversal with a for loop
+	* 8.4 String slices
+	* 8.5 Strings are immutable
+	* 8.6 Searching
+	* 8.7 Looping and counting
+	* 8.8 String methods
+	* 8.9 The in operator
+* 8.10 String comparison
+* 8.11 Debugging
+* 8.12 Glossary
+* 8.13 Exercises
+* 9 Case study: word play
+	* 9.1 Reading word lists
+	* 9.2 Exercises
+	* 9.3 Search
+	* 9.4 Looping with indices
+	* 9.5 Debugging
+	* 9.6 Glossary
+	* 9.7 Exercises
+* [10] Lists
+* [10] A list is a sequence
+* [10] Lists are mutable
+* [10] Traversing a list
+* [10] List operations
+* [10] List slices
+* [10] List methods
+* [10] Map, filter and reduce
+* [10] Deleting elements
+* [10] Lists and strings
+* [10] Objects and values
+* [10] Aliasing
+* [10] List arguments
+* [10] Debugging
+* [10] Glossary
+* [10] Exercises
+* [11] Dictionaries
+* [11] Dictionary as a set of counters
+* [11] Looping and dictionaries
+* [11] Reverse lookup
+* [11] Dictionaries and lists
+* [11] Memos
+* [11] Global variables
+* [11] Long integers
+* [11] Debugging
+* [11] Glossary
+* [11] Exercises
+* [11]* 12 Tuples
+	* 12.1 Tuples are immutable
+	* 12.2 Tuple assignment
+	* 12.3 Tuples as return values
+	* 12.4 Variable-length argument tuples
+	* 12.5 Lists and tuples
+	* 12.6 Dictionaries and tuples
+	* 12.7 Comparing tuples
+	* 12.8 Sequences of sequences
+	* 12.9 Debugging
+* 12.10 Glossary
+* 12.11 Exercises
+* 13 Case study: data structure selection
+	* 13.1 Word frequency analysis
+	* 13.2 Random numbers
+	* 13.3 Word histogram
+	* 13.4 Most common words
+	* 13.5 Optional parameters
+	* 13.6 Dictionary subtraction
+	* 13.7 Random words
+	* 13.8 Markov analysis
+	* 13.9 Data structures
+* 13.10 Debugging
+* 13.11 Glossary
+* 13.12 Exercises
+* 14 Files
+	* 14.1 Persistence
+	* 14.2 Reading and writing
+	* 14.3 Format operator
+	* 14.4 Filenames and paths
+
+**Abstract**
+
+In this thesis, we study the relationship between the \(\alpha\)-function and the \(\beta\)-function. We show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\), where \(\beta\) is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). 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We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\beta\). We also show that the \(\alpha\)-function is a function of the form \(\alpha=\beta\).
+
+* 17 Classes and methods
+	* 17.1 Object-oriented features
+	* 17.2 Printing objects
+	* 17.3 Another example
+	* 17.4 A more complicated example
+	* 17.5 The init method
+	* 17.6 The __str__ method
+	* 17.7 Operator overloading
+	* 17.8 Type-based dispatch
+	* 17.9 Polymorphism
+* 17.10 Debugging
+* 17.11 Interface and implementation
+* 17.12 Glossary
+* 17.13 Exercises
+* 18 Inheritance
+	* 18.1 Card objects
+	* 18.2 Class attributes
+	* 18.3 Comparing cards
+	* 18.4 Decks
+	* 18.5 Printing the deck
+	* 18.6 Add, remove, shuffle and sort
+	* 18.7 Inheritance
+	* 18.8 Class diagrams
+	* 18.9 Debugging
+* 18.10 Data encapsulation
+* 18.11 Glossary
+* 18.12 Exercises
+* 19 Case study: Tkinter
+	* 19.1 GUI
+	* 19.2 Buttons and callbacks
+	* 19.3 Canvas widgets
+	* 19.4 Coordinate sequences
+	* 19.5 More widgets
+	* 19.6 Packing widgets
+	* 19.7 Menus and Callables
+	* 19.8 Binding
+	* 19.9 Debugging
+* 19.10 Glossary
+* 19.11 Exercises
+* A Debugging
+* A.1 Syntax errors
+* A.2 Runtime errors
+* A.3 Semantic errors
+* B Analysis of Algorithms
+* B.1 Order of growth
+* B.2 Analysis of basic Python operations
+* B.3 Analysis of search algorithms
+* B.4 Hashtables
+* C Lumpy
+* C.1 State diagram
+* C.2 Stack diagram
+* C.3 Object diagrams
+* C.4 Function and class objects
+* C.5 Class Diagrams
+
+**Abstract**
+
+In this thesis we study the \(\alpha\)
+
+## Chapter 1 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.
+
+The single most important skill for a computer scientist is **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.
+
+### 1.1 The Python programming language
+
+The programming language you will learn is Python. Python is an example of a **high-level language**; other high-level languages you might have heard of are C, C++, Perl, and Java.
+
+There are also **low-level languages**, sometimes referred to as "machine languages" or "assembly languages." Loosely speaking, computers can only run programs written in low-level languages. So programs written in a high-level language have to be processed before they can run. This extra processing takes some time, which is a small disadvantage of high-level languages.
+
+The advantages are enormous. First, it is much easier to program in a high-level language. Programs written in a high-level language take less time to write, they are shorter and easier to read, and they are more likely to be correct. Second, high-level languages are **portable**, meaning that they can run on different kinds of computers with few or no modifications. Low-level programs can run on only one kind of computer and have to be rewritten to run on another.
+
+Introduction
+
+The purpose of this paper is to study the properties of the system of equations of motion. The system of equations of motion is a system of equations of motion, and the system of equations of motion is a system of equations of motion. The system of equations of motion is a system of equations of motion, and the system of equations of motion is a system of equations of motion. The system of equations of motion is a system of equations of motion, and the system of equations of motion is a system of equations of motion. The system of equations of motion is a system of equations of motion, and the system of equations of motion is a system of equations of motion. The system of equations of motion is a system of equations of motion, and the system of equations of motion is a system of equations of motion. The system of equations of motion is a system of equations of motion, and the system of equations of motion is a system of equations of motion. 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+
+### 1.2 What is a program?
+
+A **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 (strangely enough) compiling a program.
+
+The details look different in different languages, but a few basic instructions appear in just about every language:
+
+**input:**: Get data from the keyboard, a file, or some other device.
+**output:**: Display data on the screen or send data to a file or other device.
+**math:**: Perform basic mathematical operations like addition and multiplication.
+**conditional execution:**: Check for certain conditions and execute the appropriate code.
+**repetition:**: Perform some action repeatedly, usually with some variation.
+
+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.
+
+That may be a little vague, but we will come back to this topic when we talk about **algorithms**.
+
+### 1.3 What is debugging?
+
+Programming is error-prone. For whimsical reasons, programming errors are called **bugs** and the process of tracking them down is called **debugging**.
+
+Three kinds of errors can occur in a program: syntax errors, runtime errors, and semantic errors. It is useful to distinguish between them in order to track them down more quickly.
+
+#### Syntax errors
+
+Python can only execute a program if the syntax is correct; otherwise, the interpreter displays an error message. **Syntax** refers to the structure of a program and the rules about that structure. For example, parentheses have to come in matching pairs, so (1 + 2) is legal, but 8) is a **syntax error**.
+
+In English, readers can tolerate most syntax errors, which is why we can read the poetry of e. e. cumnings without spewing error messages. Python is not so forgiving. If there is a single syntax error anywhere in your program, Python will display an error message and quit, and you will not be able to run your program. During the first few weeks of your programming career, you will probably spend a lot of time tracking down syntax errors. As you gain experience, you will make fewer errors and find them faster.
+
+#### Runtime errors
+
+The second type of error is a runtime error, so called because the error does not appear until after the program has started running. These errors are also called **exceptions** because they usually indicate that something exceptional (and bad) has happened.
+
+Runtime errors are rare in the simple programs you will see in the first few chapters, so it might be a while before you encounter one.
+
+#### Semantic errors
+
+The third type of error is the **semantic error**. If there is a semantic error in your program, it will run successfully in the sense that the computer will not generate any error messages, but it will not do the right thing. It will do something else. Specifically, it will do what you told it to do.
+
+The problem is that the program you wrote is not the program you wanted to write. The meaning of the program (its semantics) is wrong. Identifying semantic errors can be tricky because it requires you to work backward by looking at the output of the program and trying to figure out what it is doing.
+
+#### Experimental debugging
+
+One of the most important skills you will acquire is debugging. Although it can be frustrating, debugging is one of the most intellectually rich, challenging, and interesting parts of programming.
+
+In some ways, debugging is like detective work. You are confronted with clues, and you have to infer the processes and events that led to the results you 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 the result of the modification, and you take a step closer to a working program. If your hypothesis was wrong, you have to come up with a new one. As Sherlock Holmes pointed out, "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." (A. Conan Doyle, _The Sign of Four_)
+
+For some people, programming and debugging are the same thing. That is, programming is the process of gradually debugging a program until it does what you want. The idea is that you should start with a program that does _something_ and make small modifications, debugging them as you go, so that you always have a working program.
+
+For example, Linux is an operating system that contains thousands of lines of code, but it started out as a simple program Linux Torvalds used to explore the Intel 80386 chip. According to Larry Greenfield, "One of Linux's earlier projects was a program that would switch between printing AAAA and BBBB. This later evolved to Linux." (_The Linux Users' Guide_ Beta Version 1).
+
+Later chapters will make more suggestions about debugging and other programming practices.
+
+### 1.4 Formal and natural languages
+
+**Natural languages** are the languages people speak, such as English, Spanish, and French. They were not designed by people (although people try to impose some order on them); they evolved naturally.
+
+**Formal languages** are languages that are designed by people for specific applications. For example, the notation that mathematicians use is a formal language that is particularly good at denoting relationships among numbers and symbols. Chemists use a formal language to represent the chemical structure of molecules. And most importantly:
+
+**Programming languages are formal languages that have been designed to express computations.**
+
+Formal languages tend to have strict rules about syntax. For example, \(3+3=6\) is a syntactically correct mathematical statement, but \(3+=3\$6\) is not. \(H_{2}O\) is a syntactically correct chemical formula, but \({}_{2}Zz\) is not.
+
+Syntax rules come in two flavors, pertaining to **tokens** and structure. Tokens are the basic elements of the language, such as words, numbers, and chemical elements. One of the problems with \(3+=3\$6\) is that $ is not a legal token in mathematics (at least as far as I know). Similarly, \({}_{2}Zz\) is not legal because there is no element with the abbreviation \(Zz\).
+
+The second type of syntax rule pertains to the structure of a statement; that is, the way the tokens are arranged. The statement \(3+=3\) is illegal because even though \(+\) and \(=\) are legal tokens, you can't have one right after the other. Similarly, in a chemical formula the subscript comes after the element name, not before.
+
+**Exercise 1.1**.: _Write a well-structured English sentence with invalid tokens in it. Then write another sentence with all valid tokens but with invalid structure._
+
+When you read a sentence in English or a statement in a formal language, you have to figure out what the structure of the sentence is (although in a natural language you do this subconsciously). This process is called **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 out what it means, or the semantics of the sentence. Assuming that you know what a penny is and what it means to drop, you will understand the general implication of this sentence.
+
+Although formal and natural languages have many features in common--tokens, structure, syntax, and semantics--there are some differences:
+
+**ambiguity:**: Natural languages are full of ambiguity, which people deal with by using contextual clues and other information. Formal languages are designed to be nearly or completely unambiguous, which means that any statement has exactly one meaning, regardless of context.
+**redundancy:**: In order to make up for ambiguity and reduce misunderstandings, natural languages employ lots of redundancy. As a result, they are often verbose. Formal languages are less redundant and more concise.
+
+## Chapter 1 The way of the program
+
+### 1.1 The program
+
+The program is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that
+
+### 1.6 Debugging
+
+It is a good idea to read this book in front of a computer so you can try out the examples as you go. You can run most of the examples in interactive mode, but if you put the code in a script, it is easier to try out variations.
+
+Whenever you are experimenting with a new feature, you should try to make mistakes. For example, in the "Hello, world!" program, what happens if you leave out one of the quotation marks? What if you leave out both? What if you spell print wrong?
+
+This kind of experiment helps you remember what you read; it also helps with debugging, because you get to know what the error messages mean. It is better to make mistakes now and on purpose than later and accidentally.
+
+Programming, and especially debugging, sometimes brings out strong emotions. If you are struggling with a difficult bug, you might feel angry, despondent or embarrassed.
+
+There is evidence that people naturally respond to computers as if they were people. When they work well, we think of them as teammates, and when they are obstinate or rude, we respond to them the same way we respond to rude, obstinate people (Reeves and Nass, _The Media Equation: How People Treat Computers, Television, and New Media Like Real People and Places_).
+
+Preparing for these reactions might help you deal with them. One approach is to think of the computer as an employee with certain strengths, like speed and precision, and particular weaknesses, like lack of empathy and inability to grasp the big picture.
+
+Your job is to be a good manager: find ways to take advantage of the strengths and mitigate the weaknesses. And find ways to use your emotions to engage with the problem, without letting your reactions interfere with your ability to work effectively.
+
+Learning to debug can be frustrating, but it is a valuable skill that is useful for many activities beyond programming. At the end of each chapter there is a debugging section, like this one, with my thoughts about debugging. I hope they help!
+
+### 1.7 Glossary
+
+**problem solving:**: The process of formulating a problem, finding a solution, and expressing the solution.
+**high-level language:**: A programming language like Python that is designed to be easy for humans to read and write.
+**low-level language:**: A programming language that is designed to be easy for a computer to execute; also called "machine language" or "assembly language."
+**portability:**: A property of a program that can run on more than one kind of computer.
+**interpret:**: To execute a program in a high-level language by translating it one line at a time.
+**compile:**: To translate a program written in a high-level language into a low-level language all at once, in preparation for later execution.
+
+## Chapter 1 The way of the program
+
+### 1.1 The program
+
+The program
+
+### 1.8 Exercises
+
+**Exercise 1.2**.: _Use a web browser to go to the Python website [http://python.org](http://python.org). This page contains information about Python and links to Python-related pages, and it gives you the ability to search the Python documentation._
+
+_For example, if you enter_ print _in the search window, the first link that appears is the documentation of the_ print _statement_. At this point, not all of it will make sense to you, but it is good to know where it is._
+
+**Exercise 1.3**.: _Start the Python interpreter and type_ help() _to start the online help utility. Or you can type_ help('print') _to get information about the_ print _statement_._
+
+_If this example doesn't work, you may need to install additional Python documentation or set an environment variable; the details depend on your operating system and version of Python._
+
+**Exercise 1.4**.: _Start the Python interpreter and use it as a calculator. Python's syntax for math operations is almost the same as standard mathematical notation. For example, the symbols +, - and / denote addition, subtraction and division, as you would expect. The symbol for multiplication is *._
+
+_If you run a 10 kilometer race in 43 minutes 30 seconds, what is your average time per mile? What is your average speed in miles per hour? (Hint: there are 1.61 kilometers in a mile)._
+
+## Chapter 1 The way of the program
+
+### 1.1 The program
+
+The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is designed to perform the program. The program is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that is a program that
+
+## Chapter 2 Variables, expressions and statements
+
+### 2.1 Values and types
+
+A **value** is one of the basic things a program works with, like a letter or a number. The values we have seen so far are 1, 2, and 'Hello, World!'.
+
+These values belong to different **types**: 2 is an integer, and 'Hello, World!' is a **string**, so-called because it contains a "string" of letters. You (and the interpreter) can identify strings because they are enclosed in quotation marks.
+
+If you are not sure what type a value has, the interpreter can tell you.
+
+>> type('Hello, World!') <type'str'> >> type(17) <type 'int'>
+
+Not surprisingly, strings belong to the type str and integers belong to the type int. Less obviously, numbers with a decimal point belong to a type called float, because these numbers are represented in a format called **floating-point**.
+
+>> type(3.2) <type 'float'>
+
+What about values like '17' and '3.2'? They look like numbers, but they are in quotation marks like strings.
+
+>> type('17') <type'str'> >> type('3.2') <type'str'>
+
+They're strings.
+
+When you type a large integer, you might be tempted to use commas between groups of three digits, as in 1,000,000. This is not a legal integer in Python, but it is legal:
+
+#### 2.2.1 Variable names and keywords
+
+Programmers generally choose names for their variables that are meaningful--they document what the variable is used for.
+
+Variable names can be arbitrarily long. They can contain both letters and numbers, but they have to begin with a letter. It is legal to use uppercase letters, but it is a good idea to begin variable names with a lowercase letter (you'll see why later).
+
+Figure 2.1: State diagram.
+
+The underscore character, _, can appear in a name. It is often used in names with multiple words, such as my_name or airspeed_of_unladen_swallow.
+
+If you give a variable an illegal name, you get a syntax error:
+
+```
+>>>76trombones='bigparade' SyntaxError:invalidsyntax >>>more0=100000 SyntaxError:invalidsyntax >>>class='AdvancedTheoreticalZymurgy' SyntaxError:invalidsyntax 76trombonesis illegal because it does not begin with a letter. more0 is illegal because it contains an illegal character, 0. But what's wrong with class?
+```
+
+It turns out that class is one of Python's **keywords**. The interpreter uses keywords to recognize the structure of the program, and they cannot be used as variable names.
+
+Python 2 has 31 keywords:
+
+```
+anddelfromnotwhile aselifglobalorwith assertelseifpassyield breakexceptimportprint classexecinraise continuefinallyisreturn defforlambdatry
+```
+
+In Python 3, exec is no longer a keyword, but nonlocal is.
+
+You might want to keep this list handy. If the interpreter complains about one of your variable names and you don't know why, see if it is on this list.
+
+### 2.4 Operators and operands
+
+**Operators** are special symbols that represent computations like addition and multiplication. The values the operator is applied to are called **operands**.
+
+The operators +, _, *, / and ** perform addition, subtraction, multiplication, division and exponentiation, as in the following examples:
+
+```
+20+32hour-1hour*60+minuteminute/605**2(5+9)*(15-7)
+```
+
+In some other languages, ^ is used for exponentiation, but in Python it is a bitwise operator called XOR. I won't cover bitwise operators in this book, but you can read about them at [http://wiki.python.org/moin/BitwiseOperators](http://wiki.python.org/moin/BitwiseOperators).
+
+In Python 2, the division operator might not do what you expect:
+
+```
+>>>minute=59 >>>minute/60
+```
+
+The value of minute is 59, and in conventional arithmetic 59 divided by 60 is 0.98333, not 0. The reason for the discrepancy is that Python is performing **floor division**. When both of the operands are integers, the result is also an integer; floor division chops off the fraction part, so in this example it rounds down to zero.
+
+In Python 3, the result of this division is a float. The new operator // performs floor division.
+
+If either of the operands is a floating-point number, Python performs floating-point division, and the result is a float:
+
+```
+>>>minute/60.0 0.9833333333333328
+```
+
+### 2.5 Expressions and statements
+
+An **expression** is a combination of values, variables, and operators. A value all by itself is considered an expression, and so is a variable, so the following are all legal expressions (assuming that the variable x has been assigned a value):
+
+```
+x +17
+```
+
+A **statement** is a unit of code that the Python interpreter can execute. We have seen two kinds of statement: print and assignment.
+
+Technically an expression is also a statement, but it is probably simpler to think of them as different things. The important difference is that an expression has a value; a statement does not.
+
+### 2.6 Interactive mode and script mode
+
+One of the benefits of working with an interpreted language is that you can test bits of code in interactive mode before you put them in a script. But there are differences between interactive mode and script mode that can be confusing.
+
+For example, if you are using Python as a calculator, you might type
+
+```
+>>>miles=26.2 >>>miles*1.61 42.182
+```
+
+The first line assigns a value to miles, but it has no visible effect. The second line is an expression, so the interpreter evaluates it and displays the result. So we learn that a marathon is about 42 kilometers.
+
+But if you type the same code into a script and run it, you get no output at all. In script mode an expression, all by itself, has no visible effect. Python actually evaluates the expression, but it doesn't display the value unless you tell it to:
+
+```
+miles=26.2 printmiles*1.61
+```
+
+This behavior can be confusing at first.
+
+A script usually contains a sequence of statements. If there is more than one statement, the results appear one at a time as the statements execute.
+
+For example, the script 
+### 2.7 Order of operations
+
+```
+print1 x=2 printx
+```
+
+produces the output
+
+```
+2
+```
+
+The assignment statement produces no output.
+
+**Exercise 2.1**.: _Type the following statements in the Python interpreter to see what they do:_
+
+```
+x=5 x+1
+```
+
+_Now put the same statements into a script and run it. What is the output? Modify the script by transforming each expression into a print statement and then run it again._
+
+### 2.7 Order of operations
+
+When more than one operator appears in an expression, the order of evaluation depends on the **rules of precedence**. For mathematical operators, Python follows mathematical convention. The acronym **PEMDAS** is a useful way to remember the rules:
+
+* Parentheses have the highest precedence and can be used to force an expression to evaluate in the 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 if it doesn't change the result.
+* Exponentiation has the next highest precedence, so 2**1+1 is 3, not 4, and 3*1**3 is 3, not 27.
+* Multiplication and **Division** have the same precedence, which is higher than Addition and **Subtraction**, which also have the same precedence. So 2*3-1 is 5, not 4, and 6+4/2 is 8, not 5.
+* Operators with the same precedence are evaluated from left to right (except exponentiation). So in the expression degrees / 2
+* pi, the division happens first and the result is multiplied by pi. To divide by 2\(\pi\), you can use parentheses or write degrees / 2 / pi.
+
+I don't work very hard to remember rules of precedence for other operators. If I can't tell by looking at the expression, I use parentheses to make it obvious.
+
+### 2.8 String operations
+
+In general, you can't perform mathematical operations on strings, even if the strings look like numbers, so the following are illegal:
+
+'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 the strings by linking them end-to-end. For example:
+
+first = 'throat' second = 'warbler' print first + second The output of this program is throatwarbler.
+
+The * operator also works on strings; it performs repetition. For example, 'Spam'*3 is 'SpamSpam'. If one of the operands is a string, the other has to be an integer.
+
+This use of + and * makes sense by analogy with addition and multiplication. Just as 4*3 is equivalent to 4+4+4, we expect 'Spam'*3 to be the same as 'Spam'+'Spam', and it is. On the other hand, there is a significant way in which string concatenation and repetition are different from integer addition and multiplication. Can you think of a property that addition has that string concatenation does not?
+
+### 2.9 Comments
+
+As programs get bigger and more complicated, they get more difficult to read. Formal languages are dense, and it is often difficult to look at a piece of code and figure out what it is doing, or why.
+
+For this reason, it is a good idea to add notes to your programs to explain in natural language what the program is doing. These notes are called **comments**, and they start with the # symbol:
+
+compute the percentage of the hour that has elapsed percentage = (minute * 100) / 60 In this case, the comment appears on a line by itself. You can also put comments at the end of a line:
+
+percentage = (minute * 100) / 60 # percentage of an hour Everything from the # to the end of the line is ignored--it has no effect on the program.
+
+Comments are most useful when they document non-obvious features of the code. It is reasonable to assume that the reader can figure out _what_ the code does; it is much more useful to explain _why_.
+
+This comment is redundant with the code and useless:
+
+v = 5 # assign 5 to v This comment contains useful information that is not in the code:
+
+v = 5 # velocity in meters/second. Good variable names can reduce the need for comments, but long names can make complex expressions hard to read, so there is a tradeoff.
+
+### 2.10 Debugging
+
+At this point the syntax error you are most likely to make is an illegal variable name, like class and yield, which are keywords, or odd-job and US$, which contain illegal characters.
+
+If you put a space in a variable name, Python thinks it is two operands without an operator:
+
+>>> bad name = 5 SyntaxError: invalid syntax For syntax errors, the error messages don't help much. The most common messages are SyntaxError: invalid syntax and SyntaxError: invalid token, neither of which is very informative.
+
+The runtime error you are most likely to make is a "use before def;" that is, trying to use a variable before you have assigned a value. This can happen if you spell a variable name wrong:
+
+>>> principal = 327.68 >>> interest = principle * rate NameError: name 'principle' is not defined Variables names are case sensitive, so LaTeX is not the same as latex.
+
+At this point the most likely cause of a semantic error is the order of operations. For example, to evaluate \(\frac{1}{\Sigma\pi}\), you might be tempted to write
+
+>>> 1.0 / 2.0 * pi But the division happens first, so you would get \(\pi/2\), which is not the same thing! There is no way for Python to know what you meant to write, so in this case you don't get an error message; you just get the wrong answer.
+
+### 2.11 Glossary
+
+**value:**: One of the basic units of data, like a number or string, that a program manipulates.
+**type:**: A category of values. The types we have seen so far are integers (type int), floating-point numbers (type float), and strings (type str).
+**integer:**: A type that represents whole numbers.
+**floating-point:**: A type that represents numbers with fractional parts.
+**string:**: A type that represents sequences of characters.
+**variable:**: A name that refers to a value.
+**statement:**: A section of code that represents a command or action. So far, the statements we have seen are assignments and print statements.
+**assignment:**: A statement that assigns a value to a variable.
+**state diagram:**: A graphical representation of a set of variables and the values they refer to.
+**keyword:**: A reserved word that is used by the compiler to parse a program; you cannot use keywords like if, def, and while as variable names.
+**operator:**: A special symbol that represents a simple computation like addition, multiplication, or string concatenation.
+
+## Chapter 2 Variables, expressions and statements
+
+## Chapter 3 Functions
+
+### 3.1 Function calls
+
+In 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 a **function call**:
+
+>>> type(32) <type 'int'> The name of the function is type. The expression in parentheses is called the **argument** of the function. The result, for this function, is the type of the argument.
+
+It is common to say that a function "takes" an argument and "returns" a result. The result is called the **return value**.
+
+### 3.2 Type conversion functions
+
+Python provides built-in functions that convert values from one type to another. The int function takes any value and converts it to an integer, if it can, or complains otherwise:
+
+>>> int('32')
+
+>>> int('Hello') ValueError: invalid literal for int(): Hello
+
+int can convert floating-point values to integers, but it doesn't round off; it chops off the fraction part:
+
+>>> int(3.9999)
+
+3 >>> int(-2.3) -2
+
+float converts integers and strings to floating-point numbers:
+
+#### 3.2.2 The model
+
+The model is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model that is a model 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+
+### 3.4 Composition
+
+So far, we have looked at the elements of a program--variables, expressions, and statements--in isolation, without talking about how to combine them.
+
+One of the most useful features of programming languages is their ability to take small building blocks and **compose** them. For example, the argument of a function can be any kind of expression, including arithmetic operators:
+
+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: the left side of an assignment statement has to be a variable name. Any other expression on the left side is a syntax error (we will see exceptions to this rule later).
+
+>>> minutes = hours * 60 # right >>> hours * 60 = minutes # wrong! SyntaxError: can't assigntoperator
+
+### 3.5 Adding new functions
+
+So far, we have only been using the functions that come with Python, but it is also possible to add new functions. A **function definition** specifies the name of a new function and the sequence of statements that execute when the function is called.
+
+Here is an example:
+
+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 is print_lyrics. The rules for function names are the same as for variable names: letters, numbers and some punctuation marks are legal, but the first character can't be a number. You can't use a keyword as the name of a function, and you should avoid having a variable and a function with the same name.
+
+The empty parentheses after the name indicate that this function doesn't take any arguments.
+
+The first line of the function definition is called the **header**; the rest is called the **body**. The header has to end with a colon and the body has to be indented. By convention, the indentation is always four spaces (see Section 3.14). The body can contain any number of statements.
+
+The strings in the print statements are enclosed in double quotes. Single quotes and double quotes do the same thing; most people use single quotes except in cases like this where a single quote (which is also an apostrophe) appears in the string.
+
+If you type a function definition in interactive mode, the interpreter prints ellipses (...) to let you know that the definition isn't complete:* ```
+
+## Chapter 3 Functions
+
+As you might expect, you have to create a function before you can execute it. In other words, the function definition has to be executed before the first time it is called.
+
+**Exercise 3.1**.: _Move the last line of this program to the top, so the function call appears before the definitions. Run the program and see what error message you get._
+
+**Exercise 3.2**.: _Move the function call back to the bottom and move the definition of print_lyrics after the definition of repeat_lyrics. What happens when you run this program?_
+
+### 3.7 Flow of execution
+
+In order to ensure that a function is defined before its first use, you have to know the order in which statements are executed, which is called the **flow of execution**.
+
+Execution always begins at the first statement of the program. Statements are executed one at a time, in order from top to bottom.
+
+Function definitions do not alter the flow of execution of the program, but remember that statements inside the function are not executed until the function is called.
+
+A function call is like a detour in the flow of execution. Instead of going to the next statement, the flow jumps to the body of the function, executes all the statements there, and then comes back to pick up where it left off.
+
+That sounds simple enough, until you remember that one function can call another. While in the middle of one function, the program might have to execute the statements in another function. But while executing that new function, the program might have to execute yet another function!
+
+Fortunately, Python is good at keeping track of where it is, so each time a function completes, the program picks up where it left off in the function that called it. When it gets to the end of the program, it terminates.
+
+What's the moral of this sordid tale? When you read a program, you don't always want to read from top to bottom. Sometimes it makes more sense if you follow the flow of execution.
+
+### 3.8 Parameters and arguments
+
+Some of the built-in functions we have seen require arguments. For example, when you call math.sin you pass a number as an argument. Some functions take more than one argument: math.pow takes two, the base and the exponent.
+
+Inside the function, the arguments are assigned to variables called **parameters**. Here is an example of a user-defined function that takes an argument:
+
+def print_twice(bruce) :  print bruce ```
+
+This function assigns the argument to a parameter named bruce. When the function is called, it prints the value of the parameter (whatever it is) twice.
+
+This function works with any value that can be printed.
+
+#### 3.9 Variables and parameters are local
+
+When you create a variable inside a function, it is **local**, which means that it only exists inside the function. For example:
+
+```
+defcat_twice(part1,part2): cat=part1+part2 print_twice(cat)
+```
+
+This function takes two arguments, concatenates them, and prints the result twice. Here is an example that uses it:
+
+```
+>>>line1='Bingtiddle' >>>line2='tiddlebang.' >>>cat_twice(line1,line2) Bingtiddletiddlebang. Bingtiddletiddlebang.
+```
+
+When cat_twice terminates, the variable cat is destroyed. If we try to print it, we get an exception:
+
+```
+>>>printcat NameError:name'cat'isnotdefined
+```
+
+#### 3.10 Stack diagrams
+
+To keep track of which variables can be used where, it is sometimes useful to draw a **stack diagram**. Like state diagrams, stack diagrams show the value of each variable, but they also show the function each variable belongs to.
+
+Each function is represented by a **frame**. A frame is a box with the name of a function beside it and the parameters and variables of the function inside it. The stack diagram for the previous example is shown in Figure 3.1.
+
+The frames are arranged in a stack that indicates which function called which, and so on. In this example, print_twice was called by cat_twice, and cat_twice was called by _main_, which is a special name for the topmost frame. When you create a variable outside of any function, it belongs to _main_.
+
+Each parameter refers to the same value as its corresponding argument. So, part1 has the same value as line1, part2 has the same value as line2, and bruce has the same value as cat.
+
+If an error occurs during a function call, Python prints the name of the function, and the name of the function that called it, and the name of the function that called _that_, all the way back to _main_.
+
+For example, if you try to access cat from within print_twice, you get a NameError:
+
+Traceback (inermost last):  File "test.py", line 13, in _main_  cat_twice(line1, line2)  File "test.py", line 5, in cat_twice  print_twice(cat)  File "test.py", line 9, in print_twice  print cat NameError: name 'cat' is not defined This list of functions is called a **traceback**. It tells you what program file the error occurred in, and what line, and what functions were executing at the time. It also shows the line of code that caused the error.
+
+Figure 3.1: Stack diagram.
+
+The order of the functions in the traceback is the same as the order of the frames in the stack diagram. The function that is currently running is at the bottom.
+
+### 3.11 Fruitful functions and void functions
+
+Some of the functions we are using, such as the math functions, yield results; for lack of a better name, I call them **fruitful functions**. Other functions, like print_twice, perform an action but don't return a value. They are called **void functions**.
+
+When you call a fruitful function, you almost always want to do something with the result; for example, you might assign it to a variable or use it as part of an expression:
+
+x = math.cos(radians) golden = (math.sqrt(5) + 1) / 2 When you call a function in interactive mode, Python displays the result:
+
+>>>  math.sqrt(5)
+2.2360679774997898 But in a script, if you call a fruitful function all by itself, the return value is lost forever!
+
+math.sqrt(5)
+
+This script computes the square root of 5, but since it doesn't store or display the result, it is not very useful.
+
+Void functions might display something on the screen or have some other effect, but they don't have a return value. If you try to assign the result to a variable, you get a special value called None.
+
+>>> result = print_twice('Bing') Bing Bing >>> print result None The value None is not the same as the string 'None'. It is a special value that has its own type:
+
+>>> print type(None) <type 'NoneType'> The functions we have written so far are all void. We will start writing fruitful functions in a few chapters.
+
+### 3.12 Why functions?
+
+It may not be clear why it is worth the trouble to divide a program into functions. There are several reasons:
+
+* Creating a new function gives you an opportunity to name a group of statements, which makes your program easier to read and debug.
+* Functions can make a program smaller by eliminating repetitive code. Later, if you make a change, you only have to make it in one place.
+
+* Dividing a long program into functions allows you to debug the parts one at a time and then assemble them into a working whole.
+* Well-designed functions are often useful for many programs. Once you write and debug one, you can reuse it.
+
+### 3.13 Importing with from
+
+Python provides two ways to import modules; we have already seen one:
+
+>>> import math
+
+>>> print math
+
+<module'math' (built-in)>
+
+>>> print math.pi
+
+3.14159265359
+
+If you import math, you get a module object named math. The module object contains constants like pi and functions like sin and exp.
+
+But if you try to access pi directly, you get an error.
+
+>>> print pi
+
+Traceback (most recent call last):
+
+File "<stdin>", line 1, in <module>
+
+NameError: name 'pi' is not defined
+
+As an alternative, you can import an object from a module like this:
+
+>>> from math import pi
+
+Now you can access pi directly, without dot notation.
+
+>>> print pi
+
+3.14159265359
+
+Or you can use the star operator to import _everything_ from the module:
+
+>>> from math import *
+
+>>> cos(pi)
+
+-1.0
+
+The advantage of importing everything from the math module is that your code can be more concise. The disadvantage is that there might be conflicts between names defined in different modules, or between a name from a module and one of your variables.
+
+### 3.14 Debugging
+
+If you are using a text editor to write your scripts, you might run into problems with spaces and tabs. The best way to avoid these problems is to use spaces exclusively (no tabs). Most text editors that know about Python do this by default, but some don't.
+
+Tabs and spaces are usually invisible, which makes them hard to debug, so try to find an editor that manages indentation for you.
+
+Also, don't forget to save your program before you run it. Some development environments do this automatically, but some don't. In that case the program you are looking at in the text editor is not the same as the program you are running.
+
+## Chapter 3 Functions
+
+**stack diagram:**: A graphical representation of a stack of functions, their variables, and the values they refer to.
+**frame:**: A box in a stack diagram that represents a function call. It contains the local variables and parameters of the function.
+**traceback:**: A list of the functions that are executing, printed when an exception occurs.
+
+### 3.16 Exercises
+
+**Exercise 3.3**.: _Python provides a built-in function called_ len _that returns the length of a string, so the value of_ len('allen') _is 5._
+
+_Write a function named_ right_justify _that takes a string named_ s _as a parameter and prints the string with enough leading spaces so that the last letter of the string is in column 70 of the display._
+
+>> right_justify('allen') __
+
+**Exercise 3.4**.: _A function object is a value you can assign to a variable or pass as an argument. For example,_ do_twice _is a function that takes a function object as an argument and calls it twice:_
+
+def do_twice(f): f() f() _Here's an example that uses_ do_twice _to call a function named_ print_spam _twice._
+
+def print_spam(): print'spam'
+
+do_twice(print_spam)
+
+1. _Type this example into a script and test it._
+2. _Modify_ do_twice _so that it takes two arguments, a function object and a value, and calls the function twice, passing the value as an argument._
+3. _Write a more general version of_ print_spam_, called_ print_twice_, that takes a string as a parameter and prints it twice._
+4. _Use the modified version of_ do_twice _to call_ print_twice _twice, passing_'spam' _as an argument._
+5. _Define a new function called_ do_four _that takes a function object and a value and calls the function four times, passing the value as a parameter. There should be only two statements in the body of this function, not four._
+
+_Solution:_ [http://thinkpython.com/code/do_four.py._](http://thinkpython.com/code/do_four.py._)
+
+**Exercise 3.5**.: _This exercise can be done using only the statements and other features we have learned so far._
+
+1. _Write a function that draws a grid like the following:_
+
+## Chapter 3 Functions
+
+## Chapter 4 Case study: interface design
+
+Code examples from this chapter are available from [http://thinkpython.com/code/polygon.py](http://thinkpython.com/code/polygon.py).
+
+### 4.1 TurtleWorld
+
+To accompany this book, I have written a package called Swampy. You can download Swampy from [http://thinkpython.com/swampy](http://thinkpython.com/swampy); follow the instructions there to install Swampy on your system.
+
+A **package** is a collection of modules; one of the modules in Swampy is TurtleWorld, which provides a set of functions for drawing lines by steering turtles around the screen.
+
+If Swampy is installed as a package on your system, you can import TurtleWorld like this:
+
+from swampy.TurtleWorld import *
+
+If you downloaded the Swampy modules but did not install them as a package, you can either work in the directory that contains the Swampy files, or add that directory to Python's search path. Then you can import TurtleWorld like this:
+
+from TurtleWorld import *
+
+The details of the installation process and setting Python's search path depend on your system, so rather than include those details here, I will try to maintain current information for several systems at [http://thinkpython.com/swampy](http://thinkpython.com/swampy)
+
+Create a file named mypolygon.py and type in the following code:
+
+from swampy.TurtleWorld import *
+
+world = TurtleWorld()
+
+bob = Turtle()
+
+print bob
+
+wait_for_user()The first line imports everything from the TurtleWorld module in the swampy package.
+
+The next lines create a TurtleWorld assigned to world and a Turtle assigned to bob. Printing bob yields something like:
+
+<TurtleWorld.Turtle instance at 0xb7bfbf4c> This means that bob refers to an **instance** of a Turtle as defined in module TurtleWorld. In this context, "instance" means a member of a set; this Turtle is one of the set of possible Turtles.
+
+wait_for_user tells TurtleWorld to wait for the user to do something, although in this case there's not much for the user to do except close the window.
+
+TurtleWorld provides several turtle-steering functions: fd and bk for forward and backward, and lt and rt for left and right turns. Also, each Turtle is holding a pen, which is either down or up; if the pen is down, the Turtle leaves a trail when it moves. The functions pu and pd stand for "pen up" and "pen down."
+
+To draw a right angle, add these lines to the program (after creating bob and before calling wait_for_user):
+
+fd(bob, 100) lt(bob) fd(bob, 100)
+
+The first line tells bob to take 100 steps forward. The second line tells him to turn left.
+
+When you run this program, you should see bob move east and then north, leaving two line segments behind.
+
+Now modify the program to draw a square. Don't go on until you've got it working!
+
+### 4.2 Simple repetition
+
+Chances are you wrote something like this (leaving out the code that creates TurtleWorld and waits for the user):
+
+fd(bob, 100) lt(bob) fd(bob, 100) lt(bob) fd(bob, 100) lt(bob, 100)
+
+We can do the same thing more concisely with a for statement. Add this example to mypolygon.py and run it again:
+
+for i in range(4):  print 'Hello!' You should see something like this:Hint: figure out the circumference of the circle and make sure that length * n = circumference. Another hint: if bob is too slow for you, you can speed him up by changing bob.delay, which is the time between moves, in seconds. bob.delay = 0.01 ought to get him moving.
+5. Make a more general version of circle called arc that takes an additional parameter angle, which determines what fraction of a circle to draw. angle is in units of degrees, so when angle=360, arc should draw a complete circle.
+
+### 4.4 Encapsulation
+
+The first exercise asks you to put your square-drawing code into a function definition and then call the function, passing the turtle as a parameter. Here is a solution:
+
+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, which is inside the function definition. The next line, square(bob), is flush with the left margin, so that is the end of both the for loop and the function definition.
+
+Inside the function, t refers to the same turtle bob refers to, so lt(t) has the same effect as lt(bob). So why not call the parameter bob? The idea is that t can be any turtle, not just bob, so you could create a second turtle and pass it as an argument to square:
+
+ray = Turtle() square(ray) Wrapping a piece of code up in a function is called **encapsulation**. One of the benefits of encapsulation is that it attaches a name to the code, which serves as a kind of documentation. Another advantage is that if you re-use the code, it is more concise to call a function twice than to copy and paste the body!
+
+### 4.5 Generalization
+
+The next step is to add a length parameter to square. Here is a solution:
+
+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: in the previous version, the square is always the same size; in this version it can be any size.
+
+The next step is also a generalization. Instead of drawing squares, polygon draws regular polygons with any number of sides. Here is a solution :rule
+
+def polygon(t, n, length):  angle = 360.0 / n  for i in range(n):  fd(t, length)  lt(t, angle)
+
+polygon(bob, 7, 70) This draws a 7-sided polygon with side length 70. If you have more than a few numeric arguments, it is easy to forget what they are, or what order they should be in. It is legal, and sometimes helpful, to include the names of the parameters in the argument list:
+
+polygon(bob, n=7, length=70) These are called **keyword arguments** because they include the parameter names as "keywords" (not to be confused with Python keywords like while and def).
+
+This syntax makes the program more readable. It is also a reminder about how arguments and parameters work: when you call a function, the arguments are assigned to the parameters.
+
+### 4.6 Interface design
+
+The next step is to write circle, which takes a radius, r, as a parameter. Here is a simple solution that uses polygon to draw a 50-sided polygon:
+
+def circle(t, r):  circumference = 2 * math.pi * r  n = 50  length = circumference / n  polygon(t, n, length) The first line computes the circumference of a circle with radius r using the formula \(2\pi r\). Since we use math.pi, we have to import math. By convention, import statements are usually at the beginning of the script.
+
+n is the number of line segments in our approximation of a circle, so length is the length of each segment. Thus, polygon draws a 50-sides polygon that approximates a circle with radius r.
+
+One limitation of this solution is that n is a constant, which means that for very big circles, the line segments are too long, and for small circles, we waste time drawing very small segments. One solution would be to generalize the function by taking n as a parameter. This would give the user (whoever calls circle) more control, but the interface would be less clean.
+
+The **interface** of a function is a summary of how it is used: what are the parameters? What does the function do? And what is the return value? An interface is "clean" if it is "as simple as possible, but not simpler. (Einstein)" In this example, r belongs in the interface because it specifies the circle to be drawn. n is less appropriate because it pertains to the details of _how_ the circle should be rendered.
+
+Rather than clutter up the interface, it is better to choose an appropriate value of n depending on circumference:
+
+def circle(t, r):  circumference = 2 * math.pi * r  n = int(circumference / 3) + 1  length = circumference / n  polygon(t, n, length)
+
+Now the number of segments is (approximately) circumference/3, so the length of each segment is (approximately) 3, which is small enough that the circles look good, but big enough to be efficient, and appropriate for any size circle.
+
+### 4.7 Refactoring
+
+When I wrote circle, I was able to re-use polygon because a many-sided polygon is a good approximation of a circle. But arc is not as cooperative; we can't use polygon or circle to draw an arc.
+
+One alternative is to start with a copy of polygon and transform it into arc. The result might look like this:
+
+def arc(t, r, angle):  arc_length = 2 * math.pi * r * angle / 360  n = int(arc_length / 3) + 1  step_length = arc_length / n  step_angle = float(angle) / n
+
+ for i in range(n):  fd(t, step_length)  lt(t, step_angle)
+
+The second half of this function looks like polygon, but we can't re-use polygon without changing the interface. We could generalize polygon to take an angle as a third argument, but then polygon would no longer be an appropriate name! Instead, let's call the more general function polyline:
+
+def polyline(t, n, length, angle):  for i in range(n):  fd(t, length)  lt(t, angle)
+
+Now we can rewrite polygon and arc to use polyline:
+
+def polygon(t, n, length):  angle = 360.0 / n  polyline(t, n, length, angle)
+
+def arc(t, r, angle):  arc_length = 2 * math.pi * r * angle / 360  n = int(arc_length / 3) + 1  step_length = arc_length / n  step_angle = float(angle) / n  polyline(t, n, step_length, step_angle)Finally, we can rewrite circle to use arc:
+
+def circle(t, r):  arc(t, r, 360) This process--rearranging a program to improve function interfaces and facilitate code re-use--is called **refactoring**. In this case, we noticed that there was similar code in arc and polygon, so we "factored it out" into polyline.
+
+If we had planned ahead, we might have written polyline first and avoided refactoring, but often you don't know enough at the beginning of a project to design all the interfaces. Once you start coding, you understand the problem better. Sometimes refactoring is a sign that you have learned something.
+
+### 4.8 A development plan
+
+A **development plan** is a process for writing programs. The process we used in this case study is "encapsulation and generalization." The steps of this process are:
+
+1. Start by writing a small program with no function definitions.
+2. Once you get the program working, encapsulate it in a function and give it a name.
+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 to avoid retyping (and re-debugging).
+5. Look for opportunities to improve the program by refactoring. For example, if you have similar code in several places, consider factoring it into an appropriately general function.
+
+This process has some drawbacks--we will see alternatives later--but it can be useful if you don't know ahead of time how to divide the program into functions. This approach lets you design as you go along.
+
+### 4.9 docstring
+
+A **docstring** is a string at the beginning of a function that explains the interface ("doc" is short for "documentation"). Here is an example:
+
+def polyline(t, n, length, angle):  """Draws n line segments with the given length and  angle (in degrees) between them. t is a turtle.  """  for i in range(n):  fd(t, length)  lt(t, angle)This is a triple-quoted string, also known as a multiline string because the triple quotes allow the string to span more than one line.
+
+It is terse, but it contains the essential information someone would need to use this function. It explains concisely what the function does (without getting into the details of how it does it). It explains what effect each parameter has on the behavior of the function and what type each parameter should be (if it is not obvious).
+
+Writing this kind of documentation is an important part of interface design. A well-designed interface should be simple to explain; if you are having a hard time explaining one of your functions, that might be a sign that the interface could be improved.
+
+### 4.10 Debugging
+
+An interface is like a contract between a function and a caller. The caller agrees to provide certain parameters and the function agrees to do certain work.
+
+For example, polyline requires four arguments: t has to be a Turtle; n is the number of line segments, so it has to be an integer; length should be a positive number; and angle has to be a number, which is understood to be in degrees.
+
+These requirements are called **preconditions** because they are supposed to be true before the function starts executing. Conversely, conditions at the end of the function are **postconditions**. Postconditions include the intended effect of the function (like drawing line segments) and any side effects (like moving the Turtle or making other changes in the World).
+
+Preconditions are the responsibility of the caller. If the caller violates a (properly documented!) precondition and the function doesn't work correctly, the bug is in the caller, not the function.
+
+### 4.11 Glossary
+
+**instance:**: A member of a set. The TurtleWorld in this chapter is a member of the set of TurtleWorlds.
+**loop:**: A part of a program that can execute repeatedly.
+**encapsulation:**: The process of transforming a sequence of statements into a function definition.
+**generalization:**: The process of replacing something unnecessarily specific (like a number) with something appropriately general (like a variable or parameter).
+**keyword argument:**: An argument that includes the name of the parameter as a "keyword."
+**interface:**: A description of how to use a function, including the name and descriptions of the arguments and return value.
+**refactoring:**: The process of modifying a working program to improve function interfaces and other qualities of the code.
+
+#### 4.1.1 Introduction
+
+The _true_ of a string is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a 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that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is a string that is that is a
+
+**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 a minimal number of basic elements and then write functions that draw letters of the alphabet._
+
+_You should write one function for each letter, with names_ draw_a,_ draw_b, _etc._, and put your functions in a file named_ letters.py_. You can download a "turtle typewriter" from_ [http://thinkpython.com/code/typewriter.py](http://thinkpython.com/code/typewriter.py) _to help you test your code._
+
+_Solution:_ [http://thinkpython.com/code/letters.py_](http://thinkpython.com/code/letters.py_), also requires_ [http://thinkpython.com/code/polygon.py_](http://thinkpython.com/code/polygon.py_).
+
+**Exercise 4.5**.: _Read about spirals at_ [http://en.wikipedia.org/wiki/Spiral](http://en.wikipedia.org/wiki/Spiral); then write a program that draws an Archimedian spiral (or one of the other kinds). Solution:_ [http://thinkpython.com/code/spiral.py_](http://thinkpython.com/code/spiral.py_).
+
+## Chapter 5 Conditionals and recursion
+
+### 5.1 Modulus operator
+
+The **modulus operator** works on integers and yields the remainder when the first operand is divided by the second. In Python, the modulus operator is a percent sign (%). The syntax is the same as for other operators:
+
+>>> quotient = 7 / 3
+
+>>> print quotient
+
+2
+
+>>> remainder = 7 % 3
+
+>>> print remainder
+
+1
+
+So 7 divided by 3 is 2 with 1 left over.
+
+The modulus operator turns out to be surprisingly useful. For example, you can check whether one number is divisible by another--if x % y is zero, then x is divisible by y.
+
+Also, you can extract the right-most digit or digits from a number. For example, x % 10 yields the right-most digit of x (in base 10). Similarly x % 100 yields the last two digits.
+
+### 5.2 Boolean expressions
+
+A **boolean expression** is an expression that is either true or false. The following examples use the operator --, which compares two operands and produces True if they are equal and False otherwise:
+
+>>> 5 -- 5 True
+
+>>> 5 -- 6 False
+
+True and False are special values that belong to the type bool; they are not strings:
+
+>>> type(True)
+
+<type 'bool'>
+
+>>> type(False)
+
+<type 'bool'>The -- operator is one of the **relational operators**; the others are:
+
+ x |= y # x is not equal to y  x > y # x is greater than y  x < y # x is less than y  x >= y # x is greater than or equal to y  x <= y # x is less than or equal to y
+
+Although these operations are probably familiar to you, the Python symbols are different from the mathematical symbols. A common error is to use a single equal sign (-) instead of a double equal sign (-). Remember that - is an assignment operator and -- is a relational operator. There is no such thing as - < or ->.
+
+### Logical operators
+
+There are three **logical operators**: and, or, and not. The semantics (meaning) of these operators is similar to their meaning in English. For example, x > 0 and x < 10 is true only if x is greater than 0 _and_ less than 10.
+
+m%2 == 0 or n%3 == 0 is true if _either_ of the conditions is true, that is, if the number is divisible by 2 _or_ 3.
+
+Finally, the not operator negates a boolean expression, so not (x > y) is true if x > y is false, that is, if x is less than or equal to y.
+
+Strictly speaking, the operands of the logical operators should be boolean expressions, but Python is not very strict. Any nonzero number is interpreted as "true."
+
+>>> 17 and True True
+
+This flexibility can be useful, but there are some subtleties to it that might be confusing. You might want to avoid it (unless you know what you are doing).
+
+### Conditional execution
+
+In order to write useful programs, we almost always need the ability to check conditions and change the behavior of the program accordingly. **Conditional statements** give us this ability. The simplest form is the if statement:
+
+if x > 0:  print 'x is positive' The boolean expression after if is called the **condition**. If it is true, then the indented statement gets executed. If not, nothing happens.
+
+if statements have the same structure as function definitions: a header followed by an indented body. Statements like this are called **compound statements**.
+
+There is no limit on the number of statements that can appear in the body, but there has to be at least one. Occasionally, it is useful to have a body with no statements (usually as a place keeper for code you haven't written yet). In that case, you can use the pass statement, which does nothing.
+
+if x < 0:  pass # need to handle negative values!
+
+### Alternative execution
+
+A second form of the if statement is **alternative execution**, in which there are two possibilities and the condition determines which one gets executed. The syntax looks like this:
+
+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 displays a message to that effect. If the condition is false, the second set of statements is executed. Since the condition must be true or false, exactly one of the alternatives will be executed. The alternatives are called **branches**, because they are branches in the flow of execution.
+
+### Chained conditionals
+
+Sometimes there are more than two possibilities and we need more than two branches. One way to express a computation like that is a **chained 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' elif is an abbreviation of "else if." Again, exactly one branch will be executed. There is no limit on the number of elif statements. If there is an else clause, it has to be at the end, but there doesn't have to be one.
+
+if choice == 'a':  draw_a() elif choice == 'b':  draw_b() elif choice == 'c':  draw_c() Each condition is checked in order. If the first is false, the next is checked, and so on. If one of them is true, the corresponding branch executes, and the statement ends. Even if more than one condition is true, only the first true branch executes.
+
+### Nested conditionals
+
+One conditional can also be nested within another. We could have written the trichotomy example like this:
+
+if x == y:  print 'x and y are equal' else:  if x < y:
+
+## Chapter 5Conditions and recursion
+
+### 5.1 Introduction
+
+The _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the 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of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ of the _containment_ _containment_ of the _The countdown that got n=1 returns.
+
+The countdown that got n=2 returns.
+
+The countdown that got n=3 returns.
+
+And then you're back in __main__. So, the total output looks like this:
+
+3
+2
+1
+
+Blastoff!
+
+A function that calls itself is **recursive**; the process is called **recursion**.
+
+As another example, we can write a function that prints a string n times.
+
+def print_n(s, n):  if n <= 0:  return  print s  print_n(s, n-1)
+
+If n <= 0 the return statement exits the function. The flow of execution immediately returns to the caller, and the remaining lines of the function are not executed.
+
+The rest of the function is similar to countdown: if n is greater than 0, it displays s and then calls itself to display s \(n-1\) additional times. So the number of lines of output is 1 + (n - 1), which adds up to n.
+
+For simple examples like this, it is probably easier to use a for loop. But we will see examples later that are hard to write with a for loop and easy to write with recursion, so it is good to start early.
+
+### 5.9 Stack diagrams for recursive functions
+
+In Section 3.10, we used a stack diagram to represent the state of a program during a function call. The same kind of diagram can help interpret a recursive function.
+
+Every time a function gets called, Python creates a new function frame, which contains the function's local variables and parameters. For a recursive function, there might be more than one frame on the stack at the same time.
+
+Figure 5.1 shows a stack diagram for countdown called with n = 3.
+
+As usual, the top of the stack is the frame for __main__. It is empty because we did not create any variables in __main__ or pass any arguments to it.
+
+The four countdown frames have different values for the parameter n. The bottom of the stack, where n=0, is called the **base case**. It does not make a recursive call, so there are no more frames.
+
+**Exercise 5.1**.: _Draw a stack diagram for print_n called with s = 'Hello' and n=2._
+
+**Exercise 5.2**.: _Write a function called do_n that takes a function object and a number, n, as arguments, and that calls the given function n times._
+
+### 5.10 Infinite recursion
+
+If a recursion never reaches a base case, it goes on making recursive calls forever, and the program never terminates. This is known as **infinite recursion**, and it is generally not a good idea. Here is a minimal program with an infinite recursion:
+
+def recurse():  recurse() In most programming environments, a program with infinite recursion does not really run forever. Python reports an error message when the maximum recursion depth is reached:
+
+ File "<stdin>", line 2, in recurse  File "<stdin>", line 2, in recurse  File "<stdin>", line 2, in recurse..  File "<stdin>", line 2, in recurse RuntimeError: Maximum recursion depth exceeded This traceback is a little bigger than the one we saw in the previous chapter. When the error occurs, there are 1000 recurse frames on the stack!
+
+### 5.11 Keyboard input
+
+The programs we have written so far are a bit rude in the sense that they accept no input from the user. They just do the same thing every time.
+
+Python 2 provides a built-in function called raw_input that gets input from the keyboard. In Python 3, it is called input. When this function is called, the program stops and waits for the user to type something. When the user presses Return or Enter, the program resumes and raw_input returns what the user typed as a string.
+
+>>> text = raw_input() What are you waiting for? >>> print text What are you waiting for?
+
+Figure 5.1: Stack diagram.
+
+Before getting input from the user, it is a good idea to print a prompt telling the user what to input. raw_input can take a prompt as an argument:
+
+>>> name = raw_input('What...is your name?\n') What...is your name? Arthur, King of the Britons! >>> print name Arthur, King of the Britons!
+
+The sequence \n at the end of the prompt represents a **newline**, which is a special character that causes a line break. That's why the user's input appears below the prompt.
+
+If you expect the user to type an integer, you can try to convert the return value to int:
+
+>>> 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)
+17 But if the user types something other than a string of digits, 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() with base 10 We will see how to handle this kind of error later.
+
+### Debugging
+
+The traceback Python displays when an error occurs contains a lot of information, but it can be overwhelming, especially when there are many frames on the stack. The most useful parts are usually:
+
+* What kind of error it was, and
+* Where it occurred.
+
+Syntax errors are usually easy to find, but there are a few gotchas. Whitespace errors can be tricky because spaces and tabs are invisible and we are used to ignoring them.
+
+>>> x = 5 >>> y = 6  File "<stdin>", line 1  y = 6 ^
+
+IndentationError: unexpected indent In this example, the problem is that the second line is indented by one space. But the error message points to y, which is misleading. In general, error messages indicate where the problem was discovered, but the actual error might be earlier in the code, sometimes on a previous line.
+
+The same is true of runtime errors.
+
+Suppose you are trying to compute a signal-to-noise ratio in decibels. The formula is \(SNR_{db}=10\log_{10}(P_{signal}/P_{noise})\). In Python, you might write something like this:
+
+```
+importmathsignal_power=9 noise_power=10 ratio=signal_power/noise_power decibels=10*math.log10(ratio) printdecibels
+```
+
+But when you run it in Python 2, you get an error message.
+
+```
+Traceback(mostrecentcalllast): File"snr.py",line5,in? decibels=10*math.log10(ratio) ValueError:mathdomainerror
+```
+
+The 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 and noise power with floating-point values.
+
+In general, error messages tell you where the problem was discovered, but that is often not where it was caused.
+
+In Python 3, this example does not cause an error; the division operator performs floating-point division even with integer operands.
+
+### 5.13 Glossary
+
+**modulus operator**: An operator, denoted with a percent sign (%), that works on integers and yields the remainder when one number is divided by another.
+**boolean expression**: An expression whose value is either True or False.
+**relational operator**: One of the operators that compares its operands: --,!-,!-,!-, and!-.
+**logical operator**: One of the operators that combines boolean expressions: and, or, and not.
+**conditional statement**: A statement that controls the flow of execution depending on some condition.
+**condition**: The boolean expression in a conditional statement that determines which branch is executed.
+**compound statement**: A statement that consists of a header and a body. The header ends with a colon (:). The body is indented relative to the header.
+**branch**: One of the alternative sequences of statements in a conditional statement.
+**chained conditional**: A conditional statement with a series of alternative branches.
+
+**nested conditional:**: A conditional statement that appears in one of the branches of another conditional statement.
+**recursion:**: The process of calling the function that is currently executing.
+**base case:**: A conditional branch in a recursive function that does not make a recursive call.
+**infinite recursion:**: A recursion that doesn't have a base case, or never reaches it. Eventually, an infinite recursion causes a runtime error.
+
+### 5.14 Exercises
+
+**Exercise 5.3**.: _Fermat's Last Theorem says that there are no positive integers \(a\), \(b\), and \(c\) such that_
+
+\[a^{n}+b^{n}=c^{n}\]
+
+_for any values of \(n\) greater than 2._
+
+1. _Write a function named_ check_fermat _that takes four parameters_--a, b, c _and_ n_--and that checks to see if Fermat's theorem holds. If_ \(n\) _is greater than 2 and it turns out to be true that_ \[a^{n}+b^{n}=c^{n}\] _the program should print, "Holy smokes, Fermat was wrong!" Otherwise the program should print, "No, that doesn't work."_
+2. _Write a function that prompts the user to input values for_ a, b, c _and_ n_, converts them to integers, and uses_ check_fermat _to check whether they violate Fermat's theorem._
+
+**Exercise 5.4**.: _If you are given three sticks, you may or may not be able to arrange them in a triangle. For example, if one of the sticks is 12 inches long and the other two are one inch long, it is clear that you will not be able to get the short sticks to meet in the middle. For any three lengths, there is a simple test to see if it is possible to form a triangle:_
+
+_If any of the three lengths is greater than the sum of the other two, then you cannot form a triangle. Otherwise, you can. (If the sum of two lengths equals the third, they form what is called a "degenerate" triangle.)_
+
+1. _Write a function named_ is_triangle _that takes three integers as arguments, and that prints either "Yes" or "No," depending on whether you can or cannot form a triangle from sticks with the given lengths._
+2. _Write a function that prompts the user to input three stick lengths, converts them to integers, and uses_ is_triangle _to check whether sticks with the given lengths can form a triangle._
+
+The following exercises use TurtleWorld from Chapter 4:
+
+**Exercise 5.5**.: _Read the following function and see if you can figure out what it does. Then run it (see the examples in Chapter 4)._
+
+## Chapter 5 Conditions and recursion
+
+## Chapter 6 Fruitful functions
+
+### 6.1 Return values
+
+Some of the built-in functions we have used, such as the math functions, produce results. Calling the function generates a value, which we usually assign to a variable or use as part of an expression.
+
+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 return value is None.
+
+In this chapter, we are (finally) going to write fruitful functions. The first example is area, which returns the area of a circle with the given radius:
+
+def area(radius):  temp = math.pi * radius**2  return temp We have seen the return statement before, but in a fruitful function the return statement includes an expression. This statement means: "Return immediately from this function and use the following expression as a return value." The expression can be arbitrarily complicated, so we could have written this function more concisely:
+
+def area(radius):  return math.pi * radius**2 On the other hand, **temporary variables** like temp often make debugging easier.
+
+Sometimes it is useful to have multiple return statements, one in each branch of a conditional:
+
+def absolute_value(x):  if x < 0:  return -x  else:  return xSince these return statements are in an alternative conditional, only one will be executed.
+
+As soon as a return statement executes, the function terminates without executing any subsequent statements. Code that appears after a return statement, or any other place the flow of execution can never reach, is called **dead code**.
+
+In a fruitful function, it is a good idea to ensure that every possible path through the program hits a return statement. For example:
+
+def absolute_value(x) :  if x < 0:  return -x  if x > 0:  return x This function is incorrect because if x happens to be 0, neither condition is true, and the function ends without hitting a return statement. If the flow of execution gets to the end of a function, the return value is None, which is not the absolute value of 0.
+
+>> print absolute_value(0) None By the way, Python provides a built-in function called abs that computes absolute values.
+
+**Exercise 6.1**.: _Write a_ compare _function that returns_ 1 _if_ x > y, 0 _if_ x == y, _and_ -1 _if_ x < y.
+
+### 6.2 Incremental development
+
+As you write larger functions, you might find yourself spending more time debugging.
+
+To deal with increasingly complex programs, you might want to try a process called **incremental development**. The goal of incremental development is to avoid long debugging sessions by adding and testing only a small amount of code at a time.
+
+As an example, suppose you want to find the distance between two points, given by the coordinates \((x_{1},y_{1})\) and \((x_{2},y_{2})\). By the Pythagorean theorem, the distance is:
+
+\[\text{distance}=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\]
+
+The first step is to consider what a distance function should look like in Python. In other words, what are the inputs (parameters) and what is the output (return value)?
+
+In this case, the inputs are two points, which you can represent using four numbers. The return value is the distance, which is a floating-point value.
+
+Already you can write an outline of the function:
+
+def distance(x1, y1, x2, y2) :  return 0.0 Obviously, this version doesn't compute distances; it always returns zero. But it is syntactically correct, and it runs, which means that you can test it before you make it more complicated.
+
+To test the new function, call it with sample arguments:* ```
+### Incremental development
+``` >>>distance(1,2,4,6) ```
+I chose these values so that the horizontal distance is 3 and the vertical distance is 4; that way, the result is 5 (the hypotenuse of a 3-4-5 triangle). When testing a function, it is useful to know the right answer.
+
+At this point we have confirmed that the function is syntactically correct, and we can start adding code to the body. A reasonable next step is to find the differences \(x_{2}-x_{1}\) and \(y_{2}-y_{1}\). The next version stores those values in temporary variables and prints them.
+``` defdistance(x1,y1,x2,y2): dx=x2-x1 dy=y2-y1 print'dxis',dx print'dyis',dy return0.0 ```
+If the function is working, it should display 'dxis3' and 'dyis4'. If so, we know that the function is getting the right arguments and performing the first computation correctly. If not, there are only a few lines to check.
+
+Next we compute the sum of squares of dx and dy:
+``` defdistance(x1,y1,x2,y2): dx=x2-x1 dy=y2-y1 dsquared=dx**2+dy**2 print'dsquaredis',dsquared return0.0 ```
+Again, you would run the program at this stage and check the output (which should be 25). Finally, you can use math.sqrt to compute and return the result:
+``` defdistance(x1,y1,x2,y2): dx=x2-x1 dy=y2-y1 dsquared=dx**2+dy**2 result=math.sqrt(dsquared) returnresult ```
+
+If that works correctly, you are done. Otherwise, you might want to print the value of result before the return 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 the program but is not part of the final 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, incremental development can save you a lot of debugging time.
+
+The key aspects of the process are:
+
+1. Start with a working program and make small incremental changes. At any point, if there is an error, you should have a good idea where it is.
+
+## Chapter 6 Frutiful functions
+
+### 6.1 Introduction
+
+The Frutiful functions are a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a 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function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a functionIt is common to give boolean functions names that sound like yes/no questions; is_divisible returns either True or False to indicate whether x is divisible by y.
+
+Here is an example:
+
+>>> is_divisible(6, 4) False >>> is_divisible(6, 3) True The result of the -- operator is a boolean, so we can write the function more concisely by returning it directly:
+
+def is_divisible(x, y):  return x % y == 0 Boolean functions are often used in conditional statements:
+
+if is_divisible(x, y):  print 'x isdivisible by y' It might be tempting to write something like:
+
+if is_divisible(x, y) == True:  print 'x isdivisible by y' But the extra comparison is unnecessary.
+
+**Exercise 6.3**.: _Write a function is_between(x, y, z) that returns_ True _if_ \(x\leq y\leq z\) _or_ False _otherwise._
+
+### 6.5 More recursion
+
+We have only covered a small subset of Python, but you might be interested to know that this subset is a _complete_ programming language, which means that anything that can be computed can be expressed in this language. Any program ever written could be rewritten using only the language features you have learned so far (actually, you would need a few commands to control devices like the keyboard, mouse, disks, etc., but that's all).
+
+Proving that claim is a nontrivial exercise first accomplished by Alan Turing, one of the first computer scientists (some would argue that he was a mathematician, but a lot of early computer scientists started as mathematicians). Accordingly, it is known as the Turing Thesis. For a more complete (and accurate) discussion of the Turing Thesis, I recommend Michael Sipser's book _Introduction to the Theory of Computation_.
+
+To give you an idea of what you can do with the tools you have learned so far, we'll evaluate a few recursively defined mathematical functions. A recursive definition is similar to a circular definition, in the sense that the definition contains a reference to the thing being defined. A truly circular definition is not very useful:
+
+**vorpal:** An adjective used to describe something that is vorpal.
+
+If you saw that definition in the dictionary, you might be annoyed. On the other hand, if you looked up the definition of the factorial function, denoted with the symbol!, you might get something like this:
+
+\[0! =1\] \[n! =n(n-1)!\]This definition says that the factorial of 0 is 1, and the factorial of any other value, \(n\), is \(n\) multiplied by the factorial of \(n-1\).
+
+So 3! is 3 times 2!, which is 2 times 1!, which is 1 times 0!. Putting it all together, 3! equals 3 times 2 times 1 times 1, which is 6.
+
+If you can write a recursive definition of something, you can usually write a Python program to evaluate it. The first step is to decide what the parameters should be. In this case it should be clear that factorial takes an integer:
+
+def factorial(n):
+
+def factorial(n):
+
+if n == 0:
+
+return 1
+
+Otherwise, and this is the interesting part, we have to make a recursive call to find the factorial of \(n-1\) and then multiply it by \(n\):
+
+def factorial(n):
+
+if n == 0:
+
+return 1
+
+else:
+
+recurse = factorial(n-1)
+
+result = n * recurse
+
+return result
+
+The flow of execution for this program is similar to the flow of countdown in Section 5.8. If we call factorial with the value 3:
+
+Since 3 is not 0, we take the second branch and calculate the factorial of n-1...
+
+Since 2 is not 0, we take the second branch and calculate the factorial of n-1...
+
+Since 1 is not 0, we take the second branch and calculate the factorial of n-1...
+
+Since 0 _is_ 0, we take the first branch and return 1 without
+
+making any more recursive calls.
+
+The return value (1) is multiplied by \(n\), which is 1, and the result is returned.
+
+The return value (1) is multiplied by \(n\), which is 2, and the result is returned.
+
+The return value (2) is multiplied by \(n\), which is 3, and the result, 6, becomes the return value of the function call that started the whole process.
+
+Figure 6.1 shows what the stack diagram looks like for this sequence of function calls.
+
+The return values are shown being passed back up the stack. In each frame, the return value is the value of result, which is the product of n and recurse.
+
+In the last frame, the local variables recurse and result do not exist, because the branch that creates them does not execute.
+
+### 6.6 Leap of faith
+
+Following the flow of execution is one way to read programs, but it can quickly become labyrinthine. An alternative is what I call the "leap of faith." When you come to a function call, instead of following the flow of execution, you _assume_ that the function works correctly and returns the right result.
+
+In fact, you are already practicing this leap of faith when you use built-in functions. When you call math.cos or math.exp, you don't examine the bodies of those functions. You just assume that they work because the people who wrote the built-in functions were good programmers.
+
+The same is true when you call one of your own functions. For example, in Section 6.4, we wrote a function called is_divisible that determines whether one number is divisible by another. Once we have convinced ourselves that this function is correct--by examining the code and testing--we can use the function without looking at the body again.
+
+The same is true of recursive programs. When you get to the recursive call, instead of following the flow of execution, you should assume that the recursive call works (yields the correct result) and then ask yourself, "Assuming that I can find the factorial of \(n-1\), can I compute the factorial of \(n\)?" In this case, it is clear that you can, by multiplying by \(n\).
+
+Of course, it's a bit strange to assume that the function works correctly when you haven't finished writing it, but that's why it's called a leap of faith!
+
+### 6.7 One more example
+
+After factorial, the most common example of a recursively defined mathematical function is fibonacci, which has the following definition (see [http://en.wikipedia.org/wiki/Fibonacci_number](http://en.wikipedia.org/wiki/Fibonacci_number)):
+
+\[\text{fibonacci}(0) =0\] \[\text{fibonacci}(1) =1\] \[\text{fibonacci}(n) =\text{fibonacci}(n-1)+\text{fibonacci}(n-2)\]
+
+Translated into Python, it looks like this:
+
+Figure 6.1: Stack diagram.
+
+## Chapter 6 Fruitful functions
+
+### 6.1 The main idea of the Fruitful function
+
+The Fruitful function is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that is a function that isIf we get past both checks, then we know that \(n\) is positive or zero, so we can prove that the recursion terminates.
+
+This program demonstrates a pattern sometimes called a **guardian**. The first two conditionals act as guardians, protecting the code that follows from values that might cause an error. The guardians make it possible to prove the correctness of the code.
+
+In Section 11.3 we will see a more flexible alternative to printing an error message: raising an exception.
+
+### 6.9 Debugging
+
+Breaking a large program into smaller functions creates natural checkpoints for debugging. If a function is not working, there are three possibilities to consider:
+
+* There is something wrong with the arguments the function is getting; a precondition is violated.
+* There is something wrong with the function; a postcondition is violated.
+* There is something wrong with the return value or the way it is being used.
+
+To rule out the first possibility, you can add a print statement at the beginning of the function and display the values of the parameters (and maybe their types). Or you can write code that checks the preconditions explicitly.
+
+If the parameters look good, add a print statement before each return statement that displays the return value. If possible, check the result by hand. Consider calling the function with values that make it easy to check the result (as in Section 6.2).
+
+If the function seems to be working, look at the function call to make sure the return value is being used correctly (or used at all!).
+
+Adding print statements at the beginning and end of a function can help make the flow of execution more visible. For example, here is a version of factorial with print statements:
+
+``` deffactorial(n): space=''*(4*n) printspace,'factorial',n ifn==0: printspace,'returning1' return1 else: recurse=factorial(n-1) result=n*recurse printspace,'returning',result returnresult space is a string of space characters that controls the indentation of the output. Here is the result of factorial(5) :
+
+## Chapter 6 Fruitful functions
+
+* ```
+
+**Algorithm 6** _The \(GCD\) of two numbers is based on the observation that if \(r\) is the remainder when \(a\) is divided by \(b\), then \(gcd(a,b)=gcd(b,r)\). As a base case, we can use \(gcd(a,0)=a\)._
+
+## Chapter 6 Fruitful functions
+
+## Chapter 7 Iteration
+
+### 7.1 Multiple assignment
+
+As you may have discovered, it is legal to make more than one assignment to the same variable. A new assignment makes an existing variable refer to a new value (and stop referring to the old value).
+
+bruce = 5 print bruce, bruce = 7 print bruce The output of this program is 5 7, because the first time bruce is printed, its value is 5, and the second time, its value is 7. The comma at the end of the first print statement suppresses the newline, which is why both outputs appear on the same line.
+
+Figure 7.1 shows what **multiple assignment** looks like in a state diagram.
+
+With multiple assignment it is especially important to distinguish between an assignment operation and a statement of equality. Because Python uses the equal sign (-) for assignment, it is tempting to interpret a statement like a = b as a statement of equality. It is not!
+
+First, equality is a symmetric relation and assignment is not. For example, in mathematics, if \(a=7\) then \(7=a\). But in Python, the statement a = 7 is legal and 7 - a is not.
+
+Furthermore, in mathematics, a statement of equality is either true or false, for all time. If \(a=b\) now, then \(a\) will always equal \(b\). In Python, an assignment statement can make two variables equal, but they don't have to stay that way:
+
+a = 5 b - a # a and b are now equal a = 3 # a and b are no longer equal The third line changes the value of a but does not change the value of b, so they are no longer equal.
+
+Although multiple assignment is frequently helpful, you should use it with caution. If the values of variables change frequently, it can make the code difficult to read and debug.
+
+### 7.2 Updating variables
+
+One of the most common forms of multiple assignment is an **update**, where the new value of the variable depends on the old.
+
+x = x+1 This means "get the current value of x, add one, and then update x with the new value."
+
+If you try to update a variable that doesn't exist, you get an error, because Python evaluates the right side before it assigns a value to x:
+
+>> x = x+1 NameError: name 'x' is not defined Before you can update a variable, you have to **initialize** it, usually with a simple assignment:
+
+>> x = 0 >> x = x+1 Updating a variable by adding 1 is called an **increment**; subtracting 1 is called a **decrement**.
+
+### 7.3 The while statement
+
+Computers are often used to automate repetitive tasks. Repeating identical or similar tasks without making errors is something that computers do well 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 language features to make it easier. One is the for statement we saw in Section 4.2. We'll get back to that later.
+
+Another is the while statement. Here is a version of countdown that uses a while statement:
+
+def countdown(n):  while n > 0:  print n  n = n-1  print 'Blastoff!' You can almost read the while statement as if it were English. It means, "While n is greater than 0, display the value of n and then reduce the value of n by 1. When you get to 0, display the word Blastoff!" More formally, here is the flow of execution for a while statement:
+
+1. Evaluate the condition, yielding True or False.
+
+Figure 7.1: State diagram.
+
+2. If the condition is false, exit the while statement and continue execution at the next statement.
+3. If the condition is true, execute the body and then go back to step 1.
+
+This type of flow is called a **loop** because the third step loops back around to the top.
+
+The body of the loop should change the value of one or more variables so that eventually the condition becomes false and the loop terminates. Otherwise the loop will repeat forever, which is called an **infinite loop**. An endless source of amusement for computer scientists is the observation that the directions on shampoo, "Lather, rinse, repeat," are an infinite loop.
+
+In the case of countdown, we can prove that the loop terminates because we know that the value of n is finite, and we can see that the value of n gets smaller each time through the loop, so eventually we have to get to 0. In other cases, it is not so easy to tell:
+
+def sequence(n):  while n!= 1:  print n,  if n%2 == 0: # n is even  n = n/2  else: # n is odd  n = n*3+1 The condition for this loop is n!= 1, so the loop will continue until n is 1, which makes the condition false.
+
+Each time through the loop, the program outputs the value of n and then checks whether it is even or odd. 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, if the argument passed to sequence is 3, the resulting sequence is 3, 10, 5, 16, 8, 4, 2, 1.
+
+Since n sometimes increases and sometimes decreases, there is no obvious proof that n will ever reach 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 time through the loop until it reaches 1. The previous example ends with such a sequence, starting with 16.
+
+The hard question is whether we can prove that this program terminates for _all positive values_ of n. So far, no one has been able to prove it _or_ disprove it! (See [http://en.wikipedia.org/wiki/Collatz_conjecture](http://en.wikipedia.org/wiki/Collatz_conjecture).)
+
+**Exercise 7.1**.: _Rewrite the function print_n from Section 5.8 using iteration instead of recursion_.
+
+### break
+
+Sometimes you don't know it's time to end a loop until you get half way through the body. In that case you can use the break statement to jump out of the loop.
+
+For example, suppose you want to take input from the user until they type done. You could write:
+
+## Chapter 7 Iteration
+
+### 7.1 Introduction
+
+The main goal of this thesis is to develop a new method for computing a set of functions that are* ```
+``` >>>x=y >>>y=(x+a/x)/2 >>>printy 2.00001024003>>x=y >>>y=(x+a/x)/2 >>>printy 2.0000000003
+```
+
+In general we don't know ahead of time how many steps it takes to get to the right answer, but we know when we get there because the estimate stops changing:
+
+```
+>>>x=y >>>y=(x+a/x)/2 >>>printy 2.0 >>>x=y >>>y=(x+a/x)/2 >>>printy 2.0
+```
+
+When y ==x, we can stop. Here is a loop that starts with an initial estimate, x, and improves it until it stops changing:
+
+```
+whileTrue:  printx  y=(x+a/x)/2  ify==x:  break x=y
+```
+
+For most values of a this works fine, but in general it is dangerous to test float equality. Floating-point values are only approximately right: most rational numbers, like \(1/3\), and irrational numbers, like \(\sqrt{2}\), can't be represented exactly with a float.
+
+Rather than checking whether x and y are exactly equal, it is safer to use the built-in function abs to compute the absolute value, or magnitude, of the difference between them:
+
+```
+ifabs(y-x)<epsilon:  break
+```
+
+Where epsilon has a value like 0.0000001 that determines how close is close enough.
+
+**Exercise 7.2**.: _Encapsulate this loop in a function called square_root that takes a as a parameter, chooses a reasonable value of x, and returns an estimate of the square root of a._
+
+### 7.6 Algorithms
+
+Newton's method is an example of an **algorithm**: it is a mechanical process for solving a category of problems (in this case, 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 multiplication table. In effect, you memorized 100 specific solutions. That kind of knowledge is not algorithmic.
+
+## Chapter 7 Iteration
+
+### 7.1 Introduction
+
+The problem of finding a set of axioms is to find a set of axioms that are not necessarily satisfied. The axioms are axioms that are not satisfied, and the axioms are axioms that are not satisfied. The axioms are axioms that are not satisfied, and the axioms are axioms that are not satisfied. The axioms are axioms that are not satisfied, and the axioms are axioms that are axioms that are not satisfied. The axioms are axioms that are axioms that are not satisfied, and the axioms are axioms that are axioms that are not satisfied. The axioms are axioms that are axioms that are not satisfied, and the axioms are axioms that are axioms that are not satisfied. The axioms are axioms that are axioms that are axioms that are not satisfied, and the axioms are axioms that are axioms that are axioms that are not satisfied. The axioms are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms that are axioms 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+
+**update:**: An assignment where the new value of the variable depends on the old.
+**initialization:**: An assignment that gives an initial value to a variable that will be updated.
+**increment:**: An update that increases the value of a variable (often by one).
+**decrement:**: An update that decreases the value of a variable.
+**iteration:**: Repeated execution of a set of statements using either a recursive function call or a loop.
+**infinite loop:**: A loop in which the terminating condition is never satisfied.
+
+### 7.9 Exercises
+
+**Exercise 7.3**.: _To test the square root algorithm in this chapter, you could compare it with_ math.sqrt_. Write a function named_ test_square_root _that prints a table like this:_
+
+1.0 1.0 1.0 0.0
+2.0 1.41421356237 1.41421356237 2.22044604925e-16
+3.0 1.73205080757 1.73205080757 0.0
+4.0 2.0 2.0 0.0
+5.0 2.2360679775 2.2360679775 0.0
+6.0 2.44948974278 2.44948974278 0.0
+7.0 2.64575131106 2.64575131106 0.0
+8.0 2.82842712475 2.82842712475 4.4408920985e-16
+9.0 3.0 3.0 0.0
+
+_The first column is a number, a; the second column is the square root of a computed with the function from Section 7.5; the third column is the square root computed by_ math.sqrt_; the fourth column is the absolute value of the difference between the two estimates._
+
+**Exercise 7.4**.: _The built-in function_ eval _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)')
+
+<type 'float'>
+
+_Write a function called_ eval_loop _that iteratively prompts the user, takes the resulting input and evaluates it using_ eval_, and prints the result._
+
+_It should continue until the user enters 'done', and then return the value of the last expression it evaluated._
+
+**Exercise 7.5**.: _The mathematician Srinivasa Ramanujan found an infinite series that can be used to generate a numerical approximation of \(1/\pi\):_
+
+\[\frac{1}{\pi}=\frac{2\sqrt{2}}{9801}\sum_{k=0}^{\infty}\frac{(4k)!(1103+26390k )}{(k!)^{4}396^{4k}}\]
+
+## Chapter 7 Iteration
+
+## Chapter 8 Strings
+
+### 8.1 A string is a sequence
+
+A string is a **sequence** of characters. You can access the characters one at a time with the bracket operator:
+
+>>> fruit = 'banana' >>> letter = fruit[1]
+
+The second statement selects character number 1 from fruit and assigns it to letter.
+
+The expression in brackets is called an **index**. The index indicates which character in the sequence you want (hence the name).
+
+But you might not get what you expect:
+
+>>> print letter a
+
+For most people, the first letter of 'banana' is b, not a. But for computer scientists, the index is an offset from the beginning of the string, and the offset of the first letter is zero.
+
+>>> letter = fruit[0]
+
+>>> print letter b
+
+So b is the 0th letter ("zero-eth") of 'banana', a is the 1th letter ("one-eth"), and n is the 2th ("two-eth") letter.
+
+You can use any expression, including variables and operators, as an index, but the value of the index has to be an integer. Otherwise you get:
+
+>>> letter = fruit[1.5]
+
+TypeError: string indices must be integers, not float
+
+### 8.2 len
+
+len is a built-in function that returns the number of characters in a string:
+
+## Chapter 8 Strings* [25] **The** \(\pi\)**
+
+## Chapter 8 Strings
+
+### 8.7 Looping and counting
+
+The following program counts the number of times the letter a appears in a string:
+
+```
+word='banana' count=0 forletterinword: ifletter=='a': count=count+1 printcount
+```
+
+This program demonstrates another pattern of computation called a **counter**. The variable count is initialized to 0 and then incremented each time an a is found. When the loop exits, count contains the result--the total number of a's.
+
+**Exercise 8.5**.: _Encapsulate this code in a function named_ count_, and generalize it so that it accepts the string and the letter as arguments._
+
+**Exercise 8.6**.: _Rewrite this function so that instead of traversing the string, it uses the three-parameter version of_ find _from the previous section._
+
+### 8.8 String methods
+
+A **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 uppercase letters:
+
+Instead of the function syntax upper(word), it uses the method syntax word.upper().
+
+```
+>>>word='banana' >>>new_word=word.upper() >>>printnew_word BANANA
+```
+
+This form of dot notation specifies the name of the method, upper, and the name of the string to apply the method to, word. The empty parentheses indicate that this method takes no argument.
+
+A method call is called an **invocation**; in this case, we would say that we are invoking upper on the word.
+
+As it turns out, there is a string method named find that is remarkably similar to the function we wrote:
+
+```
+>>>word='banana' >>>index=word.find('a') >>>printindex
+```
+
+In this example, we invoke find on word and pass the letter we are looking for as a parameter.
+
+Actually, the find method is more general than our function; it can find substrings, not just characters:
+
+``` >>>word.find('na')
+
+## Chapter 8 Strings
+
+### 8.1 String comparison
+
+The relational operators work on strings. To see if two strings are equal:* ```
+``` ifword=='banana': print'Allright,bananas.'
+```
+
+Other relational operations are useful for putting words in alphabetical order:
+
+```
+ifword<'banana': print'Yourword,'+word+',comesbeforebanana.' elifword>'banana': print'Yourword,'+word+',comesafterbanana.' else: print'Allright,bananas.'
+```
+
+Python does not handle uppercase and lowercase letters the same way that people do. All the uppercase letters come before all the lowercase letters, so:
+
+```
+Yourword,Pineapple,comesbeforebanana.
+```
+
+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 yourself against a man armed with a Pineapple.
+
+### 8.11 Debugging
+
+When you use indices to traverse the values in a sequence, it is tricky to get the beginning and end of the traversal right. Here is a function that is supposed to compare two words and return True if one of the words is the reverse of the other, but it contains two errors:
+
+```
+defis_reverse(word1,word2): iflen(word1)!=len(word2): returnFalse
+``` i-0 j-len(word2) whilej>0: ifword1[i]!=word2[j]: returnFalse i-i+1 j-j-1 returnTrue ```
+The first if statement checks whether the words are the same length. If not, we can return False immediately and then, for the rest of the function, we can assume that the words are the same length. This is an example of the guardian pattern in Section 6.8.
+
+i and j are indices: i traverses word1 forward whilej traverses word2 backward. If we find two letters that don't match, we can return False immediately. If we get through the whole loop and all the letters match, we return True.
+
+If we test this function with the words "pots" and "stop", we expect the return value True, but we get an IndexError:
+``` >>>is_reverse('pots','stop')
+
+## Chapter 8 Strings
+
+### 8.12 Glossary
+
+**object:**: Something a variable can refer to. For now, you can use "object" and "value" interchangeably.
+
+Figure 8.2: State diagram.
+
+**sequence:**: An ordered set; that is, a set of values where each value is identified by an integer index.
+**item:**: One of the values in a sequence.
+**index:**: An integer value used to select an item in a sequence, such as a character in a string.
+**slice:**: A part of a string specified by a range of indices.
+**empty string:**: A string with no characters and length 0, represented by two quotation marks.
+**immutable:**: The property of a sequence whose items cannot be assigned.
+**traverse:**: To iterate through the items in a sequence, performing a similar operation on each.
+**search:**: A pattern of traversal that stops when it finds what it is looking for.
+**counter:**: A variable used to count something, usually initialized to zero and then incremented.
+**method:**: A function that is associated with an object and called using dot notation.
+**invocation:**: A statement that calls a method.
+
+### 8.13 Exercises
+
+**Exercise 8.10**.: _A string slice can take a third index that specifies the "step size;" that is, the number of spaces between successive characters. A step size of 2 means every other character; 3 means every third, etc._
+
+>>> fruit = 'banana' >>> fruit[0:5:2] 'bnn' _A step size of -1 goes through the word backwards, so the slice [: :-1] generates a reversed string._
+
+_Use this idiom to write a one-line version of is_palindrome from Exercise 6.6._
+
+**Exercise 8.11**.: _The following functions are all intended to check whether a string contains any lowercase letters, but at least some of them are wrong. For each function, describe what the function actually does (assuming that the parameter is a string)._
+
+def any_lowercase1(s):  for cins:  if c.islower():  return True  else:  return False
+
+def any_lowercase2(s):  for cins:  if 'c'.islower():  return 'True'
+
+## Chapter 8 Strings
+
+### 8.1 String theory
+
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+
+## Chapter 9 Case study: word play
+
+### 9.1 Reading word lists
+
+For the exercises in this chapter we need a list of English words. There are lots of word lists available on the Web, but the one most suitable for our purpose is one of the word lists collected and contributed to the public domain by Grady Ward as part of the Moby lexicon project (see [http://wikipedia.org/wiki/Moby_Project](http://wikipedia.org/wiki/Moby_Project)). It is a list of 113,809 official crosswords; that is, words that are considered valid in crossword puzzles and other word games. In the Moby collection, the filename is 113809of.fic; you can download a copy, with the simpler name words.txt, from [http://thinkpython.com/code/words.txt](http://thinkpython.com/code/words.txt).
+
+This file is in plain text, so you can open it with a text editor, but you can also read it from Python. The built-in function open takes the name of the file as a parameter and returns a **file object** you can use to read the file.
+
+```
+>>>fin=open('words.txt') >>>printfin <openfile'words.txt',mode'r'at0xb7f4b380> finis a common name for a file object used for input. Mode 'r' indicates that this file is open for reading (as opposed to 'w' for writing).
+
+The file object provides several methods for reading, including readine, which reads characters from the file until it gets to a newline and returns the result as a string:
+``` >>>fin.readline() 'aa\r\n' ```
+The first word in this particular list is "aa," which is a kind of lava. The sequence \r\n represents two whitespace characters, a carriage return and a newline, that separate this word from the next.
+
+The file object keeps track of where it is in the file, so if you call readine again, you get the next word:
+``` >>>fin.readline() 'aa\r\n' ```
+
+The next word is "aah," which is a perfectly legitimate word, so stop looking at me like that. Or, if it's the whitespace that's bothering you, we can get rid of it with the string method strip:
+```
+>>>line=fin.readline() >>>word=line.strip() >>>printword aahed You can also use a file object as part of a for loop. This program reads words.txt and prints each word, one per line: fin=open('words.txt') forlineinfin: word=line.strip() printword
+```
+
+**Exercise 9.1**.: _Write a program that reads words.txt and prints only the words with more than 20 characters (not counting whitespace)._
+
+### 9.2 Exercises
+
+There are solutions to these exercises in the next section. You should at least attempt each one before you read the solutions.
+
+**Exercise 9.2**.: _In 1939 Ernest Vincent Wright published a 50,000 word novel called_ Gadsby _that does not contain the letter "e." Since "e" is the most common letter in English, that's not easy to do._
+
+_In fact, it is difficult to construct a solitary thought without using that most common symbol. It is slow going at first, but with caution and hours of training you can gradually gain facility._
+
+_All right, I'll stop now._
+
+_Write a function called_ has_no_e _that returns_ True _if the given word doesn't have the letter "e" in it._
+
+_Modify your program from the previous section to print only the words that have no "e" and compute the percentage of the words in the list have no "e."_
+
+**Exercise 9.3**.: _Write a function named_ avoids _that takes a word and a string of forbidden letters, and that returns_ True _if the word 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 the number of words that don't contain any of them. Can you find a combination of 5 forbidden letters that excludes the smallest number of words?_
+
+**Exercise 9.4**.: _Write a function named_ uses_only _that takes a word and a string of letters, and that returns_ True _if the word contains only letters in the list. Can you make a sentence using only the letters_ acefhlo? _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 are there that use all the vowels_ aeiou_? _How about_ aeiouy?_
+
+**Exercise 9.6**.: _Write a function called_ is_abecdarian _that returns_ True _if the letters in a word appear in alphabetical order (double letters are ok). How many abecdarian words are there?_
+
+### 9.3 Search
+
+All of the exercises in the previous section have something in common; they can be solved with the search pattern we saw in Section 8.6. The simplest example is:
+
+## Chapter 9 Case study: word play
+
+### 9.1 Case study: word play
+
+The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word play_. The word play is a _word_.
+
+### 9.5 Debugging
+
+Or, if you noticed that this is an instance of a previously-solved problem, you might have written:
+
+def is_palindrome(word) :  return is_reverse(word, word) Assuming you did Exercise 8.9.
+
+### 9.5 Debugging
+
+Testing programs is hard. The functions in this chapter are relatively easy to test because you can check the results by hand. Even so, it is somewhere between difficult and impossible to choose a set of words that test for all possible errors.
+
+Taking has_no_e as an example, there are two obvious cases to check: words that have an 'e' should return False; words that don't should return True. You should have no trouble coming up with one of each.
+
+Within each case, there are some less obvious subcases. Among the words that have an "e," you should test words with an "e" at the beginning, the end, and somewhere in the middle. You should test long words, short words, and very short words, like the empty string. The empty string is an example of a **special case**, which is one of the non-obvious cases where errors often lurk.
+
+In addition to the test cases you generate, you can also test your program with a word list like words.txt. By scanning the output, you might be able to catch errors, but be careful: you might catch one kind of error (words that should not be included, but are) and not another (words that should be included, but aren't).
+
+In general, testing can help you find bugs, but it is not easy to generate a good set of test cases, and even if you do, you can't be sure your program is correct.
+
+According to a legendary computer scientist:
+
+Program testing can be used to show the presence of bugs, but never to show their absence!
+
+-- Edsger W. Dijkstra
+
+### 9.6 Glossary
+
+**file object:**: A value that represents an open file.
+**problem recognition:**: A way of solving a problem by expressing it as an instance of a previously-solved problem.
+**special case:**: A test case that is atypical or non-obvious (and less likely to be handled correctly).
+
+## Chapter 9 Case study: word play
+
+### 9.7 Exercises
+
+**Exercise 9.7**.: _This question is based on a Puzzler that was broadcast on the radio program_ Car Talk (_[http://www.cartalk.com/content/puzzlers_](http://www.cartalk.com/content/puzzlers_)):_
+
+_Give me a word with three consecutive double letters. I'll give you a couple of words that almost qualify, but don't. For example, the word committee, c-o-m-m-i-t-t-e-e. It would be great except for the 'i' that sneaks in there. Or Mississippi: M-i-s-s-i-s-i-p-i. If you could take out those i's it would work. But there is a word that has three consecutive pairs of letters and to the best of my knowledge this may be the only word. Of course there are probably 500 more but I can only think of one. What is the word?_
+
+_Write a program to find it. Solution: [http://thinkpython.com/code/cartalk1.py._](http://thinkpython.com/code/cartalk1.py._)
+
+**Exercise 9.8**.: _Here's another_ Car Talk _Puzzler_ (_[http://www.cartalk.com/content/puzzlers_](http://www.cartalk.com/content/puzzlers_)):_
+
+_"I was driving on the highway the other day and I happened to notice my odometer. Like most odometers, it shows six digits, in whole miles only. So, if my car had 300,000 miles, for example, I'd see 3-0-0-0-0-0._
+
+_"Now, what I saw that day was very interesting. I noticed that the last 4 digits were palindromic; that is, they read the same forward as backward. For example, 5-4-4-5 is a palindrome, so my odometer could have read 3-1-5-4-5._
+
+_"One mile later, the last 5 numbers were palindromic. For example, it could have read 3-6-5-4-5-6. One mile after that, the middle 4 out of 6 numbers were palindromic. And you ready for this? One mile later, all 6 were palindromic!_
+
+_"The question is, what was on the odometer when I first looked?"_
+
+_Write a Python program that tests all the six-digit numbers and prints any numbers that satisfy these requirements. Solution: [http://thinkpython.com/code/cartalk2.py._](http://thinkpython.com/code/cartalk2.py._)
+
+**Exercise 9.9**.: _Here's another_ Car Talk _Puzzler you can solve with a search ([http://www.cartalk.com/content/puzzlers_](http://www.cartalk.com/content/puzzlers_)):_
+
+_"Recently I had a visit with my mom and we realized that the two digits that make up my age when reversed resulted in her age. For example, if she's 73, I'm 37. We wondered how often this has happened over the years but we got sidetracked with other topics and we never came up with an answer._
+
+_"When I got home I figured out that the digits of our ages have been reversible six times so far. I also figured out that if we're lucky it would happen again in a few years, and if we're really lucky it would happen one more time after that. In other words, it would have happened 8 times over all. So the question is, how old am I now?"_
+
+_Write a Python program that searches for solutions to this Puzzler. Hint: you might find the string method_ zfill _useful._
+
+_Solution: [http://thinkpython.com/code/cartalk3.py._](http://thinkpython.com/code/cartalk3.py._)
+
+## Chapter 10 Lists
+
+### 10.1 A list is a sequence
+
+Like a string, a **list** is a sequence of values. In a string, the values are characters; in a list, they can be any type. The values in a list are called **elements** or sometimes **items**.
+
+There are several ways to create a new list; the simplest is to enclose the elements in square brackets ([ 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 a list 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 list within another list is **nested**.
+
+A list that contains no elements is called an empty list; you can create one with empty brackets, [].
+
+As you might expect, you can assign list values to variables:
+
+>> cheeses = ['Cheddar', 'Edam', 'Gouda']
+
+>> numbers = [17, 123]
+
+>> empty = []
+
+>> print cheeses, numbers, empty
+
+['Cheddar', 'Edam', 'Gouda'] [17, 123] []
+
+### 10.2 Lists are mutable
+
+The syntax for accessing the elements of a list is the same as for accessing the characters of a string--the bracket operator. The expression inside the brackets specifies the index. Remember that the indices start at 0:
+
+>> print cheeses[0]
+
+Cheddar
+
+### 10.10.
+
+The first step is to use the "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol " "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol " "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol " "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol " "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol " "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol " "\(\times\)" symbol "\(\times\)" symbol "\(\times\)" symbol " "\(\times\)" symbol
+
+### 10.3 Traversing a list
+
+The most common way to traverse the elements of a list is with a for loop. The syntax is the same as for strings:
+
+```
+forcheeseinchees:  printcheese
+```
+
+This works well if you only need to read the elements of the list. But if you want to write or update the elements, you need the indices. A common way to do that is to combine the functions range and len:
+
+```
+foriinrange(len(numbers)):  numbers[i]=numbers[i]*2
+```
+
+This loop traverses the list and updates each element. len returns the number of elements in the list. range returns a list of indices from 0 to \(n-1\), where \(n\) is the length of the list. Each time through the loop i gets the index of the next element. The assignment statement in the body uses i to read the old value of the element and to assign the new value.
+
+A for loop over an empty list never executes the body:
+
+```
+forxin[]:  print'Thisneverhappens.'
+```
+
+Although a list can contain another list, the nested list still counts as a single element. The length of this list is four:
+
+```
+['spam',1,['Brie','Roquefort','PolleVeq'],[1,2,3]]
+```
+
+### 10.4 List operations
+
+The + operator concatenates lists:
+
+```
+>>>a=[1,2,3] >>>b-[4,5,6] >>>c=a+b >>>printc [1,2,3,4,5,6]
+```
+
+Similarly, the * operator repeats a list a given number of times:
+
+```
+>>>[0]*4 [0,0,0,0] >>>[1,2,3]*3 [1,2,3,1,2,3]
+```
+
+The first example repeats [0] four times. The second example repeats the list [1,2,3] three times.
+
+### 10.5 List slices
+
+The slice operator also works on lists:* ['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 to the end. So if you omit both, the slice is a copy 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 mutilate lists.
+
+A slice operator on the left side of an assignment can update multiple elements:
+
+>>> t - ['a', 'b', 'c', 'd', 'e', 'f'] >>> t[1:3] = ['x', 'y'] >>> print t
+
+['a', 'x', 'y', 'd', 'e', 'f']
+
+### 10.6 List methods
+
+Python provides methods that operate on lists. For example, append adds a new element to the end of a list:
+
+>>> t - ['a', 'b', 'c'] >>> t.append('d') >>> print t
+
+['a', 'b', 'c', 'd']
+
+extend takes a list as an argument and appends all of the elements:
+
+>>> t1 - ['a', 'b', 'c'] >>> t2 - ['d', 'e'] >>> t1.extend(t2) >>> print t1
+
+['a', 'b', 'c', 'd', 'e']
+
+This example leaves t2 unmodified.
+
+sort arranges the elements of the list from low to high:
+
+>>> t - ['d', 'c', 'e', 'b', 'a'] >>> t.sort() >>> print t
+
+['a', 'b', 'c', 'd', 'e']
+
+List methods are all void; they modify the list and return None. If you accidentally write t - t.sort(), you will be disappointed with the result.
+
+### 10.7 Map, filter and reduce
+
+To add up all the numbers in a list, you can use a loop like this:
+
+def add_all(t):  total = 0  for x int t:  total += x  return total is initialized to 0. Each time through the loop, x gets one element from the list. The +- operator provides a short way to update a variable. This **augmented assignment statement**:  total += x is equivalent to:  total = total + x As the loop executes, total accumulates the sum of the elements; a variable used this way is sometimes called an **accumulator**. Adding up the elements of a list is such a common operation that Python provides it as a built-in function, sum:
+
+>> t - [1, 2, 3] >> sum(t)
+
+An operation like this that combines a sequence of elements into a single value is sometimes called **reduce**.
+
+**Exercise 10.1**.: _Write a function called nested_sum that takes a nested list of integers and add up the elements from all of the nested lists._
+
+Sometimes you want to traverse one list while building another. For example, the following function takes a list of strings and returns a new list that contains capitalized strings:
+
+def capitalize_all(t):  res = []  for sint t:  res.append(s.capitalize())  return res res is initialized with an empty list; each time through the loop, we append the next element. So res is another kind of accumulator. An operation like capitalize_all is sometimes called a **map** because it "maps" a function (in this case the method capitalize) onto each of the elements in a sequence. **Exercise 10.2**.: _Use capitalize_all to write a function named capitalize_nested that takes a nested list of strings and returns a new nested list with all strings capitalized._ Another common operation is to select some of the elements from a list and return a sublist. For example, the following function takes a list of strings and returns a list that contains only the uppercase strings:
+
+def only_upper(t):  res = []  for sint t:
+
+## Chapter 10 Lists
+
+### 10.11 Thesis
+
+The Lists are the first and second chapters of the thesis.
+
+[MISSING_PAGE_POST]
+
+### 10.9 Lists and strings
+
+A string is a sequence of characters and a list is a sequence of values, but a list of characters is not the same as a string. To convert from a string to a list of characters, you can use list:
+
+>>s ='spam' >>> t - list(s) >>> print t ['s', 'p', 'a','m'] Because list is the name of a built-in function, you should avoid using it as a variable name. I also avoid 1 because it looks too much like 1. So that's why I use t.
+
+The list function breaks a string into individual letters. If you want to break a string into words, you can use the split method:
+
+>>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. The following example uses a hyphen as a delimiter:
+
+>>s ='spam-spam' >>> delimiter = '-' >>> s.split(delimiter) ['spam','spam','spam'] join is the inverse of split. It takes a list of strings and concatenates the elements. join is a string method, so you have to invoke it on the delimiter and pass the list as a parameter:
+
+>>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 concatenate strings without spaces, you can use the empty string,'', as a delimiter.
+
+### 10.10 Objects and values
+
+If we execute these assignment statements:
+
+a = 'banana' b - 'banana' We know that a and b both refer to a string, but we don't know whether they refer to the _same_ string. There are two possible states, shown in Figure 10.2.
+
+In one case, a and b refer to two different objects that have the same value. In the second case, they refer to the same object.
+
+To check whether two variables refer to the same object, you can use the is operator.
+
+#### 10.1.1 Aliasing
+
+If a refers to an object and you assign b - a, then both variables refer to the same object:
+
+```
+>>>a=[1,2,3] >>>b-a >>>bisaTrue
+```
+
+The state diagram looks like Figure 10.4.
+
+The association of a variable with an object is called a **reference**. In this example, there are two references to the same object.
+
+An object with more than one reference has more than one name, so we say that the object is **aliased**.
+
+If the aliased object is mutable, changes made with one alias affect the other:
+
+Figure 10.3: State diagram.
+
+Figure 10.2: State diagram.
+
+#### 10.1.2 List arguments
+
+The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. The list is stored in the list. 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The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. 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The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list. The list.
+
+#### 10.1.2 The "Master"
+
+The "Master" is a "Master". The "Master" is a "Master".
+
+2. Pick an idiom and stick with it. Part of the problem with lists is that there are too many ways to do things. For example, to remove an element from a list, you can use pop, remove, del, or even a slice assignment. To add an element, you can use the append method or the + operator. Assuming that t is a list and x is a list element, these are right:  t.append(x)  t - t + [x]  And these are wrong:  t.append([x]) # WRONG!  t - t.append(x) # WRONG!  t + [x] # WRONG!  t - t + x # WRONG!  Try out each of these examples in interactive mode to make sure you understand what they do. Notice that only the last one causes a runtime error; the other three are legal, but they do the wrong thing.
+3. Make copies to avoid aliasing. If you want to use a method like sort that modifies the argument, but you need to keep the original list as 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, sorted list and leaves the original alone. But in that case you should avoid using sorted as a variable name!
+
+### 10.14 Glossary
+
+**list:**: A sequence of values.
+**element:**: One of the values in a list (or other sequence), also called items.
+**index:**: An integer value that indicates an element in a list.
+**nested list:**: A list that is an element of another list.
+**list traversal:**: The sequential accessing of each element in a list.
+**mapping:**: A relationship in which each element of one set corresponds to an element of another set. For example, a list is a mapping from indices to elements.
+**accumulator:**: A variable used in a loop to add up or accumulate a result.
+**augmented assignment:**: A statement that updates the value of a variable using an operator like +-.
+**reduce:**: A processing pattern that traverses a sequence and accumulates the elements into a single result.
+
+## Chapter 10 Lists
+
+### 10.11 Thesis
+
+Thesis is a _list_ and is a list of the elements that satisfy some criterion.
+
+**Exercise 10.12**.: _Write a function called \(\mathtt{remove\_duplicates}\) that takes a list and returns a new list with only the unique elements from the original._
+
+**Exercise 10.13**.: _Write a function that reads the file words.txt and builds a list with one element per word. Write two versions of this function, one using the append method and the other using the idiom t - t + [x]. Which one takes longer to run? Why?_
+
+_Hint: use the time module to measure elapsed time. Solution: [http://thinkpython.com/code/wordlist.py._](http://thinkpython.com/code/wordlist.py._)
+
+**Exercise 10.14**.: _To check whether a word is in the word list, you could use the in operator, but it would be slow because it searches through the words in order._
+
+_Because the words are in alphabetical order, we can speed things up with a bisection search (also known as binary search), which is similar to what you do when you look a word up in the dictionary._You start in the middle and check to see whether the word you are looking for comes before the word in the middle of the list. If so, then you search the first half of the list the same way. Otherwise you search the second half. Either way, you cut the remaining search space in half. If the word list has 113,809 words, it will take about 17 steps to find the word or conclude that it's not there. Write a function called bisect that takes a sorted list and a target value and returns the index of the value in the list, if it's there, or None if it's not. Or you could read the documentation of the bisect module and use that! Solution: [http://thinkpython.com/code/inlist.py](http://thinkpython.com/code/inlist.py). Exercise 10.12. Two words are a "reverse pair" if each is the reverse of the other. Write a program that finds all the reverse pairs in the word list. Solution: [http://thinkpython.com/code/reverse_pair.py](http://thinkpython.com/code/reverse_pair.py). Exercise 10.13. Two words "interlock" if taking alternating letters from each forms a new word. For example, "shoe" and "cold" interlock to form "schooled." Solution: [http://thinkpython.com/code/interlock.py](http://thinkpython.com/code/interlock.py). Credit: This exercise is inspired by an example at [http://puzzlers.org._](http://puzzlers.org._)
+
+1. _Write a program that finds all pairs of words that interlock. Hint: don't enumerate all pairs!_
+2. _Can you find any words that are three-way interlocked; that is, every third letter forms a word, starting from the first, second or third?_
+
+## Chapter 10 List
+
+## Chapter 11 Dictionaries
+
+A **dictionary** is like a list, but more general. In a list, the indices have to be integers; in a dictionary they can be (almost) any type.
+
+You can think of a dictionary as a mapping between a set of indices (which are called **keys**) and a set of values. Each key maps to a value. The association of a key and a value is called a **key-value pair** or sometimes an **item**.
+
+As an example, we'll build a dictionary that maps from English to Spanish words, so the keys and the values are all strings.
+
+The function dict creates a new dictionary with no items. Because dict is the name of a built-in function, you should avoid using it as a variable name.
+
+>>> eng2sp = dict() >>> print eng2sp {} The squiggly-brackets, {}, represent an empty dictionary. To add items to the dictionary, you can use square brackets:
+
+>>> eng2sp['one'] - 'uno' This line creates an item that maps from the key 'one' to the value 'uno'. If we print the dictionary again, we see a key-value pair with a colon 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 three items:
+
+>>> eng2sp = {'one': 'uno', 'two': 'dos', 'three': 'tres'} But if you print eng2sp, you might be surprised:
+
+>>> print eng2sp {'one': 'uno', 'three': 'tres', 'two': 'dos'} The order of the key-value pairs is not the same. In fact, if you type the same example on your computer, you might get a different result. In general, the order of items in a dictionary is unpredictable.
+
+But that's not a problem because the elements of a dictionary are never indexed with integer indices. Instead, you use the keys to look up the corresponding values:
+
+#### 11.1.1 Dictionary as a set of counters
+
+Suppose you are given a string and you want to count how many times each letter appears. There are several ways you could do it:
+
+1. You could create 26 variables, one for each letter of the alphabet. Then you could traverse the string and, for each character, increment the corresponding counter, probably using a chained conditional.
+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 the appropriate counter.
+
+3. You could create a dictionary with characters as keys and counters as the corresponding values. The first time you see a character, you would add an item to the dictionary. After that you would increment the value of an existing item.
+
+Each of these options performs the same computation, but each of them implements that computation in a different way.
+
+An **implementation** is a way of performing a computation; some implementations are better than others. For example, an advantage of the dictionary implementation is that we don't have to know ahead of time which letters appear in the string and we only have to make room for the letters that do appear.
+
+Here is what the code might look like:
+
+def histogram(s):  d - dict()  for c in s:  if c not in d:  d[c] = 1  else:  d[c] += 1  return d The 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 f or loop traverses the string. Each time through the loop, if the character c is not in the dictionary, we create a new item with key c and the initial value 1 (since we have seen this letter once). If c is already in the dictionary we increment d[c].
+
+Here's how it works:
+
+>>> 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 the letters 'a' and 'b' appear once; 'o' appears twice, and so on.
+
+**Exercise 11.2**.: _Dictionaries have a method called get that takes a key and a default value. If the key appears in the dictionary, get returns the corresponding value; otherwise it returns the default value. For example:_
+
+>>> h - histogram('a') >>> print h {'a': 1} >>> h.get('a', 0) 1 >>> h.get('b', 0) 0 _Use get to write_histogram _more concisely. You should be able to eliminate the_if_statement_.
+
+### 11.2 Looping and dictionaries
+
+If you use a dictionary in a f or statement, it traverses the keys of the dictionary. For example, print_hist prints each key and the corresponding value:
+
+## Chapter 11 Dictionaries
+
+### 11.1 Dictionaries
+
+The Dictionaries are the most popular ones of the Dictionaries. The Dictionaries are the most popular ones of the Dictionaries.
+
+* >>k-reverse_lookup(h, 3) Traceback(mostrecentcalllast): File"<stdin>",line1,in? File"<stdin>",line5,inreverse_lookupValueError The result when you raise an exception is the same as when Python raises one: it prints a traceback and an error message.
+
+The raise statement takes a detailed error message as an optional argument. For example:
+
+>>raiseValueError('valuedoesnotappearinthedictionary') Traceback(mostrecentcalllast): File"<stdin>",line1,in?ValueError:valuedoesnotappearinthedictionary A reverse lookup is much slower than a forward lookup; if you have to do it often, or if the dictionary gets big, the performance of your program will suffer.
+
+**Exercise 11.4**.: _Modifyreverse_lookup so that it builds and returns a list of all keys that map to \(v\), or an empty list if there are none._
+
+### 11.4 Dictionaries and lists
+
+Lists can appear as values in a dictionary. For example, if you were given a dictionary that maps from letters to frequencies, you might want to invert it; that is, create a dictionary that maps from frequencies to letters. Since there might be several letters with the same frequency, each value in the inverted dictionary should be a list of letters.
+
+Here is a function that inverts a dictionary:
+
+```
+definvert_dict(d): inverse=dict() forkeyind: val=d[key] ifvalnotininverse: inverse[val]=[key] else: inverse[val].append(key) returninverse
+```
+
+Each time through the loop, key gets a key from d and val gets the corresponding value. If val is not in inverse, that means we haven't seen it before, so we create a new item and initialize it with a **singleton** (a list that contains a single element). Otherwise we have seen this value before, so we append the corresponding key to the list.
+
+Here is an example:
+
+``` >>>hist=histogram('parrot') >>>printhist {'a':1,'p':1,'r':2,'t':1,'o':1} >>>inverse=invert_dict(hist) >>>printinverse {[:'a','p','t','o'],2:['r']}
+
+Figure 11.1 is a state diagram showing hist and inverse. A dictionary is represented as a box with the type dict above it and the key-value pairs inside. If the values are integers, floats or strings, I usually draw them inside the box, but I usually draw lists outside the box, just to keep the diagram simple.
+
+Lists can be values in a dictionary, as this example shows, but they cannot be keys. Here's what happens if you try:
+
+``` >>>t-[1,2,3] >>>d-dict() >>>d[t]-'oops' Traceback(mostrecentcalllast): File"<stdin>",line1,in? TypeError:listobjectsareunhashable I mentioned earlier that a dictionary is implemented using a hashtable and that means that the keys have to behashable.
+
+Ahash is a function that takes a value (of any kind) and returns an integer. Dictionaries use these integers, called hash values, to store and look up key-value pairs.
+
+This system works fine if the keys are immutable. But if the keys are mutable, like lists, bad things happen. For example, when you create a key-value pair, Python hashes the key and stores it in the corresponding location. If you modify the key and then hash it again, it would go to a different location. In that case you might have two entries for the same key, or you might not be able to find a key. Either way, the dictionary wouldn't work correctly.
+
+That's why the keys have to be hashable, and why mutable types like lists aren't. The simplest way to get around this limitation is to use tuples, which we will see in the next chapter.
+
+Since lists and dictionaries are mutable, 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 a more concise version of_ invert_dict_. Solution:_[http://thinkpython.com/code/invert_dict.py._](http://thinkpython.com/code/invert_dict.py._)
+
+### 11.5 Memos
+
+If you played with the fibonacci function from Section 6.7, you might have noticed that the bigger the argument you provide, the longer the function takes to run. Furthermore,
+
+Figure 11.1: State diagram.
+
+the run time increases very quickly.
+
+To understand why, consider Figure 11.2, which shows the **call graph** for fibonacci with n=4:
+
+A call graph shows a set of function frames, with lines connecting each frame to the frames of the functions it calls. At the top of the graph, fibonacci with n=4 calls fibonacci with n=3 and n=2. In turn, fibonacci with n=3 calls fibonacci with n=2 and n=1. And so on.
+
+Count how many times fibonacci(0) and fibonacci(1) are called. This is an inefficient solution to the problem, and it gets worse as the argument 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**. Here is a "memoized" version of fibonacci:
+
+known = {0:0, 1:1}
+
+def fibonacci(n) :  if n in known:  return known[n]
+
+ res = fibonacci(n-1) + fibonacci(n-2)  known[n] = res  return res
+
+known is a dictionary that keeps track of the Fibonacci numbers we already know. It starts with two items: 0 maps to 0 and 1 maps to 1.
+
+Whenever fibonacci is called, it checks known. If the result is already there, it can return immediately. Otherwise it has to compute the new value, add it to the dictionary, and return it.
+
+**Exercise 11.6**.: _Run this version of fibonacci and the original with a range of parameters and compare their run times._
+
+**Exercise 11.7**.: _Memoize the Ackermann function from Exercise 6.5 and see if memoization makes it possible to evaluate the function with bigger arguments. Hint: no. Solution: [http://thinkpython.com/code/ackermann_memo.py._](http://thinkpython.com/code/ackermann_memo.py._)
+
+Figure 11.2: Call graph.
+
+### 11.6 Global variables
+
+In the previous example, known is created outside the function, so it belongs to the special frame called __main__. Variables in __main__ are sometimes called **global** because they can be accessed from any function. Unlike local variables, which disappear when their function ends, global variables persist from one function call to the next.
+
+It is common to use global variables for **flags**; that is, boolean variables that indicate ("flag") whether a condition is true. For example, some programs use a flag named verbose to control the level of detail in the output:
+
+verbose = True
+
+def example1():  if verbose:  print 'Running example1' If you try to reassign a global variable, you might be surprised. The following example is supposed to keep track of whether the function has been called:
+
+been_called = False
+
+def example2():  been_called = True # WRONG But if you run it you will see that the value of been_called doesn't change. The problem is that example2 creates a new local variable named been_called. The local variable goes away when the function ends, and has no effect on the global variable.
+
+To reassign a global variable inside a function you have to **declare** the global variable before you use it:
+
+been_called = False
+
+def example2():  global been_called  been_called = True The global statement tells the interpreter something like, "In this function, when I say been_called, I mean the global variable; don't create a local one."
+
+Here's an example that tries to update a global variable:
+
+count = 0
+
+def example3():  count = count + 1 # WRONG If you run it you get:
+
+UnboundLocalError: local variable 'count' referenced before assignment Python assumes that count is local, which means that you are reading it before writing it. The solution, again, is to declare count global.
+
+def example3():  global count += 1 If the global value is mutable, you can modify it without declaring it:
+* [99] *
+
+## Chapter 11 Dictionaries
+
+### 11.1 Dictionaries
+
+The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics. The Dictionaries are most widely used in the field of mathematics. The Dictionaries are the most widely used in the field of mathematics.
+
+**global variable:**: A variable defined outside a function. Global variables can be accessed from any function.
+**flag:**: A boolean variable used to indicate whether a condition is true.
+**declaration:**: A statement like global that tells the interpreter something about a variable.
+
+### 11.10 Exercises
+
+**Exercise 11.9**.: _If you did Exercise 10.8, you already have a function named has_duplicates that takes a list as a parameter and returns_ True _if there is any object that appears more than once in the list._
+
+_Use a dictionary to write a faster, simpler version of has_duplicates. Solution:_ [http://thinkpython.com/code/has_duplicates.py](http://thinkpython.com/code/has_duplicates.py).
+**Exercise 11.10**.: _Two words are "rotate pairs" if you can rotate one of them and get the other (see_ rotate_word _in Exercise 8.12_)._
+
+_Write a program that reads a wordlist and finds all the rotate pairs. Solution:_ [http://thinkpython.com/code/rotate_pairs.py](http://thinkpython.com/code/rotate_pairs.py).
+**Exercise 11.11**.: _Here's another Puzzler from_ Car Talk _([http://www.cartalk.com/content/puzzlers](http://www.cartalk.com/content/puzzlers)):_
+
+_This was sent in by a fellow named Dan O'Leary. He came upon a common one-syllable, five-letter word recently that has the following unique property. When you remove 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 back and remove the second letter and the result is yet another homophone of the original word. And the question is, what's the word?_
+
+_Now I'm going to give you an example that doesn't work. Let's look at the five-letter word, 'wrack.' W-R-A-C-K, you know like to 'wrack with pain.' If I remove the first letter, I am left with a four-letter word, 'R-A-C-K.' As in, 'Holy cow, did you see the rack on that buck! It must have been a nine-pointer! It's a perfect homophone. If you put the 'w' back, and remove the 'r,' instead, you're left with the word, 'wack,' which is a real word, it's just not a homophone of the other two words._
+
+_But there is, however, at least one word that Dan and we know of, which will yield two homophones if you remove either of the first two letters to make two, new four-letter words. The question is, what's the word?_
+
+_You can use the dictionary from Exercise 11.1 to check whether a string is in the word list._
+
+_To check whether two words are homophones, you can use the CMU Pronuncing Dictionary. You can download it from_ [http://www.speech.cs.cmu.edu/cgi-bin/cmudict](http://www.speech.cs.cmu.edu/cgi-bin/cmudict) or from_ [http://thinkpython.com/code/pronounce.py_](http://thinkpython.com/code/pronounce.py_), which provides a function named_ read_dictionary that reads the pronouncing dictionary and returns a Python dictionary that maps from each word to a string that describes its primary pronunciation._
+
+_Write a program that lists all the words that solve the Puzzler. Solution:_ [http://thinkpython.com/code/homophone.py_._](http://thinkpython.com/code/homophone.py_._)
+
+## Chapter 11 Dictionaries
+
+## Chapter 12 Tuples
+
+### 12.1 Tuples are immutable
+
+A tuple is a sequence of values. The values can be any type, and they are indexed by integers, so in that respect tuples are a lot like lists. The important difference is that tuples are immutable.
+
+Syntactically, a tuple is a comma-separated list of values:
+
+>>> t - 'a', 'b', 'c', 'd', 'e'
+
+Although it is not necessary, it is common to enclose tuples in parentheses:
+
+>>> t - ('a', 'b', 'c', 'd', 'e')
+
+To create a tuple with a single element, you have to include a final comma:
+
+>>> t1 - 'a',
+
+>>> type(t1)
+
+<type 'tuple'>
+
+A value in parentheses is not a tuple:
+
+>>> t2 - ('a')
+
+>>> type(t2)
+
+<type'str'>
+
+Another way to create a tuple is the built-in function tuple. With no argument, it creates an empty tuple:
+
+>>> t - tuple()
+
+>>> print t
+
+()
+
+If the argument is a sequence (string, list or tuple), the result is a tuple with the elements of the sequence:
+
+>>> t - tuple('lupins')
+
+>>> print t
+
+('l', 'u', 'P', 'i', 'n','s')
+
+Because tuple is the name of a built-in function, you should avoid using it as a variable name.
+
+Most list operators also work on tuples. The bracket operator indexes an element:* ```
+### 12.1 **Tuple assignment**
+
+It is often useful to swap the values of two variables. With conventional assignments, you have to use a temporary variable. For example, to swap a and b:
+``` >>>temp=a >>>a=b >>>b-temp ```
+This solution is cumbersome; **tuple assignment** is more elegant:
+``` >>>a,b=b,a ```
+The left side is a tuple of variables; the right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+``` >>>a,b=1,2,3 ```
+``` ValueError:toomanyvaluestounpack
+```
+
+More generally, the right side can be any kind of sequence (string, list or tuple). For example, to split an email address into a user name and a domain, you could write:
+
+```
+>>>add='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, the second to domain.
+
+```
+>>>printuname
+```
+
+```
+>>>printdomain
+```
+
+### 12.2 **Tuple assignment**
+
+It is often useful to swap the values of two variables. With conventional assignments, you have to use a temporary variable. For example, to swap a and b:
+
+```
+>>>a=b >>>b-temp >>>a,b=b,a
+```
+
+The left side is a tuple of variables; the right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The right side is a tuple of expressions. Each value is assigned to its respective variable. All the expressions on the right side are evaluated before any of the assignments.
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the left and the number of values on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+The number of variables on the right have to be the same:
+
+```
+>>>a,b=1,2,3
+```
+
+### 12.3 Tuples as return values
+
+Strictly speaking, a function can only return one value, but if the value is a tuple, the effect is the same as returning multiple values. For example, if you want to divide two integers and compute the quotient and remainder, it is inefficient to compute \(x/y\) and then \(x\%y\). It is better to compute them both at the same time.
+
+The built-in function divmod takes two arguments and returns a tuple of two values, the quotient and remainder. You can store the result as a tuple:
+
+```
+>>>t-divmod(7,3) >>>printt (2,1) Or use tuple assignment to store the elements separately:
+``` >>>quot,rem=divmod(7,3) >>>printquot 2 >>>printrem ```
+Here is an example of a function that returns a tuple:
+```  returnmin(t),max(t) maxandminarebuilt-infunctionsthatfindthelargestandsmallestelementsofsequence.min_maxcomputesbothandreturnsttupleoftwovalues. ```
+### 12.4 Variable-length argument tuples
+
+Functions can take a variable number of arguments. A parameter name that begins with \(*\)**gathers** arguments into a tuple. For example, printalltakesanynumberofargumentsandprintsthem:
+``` defprintall(*args):  printargs Thegatherparametercanhaveanynameyoulike,butargsisconventional.Here'showthefunctionworks:
+
+```
+>>>printall(1,2.0,'3') (1,2.0,'3') Thecomplementofgatherisscatter.Ifyouhavesequenceofvaluesandyouwanttopassittoafunctionasmultiplearguments,youcanusethe*operator.Forexample,divmodtakesexactlytwoarguments;itdoesn'tworkwithatuple:
+``` >>>t-(7,3) >>>divmod(t) TypeError:divmodexpected2arguments,got1 ```
+Butifyouscatterthetuple,itworks:
+``` >>>divmod(*t) (2,1) ```
+
+**Exercise 12.1**.: _Manyofthebuilt-infunctionsusevariable-lengthargumenttuples.Forexample,maxandmincantakeanynumberofarguments:_
+
+#### 12.5.1 The "Lisp"
+
+The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp". The "Lisp" is a "Lisp".
+
+The output of this loop is:
+
+```
+0a
+1b
+2c
+
+Again.
+
+### 12.6 Dictionaries and tuples
+
+Dictionaries have a method called items that returns a list of tuples, where each tuple is a key-value pair.
+``` >>>d-{'a':0,'b':1,'c':2} >>>t-d.items() >>>printt
+[('a',0),('c',2),('b',1)] ```
+As you should expect from a dictionary, the items are in no particular order. In Python 3, items returns an iterator, but for many purposes, iterators behave like lists.
+
+Going in the other direction, you can use a list of tuples to initialize a new dictionary:
+``` >>>t-[('a',0),('c',2),('b',1)] >>>d-dict(t) >>>printd {'a':0,'c':2,'b':1} ```
+Combining dict with zip yields a concise way to create a dictionary:
+``` >>>d-dict(zip('abc',range(3))) >>>printd {'a':0,'c':2,'b':1} ```
+The dictionary method update also takes a list of tuples and adds them, as key-value pairs, to an existing dictionary.
+
+Combining items, tuple assignment and for, you get the idiom for traversing the keys and values of a dictionary:
+``` forkey,valind.items(): printval,key ```
+The output of this loop is:
+``` 0a
+2c
+1b
+
+Again.
+
+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 we have defined last, first and number, we could write:
+
+```
+directory[last,first]=number
+```
+
+The expression in brackets is a tuple. We could use tuple assignment to traverse this dictionary.
+
+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 tuple to last and first, then prints the name and corresponding telephone number.
+
+There are two ways to represent tuples in a state diagram. The more detailed version shows the indices and elements just as they appear in a list. For example, the tuple ('Cleese', 'John') would appear as in Figure 12.1.
+
+But in a larger diagram you might want to leave out the details. For example, a diagram of the telephone directory might appear as in Figure 12.2.
+
+Here the tuples are shown using Python syntax as a graphical shorthand.
+
+The telephone number in the diagram is the complaints line for the BBC, so please don't call it.
+
+### 12.7 Comparing tuples
+
+The relational operators work with tuples and other sequences; Python starts by comparing the first element from each sequence. If they are equal, it goes on to the next elements, and so on, until it finds elements that differ. Subsequent elements are not considered (even if they are really big).
+
+```
+>>>(0,1,2)<(0,3,4) True >>>(0,1,2000000)<(0,3,4) True
+```
+
+The sort function works the same way. It sorts primarily by first element, but in the case of a tie, it sorts by second element, and so on.
+
+This feature lends itself to a pattern called **DSU** for
+
+Figure 12.1: State diagram.
+
+Figure 12.2: State diagram.
+
+* **Decorate**: a sequence by building a list of tuples with one or more sort keys preceding the elements from the sequence,
+* **Sort**: the list of tuples, and
+* **Undecorate**: by extracting the sorted elements of the sequence.
+
+For example, suppose you have a list of words and you want to sort them from longest to shortest:
+
+```
+defsort_by_length(words): t-[] forwordinwords: t.append((len(word),word)) t.sort(reverse=True) res=[] forlength,wordint: res.append(word) returnres
+```
+
+The first loop builds a list of tuples, where each tuple is a word preceded by its length.
+
+```
+sortcomparesthefirstelement,length,first,andonlyconsidersthesecondelementtobreakties.Thekeywordargumentreverse=Truetellssorttogoindecreasingorder.
+```
+
+The second loop traverses the list of tuples and builds a list of words in descending order of length.
+
+**Exercise 12.2**.: _In this example, ties are broken by comparing words, so words with the same length appear 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 the random function in the random module. Solution: [http://thinkpython.com/code/unstable_sort.py._](http://thinkpython.com/code/unstable_sort.py._)
+
+### 12.8 Sequences of sequences
+
+I have focused on lists of tuples, but almost all of the examples in this chapter also work with lists of lists, tuples of tuples, and tuples of lists. To avoid enumerating the possible combinations, it is sometimes easier to talk about sequences of sequences.
+
+In many contexts, the different kinds of sequences (strings, lists and tuples) can be used interchangeably. So how and why do you choose one over the others?
+
+To start with the obvious, strings are more limited than other sequences because the elements have to be characters. They are also immutable. If you need the ability to change the characters in a string (as opposed to creating a new string), you might want to use a list of characters instead.
+
+Lists are more common than tuples, mostly because they are mutable. But there are a few cases where you might prefer tuples:
+
+1. In some contexts, like a return statement, it is syntactically simpler to create a tuple than a list. In other 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 a tuple or string.
+3. If you are passing a sequence as an argument to a function, using tuples reduces the potential for unexpected behavior due to aliasing.
+
+Because tuples are immutable, they don't provide methods like sort and reverse, which modify existing lists. But Python provides the built-in functions sorted and reversed, which take any sequence as a parameter and return a new list with the same elements in a different order.
+
+### 12.9 Debugging
+
+Lists, dictionaries and tuples are known generically as **data structures**; in this chapter we are starting to see compound data structures, like lists of tuples, and dictionaries that contain tuples as keys and lists as values. Compound data structures are useful, but they are prone to what I call **shape errors**; that is, errors caused when a data structure has the wrong type, size or composition. For example, if you are expecting a list with one integer and I give you a plain old integer (not in a list), it won't work.
+
+To help debug these kinds of errors, I have written a module called structshape that provides a function, also called structshape, that takes any kind of data structure as an argument and returns a string that summarizes its shape. You can download it from [http://thinkpython.com/code/strucshape.py](http://thinkpython.com/code/strucshape.py)
+
+Here's the result for a simple list:
+
+```
+>>>fromstrucshapeimportstrucshape >>>t-[1,2,3] >>>printstrucshape(t) listof3int A fancier program might write "list of 3 into," but it was easier not to deal with plurals. Here's a list of lists:
+``` >>>t2-[[1,2],[3,4],[5,6]] >>>printstrucshape(t2) listof3listof2int ```
+If the elements of the list are not the same type, structshape groups them, in order, by type:
+``` >>>t3-[1,2,3,4.0,'5','6',[7],[8],9] >>>printstrucshape(t3) listof(3int,float,2str,2listofint,int) Here's a list of tuples:
+
+```
+>>>s='abc' >>>lt-zip(t,s) >>>printstrucshape(lt) listof3tupleof(int,str) And here's a dictionary with 3 items that map integers to strings.
+``` >>>d-dict(lt) >>>printstrucshape(d) dictof3int->str ```
+
+If you are having trouble keeping track of your data structures, structshape can help.
+
+### 12.10 Glossary
+
+**tuple:**: An immutable sequence of elements.
+**tuple assignment:**: An assignment with a sequence on the right side and a tuple of variables on the left. The right side is evaluated and then its elements are assigned to the variables on the left.
+**gather:**: The operation of assembling a variable-length argument tuple.
+**scatter:**: The operation of treating a sequence as a list of arguments.
+**DSU:**: Abbreviation of "decorate-sort-undecorate," a pattern that involves building a list of tuples, sorting, and extracting part of the result.
+**data structure:**: A collection of related values, often organized in lists, dictionaries, tuples, etc.
+**shape (of a data structure):**: A summary of the type, size and composition of a data structure.
+
+### 12.11 Exercises
+
+**Exercise 12.3**.: _Write a function called_ most_frequent _that takes a string and prints the letters in decreasing order of frequency. Find text samples from several different languages and see how better frequency varies between languages. Compare your results with the tables at_ [http://en.wikipedia.org/wiki/Letter_frequencies_](http://en.wikipedia.org/wiki/Letter_frequencies_). Solution:_ [http://thinkpython.com/code/most_frequent.py](http://thinkpython.com/code/most_frequent.py).
+**Exercise 12.4**.: _More anagrams!_
+
+1. _Write a program that reads a word list from a file (see Section_ 9.1_) and prints all the sets of words that are anagrams._ _Here is an example of what the output might look like:_ ['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 words that can be spelled with those letters. The question is, how can you represent the set of letters in a way that can be used as a key?_
+2. _Modify the previous program so that it prints the largest set of anagrams first, followed by the second largest set, and so on._
+3. _In Scrable a "bingo" is when you play all seven tiles in your rack, along with a letter on the board, to form an eight-letter word. What set of 8 letters forms the most possible bingos? Hint: there are seven._ _Solution:_ [http://thinkpython.com/code/anagram_sets.py._](http://thinkpython.com/code/anagram_sets.py._)
+
+**Exercise 12.5**.: _Two words form a "metathesis pair" if you can transform one into the other by swapping two letters; for example, "converse" and "conserve." Write a program that finds all of the metathesis pairs in the dictionary. Hint: don't test all pairs of words, and don't test all possible swaps. Solution: [http://thinkpython.com/code/metathesis.py](http://thinkpython.com/code/metathesis.py). Credit: This exercise is inspired by an example at [http://puzzlers.org._](http://puzzlers.org._)
+
+**Exercise 12.6**.: _Here's another Car Talk Puzzler ([http://www.cartalk.com/content/puzzlers](http://www.cartalk.com/content/puzzlers)):_
+
+_What is the longest English word, that remains a valid English word, as you remove its letters one at a time?_
+
+_Now, letters can be removed from either end, or the middle, but you can't rearrange any of 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 going to be an English word--one that's found in the dictionary. I want to know what's the longest word and how many letters does it have?_
+
+_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 left with the word sprite, then we take the e off the end, we're left with spit, we take the s off, we're left with pit, it, and I._
+
+_Write a program to find all words that can be reduced in this way, and then find the longest one._
+
+_This exercise is a little more challenging than most, so here are some suggestions:_
+
+1. _You might want to write a function that takes a word and computes a list of all the words that can be formed by removing one letter. These are the "children" of the word._
+2. _Recursively, a word is reducible if any of its children are reducible. As a base case, you can consider the empty string reducible._
+3. _The wordlist I provided,_ words.txt_, doesn't contain single letter words. So you might want to add "I", "a", and the empty string._
+4. _To improve the performance of your program, you might want to memoize the words that are known to be reducible._
+
+_Solution: [http://thinkpython.com/code/reducible.py._](http://thinkpython.com/code/reducible.py._)
+
+## Chapter 13 Case study: data structure selection
+
+### 13.1 Word frequency analysis
+
+As usual, you should at least attempt the following exercises before you read my solutions.
+
+**Exercise 13.1**.: _Write a program that reads a file, breaks each line into words, strips whitespace and punctuation from the words, and converts them to lowercase._
+
+_Hint: The string module provides strings named whitespace, which contains space, tab, newline, etc., and punctuation which contains the punctuation characters. Let's see if we can make Python swear:_
+
+>>> import string >>> print string.punctuation!!#$%^()*+,_/:;<=>?@[]^_'{|}^
+
+_Also, you might consider using the string methods strip, replace and translate._
+
+**Exercise 13.2**.: _Go to Project Gutenberg ([http://gutenberg.org](http://gutenberg.org)) and download your favorite out-of-copyright book in plain text format._
+
+_Modify your program from the previous exercise to read the book you downloaded, skip over the header information at the beginning of the file, and process the rest of the words as before._
+
+_Then modify the program to count the total number of words in the book, and the number of times each word is used._
+
+_Print the number of different words used in the book. Compare different books by different authors, written in different eras. Which author uses the most extensive vocabulary?_
+
+**Exercise 13.3**.: _Modify the program from the previous exercise to print the 20 most frequently-used words in the book._
+
+**Exercise 13.4**.: _Modify the previous program to read a word list (see Section 9.1) and then print all the words in the book that are not in the word list. How many of them are typos? How many of them are common words that should be in the word list, and how many of them are really obscure?_
+
+### 13.2 Random numbers
+
+Given the same inputs, most computer programs generate the same outputs every time, so they are said to be **deterministic**. Determinism is usually a good thing, since we expect the same calculation to yield the same result. For some applications, though, we want the computer to be unpredictable. Games are an obvious example, but there are more.
+
+Making a program truly nondeterministic turns out to be not so easy, but there are ways to make it at least seem nondeterministic. One of them is to use algorithms that generate **pseudorandom** numbers. Pseudorandom numbers are not truly random because they are generated by a deterministic computation, but just by looking at the numbers it is all but impossible to distinguish them from random.
+
+The random module provides functions that generate pseudorandom numbers (which I will simply call "random" from here on).
+
+The function random returns a random float between 0.0 and 1.0 (including 0.0 but not 1.0). Each time you call random, you get the next number in a long series. To see a sample, run this loop:
+
+import random
+
+for i in range(10):  x = random.random()  print x
+
+The function randint takes parameters low and high and returns an integer between low and high (including both).
+
+>>> random.randint(5, 10)
+
+5 >>> random.randint(5, 10)
+
+To choose an element from a sequence at random, you can use choice:
+
+>>> t - [1, 2, 3] >>> random.choice(t)
+
+2 >>> random.choice(t)
+
+3
+
+The random module also provides functions to generate random values from continuous distributions including Gaussian, exponential, gamma, and a few more.
+
+**Exercise 13.5**.: _Write a function named choose_from_hist that takes a histogram as defined in Section 11.1 and returns a random value from the histogram, chosen with probability in proportion to frequency. For example, for this histogram:_
+
+>>> t - ['a', 'a', 'b'] >>> hist = histogram(t) >>> print hist {'a': 2, 'b': 1}
+
+_your function should return 'a' with probability \(2/3\) and 'b' with probability \(1/3\)._
+
+### Word histogram
+
+You should attempt the previous exercises before you go on. You can download my solution from [http://thinkpython.com/code/analyze_book.py](http://thinkpython.com/code/analyze_book.py). You will also need [http://thinkpython.com/code/emma.txt](http://thinkpython.com/code/emma.txt).
+
+Here is a program that reads a file and builds a histogram of the words in the file:
+
+```
+importstring defprocess_file(filename): hist=dict() fp=open(filename) forlineinfp: process_line(line,hist) returnhist defprocess_line(line,hist): line=line.replace('-','') forwordinline.split(): word=word.strip(string.punctuation+string.whitespace) word=word.lower() hist[word]=hist.get(word,0)+1 hist=process_file('emma.txt')
+```
+
+This program reads emma.txt, which contains the text of _Emma_ by Jane Austen.
+
+process_file loops through the lines of the file, passing them one at a time to process_line. The histogram hist is being used as an accumulator.
+
+process_line uses the string method replace to replace hyphens with spaces before using split to break the line into a list of strings. It traverses the list of words and uses strip and lower to remove punctuation and convert to lower case. (It is a shorthand to say that strings are "converted;" remember that string are immutable, so methods like strip and lower return new strings.)
+
+Finally, process_line updates the histogram by creating a new item or incrementing an existing one.
+
+To count the total number of words in the file, we can add up the frequencies in the histogram:
+
+```
+deftotal_words(hist): returnsum(hist.values())
+```
+
+The number of different words is just the number of items in the dictionary:
+
+```
+defdifferent_words(hist): returnlen(hist)
+```
+
+Here is some code to print the results:
+
+```
+print'Totalnumberofwords:',total_words(hist) print'Numberofdifferentwords:',different_words(hist)
+```
+
+### 13.4 Most common words
+
+To find the most common words, we can apply the DSU pattern; most_common takes a histogram and returns a list of word-frequency tuples, sorted in reverse order by frequency:
+
+```
+defmost_common(hist): t-[] forkey,valueinhist.items(): t.append((value,key))
+```
+
+```
+t.sort(reverse=True) return
+```
+
+Here is a loop that prints the ten most common words:
+
+```
+t-most_common(hist) print'Themostcommonwordsare:' forfreq,wordint[0:10]: printword,'\t',freq And here are the results from _Emma_:
+``` Themostcommonwordsare: to5242 the5205 and4897 of4295 i3191 a3130 it2529 her2483 was2400 she2364 ```
+### 13.5 Optional parameters
+
+We have seen built-in functions and methods that take a variable number of arguments. It is possible to write user-defined functions with optional arguments, too. For example, here is a function that prints the most common words in a histogram
+``` defprint_most_common(hist,num=10): t-most_common(hist) print'Themostcommonwordsare:' forfreq,wordint[:num]: printword,'\t',freq The first parameter is required; the second is optional. The **default value** of num is 10.
+
+If you only provide one argument:
+```
+print_most_common(hist) numgets the default value. If you provide two arguments: print_most_common(hist, 20) numgets the value of the argument instead. In other words, the optional argument overrides the default value.
+```
+
+If a function has both required and optional parameters, all the required parameters have to come first, followed by the optional ones.
+
+### Dictionary subtraction
+
+Finding the words from the book that are not in the word list from words.txt is a problem you might recognize as set subtraction; that is, we want to find all the words from one set (the words in the book) that are not in another set (the words in the list).
+
+```
+subtracttakes dictionariesd1andd2andreturnsanewdictionarythatcontainsallthekeysfromd1thatarenotind2.Sincewedon'treallycareaboutthevalues,wesetthemalltoNone. defsubtract(d1, d2): res=dict() forkeyind1: ifkeynotind2: res[key]=None returnres
+```
+
+To find the words in the book that are not in words.txt, we can use process_file to build a histogram for words.txt, and then subtract: words=process_file('words.txt') diff-subtract(hist,words) print"Thewordsinthebookthataren'tinthewordlistare:" forwordindiff.keys(): printword, Herearesomeoftheresultsfrom_Emma: Thewordsinthebookthataren'tinthewordlistare: rencontrejane'sblanchewoodhousesdisingenuousness friend'sveniceapartment... Someofthesewordsarenamesandpossessives.Others,like"rencontre,"arenolongerincommonuse.Butafewarecommonwordsthatshouldreallybeinthelist!
+
+**Exercise 13.6**.: _Python provides a data structure called set that provides many common set operations. Readthedocumentationat[http://docs.python.org/2/library/statypes.html#types-setandwriteaprogramthatusessetsubtractiontofindwordsinthebookthatarenotinthewordlist.Solution:http://thinkpython.com/code/analyze.book2.py._](http://docs.python.org/2/library/statypes.html#types-setandwriteaprogramthatusessetsubtractiontofindwordsinthebookthatarenotinthewordlist.Solution:http://thinkpython.com/code/analyze.book2.py._)
+
+### 13.7 Random words
+
+To choose a random word from the histogram, the simplest algorithm is to build a list with multiple copies of each word, according to the observed frequency, and then choose from the list:
+
+## Chapter 13 Case study: data structure selection
+
+### 13.1 Case study: data structure selection
+
+The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. The main purpose of this chapter is to develop a method for the data structure selection. 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+
+In 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 all possible suffixes (like "has" and "is").
+
+Given this mapping, you can generate a random text by starting with any prefix and choosing at random from the possible suffixes. Next, you can combine the end of the prefix and the new suffix to form the next prefix, and repeat.
+
+For example, if you start with the prefix "Half a," then the next word has to be "bee," because the 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 any prefix length. The length of the prefix is called the "order" of the analysis.
+
+**Exercise 13.8**.: _Markov analysis:_
+
+1. _Write a program to read a text from a file and perform Markov analysis. The result should be a dictionary that maps from prefixes to a collection of possible suffixes. The collection might be a list, tuple, or dictionary; it is up to you to make an appropriate choice. You can test your program with prefix length two, but you should write the program in a way that makes it easy to try other lengths._
+2. _Add a function to the previous program to generate random text based on the Markov analysis. Here is an example from_ Lemma _with prefix length 2:_ _He was very clever, be it sweetness or be angry, ashamed or only amused, at such a stroke. She had never thought of Hannah till you were never meant for me? "I cannot make speeches, Emma:" he soon cut it all himself._ _For this example, I left the punctuation attached to the words. The result is almost syntactically correct, but not quite. Semantically, it almost makes sense, but not quite._ _What happens if you increase the prefix length? Does the random text make more sense?_
+3. _Once your program is working, you might want to try a_ _mash-up: if you analyze text from two or more books, the random text you generate will blend the vocabulary and phrases from the sources in interesting ways._
+
+_Credit: This case study is based on an example from Kernighan and Pike, The Practice of Programming, Addison-Wesley, 1999._
+
+You should attempt this exercise before you go on; then you can can download my solution from [http://thinkpython.com/code/markov.py](http://thinkpython.com/code/markov.py). You will also need [http://thinkpython.com/code/emma.txt](http://thinkpython.com/code/emma.txt).
+
+### 13.9 Data structures
+
+Using Markov analysis to generate random text is fun, but there is also a point to this exercise: data structure selection. In your solution to the previous exercises, you had to choose:
+
+* How to represent the prefixes.
+
+* How to represent the collection of possible suffixes.
+* How to represent the mapping from each prefix to the collection of possible suffixes.
+
+Ok, the last one is easy; the only mapping type we have seen is a dictionary, so it is the natural choice.
+
+For the prefixes, the most obvious options are string, list of strings, or tuple of strings. For the suffixes, one option is a list; another is a histogram (dictionary).
+
+How should you choose? The first step is to think about the operations you will need to implement for each data structure. For the prefixes, we need to be able to remove words from the beginning and add to the end. For example, if the current prefix is "Half a," and the next word is "bee," you need to be able to form the 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 be able to use the prefixes as keys in a dictionary, so that rules out lists. With tuples, you can't append or remove, but you can use the addition operator to form a new tuple:
+
+``` defshift(prefix, word): returnprefix[1:]+(word,) shifttakes a tuple of words, prefix, and a string, word, and forms a new tuple that has all the words in prefix except the first, and word added to the end.
+
+For the collection of suffixes, the operations we need to perform include adding a new suffix (or increasing the frequency of an existing one), and choosing a random suffix.
+
+Adding a new suffix is equally easy for the list implementation or the histogram. Choosing a random element from a list is easy; choosing from a histogram is harder to do efficiently (see Exercise 13.7).
+
+So far we have been talking mostly about ease of implementation, but there are other factors to consider in choosing data structures. One is run time. Sometimes there is a theoretical reason to expect one data structure to be faster than other; for example, I mentioned that the in operator is faster for dictionaries than for lists, at least when the number of elements is large.
+
+But often you don't know ahead of time which implementation will be faster. One option is to implement both of them and see which is better. This approach is called **benchmarking**. A practical alternative is to choose the data structure that is easiest to implement, and then see if it is fast enough for the intended application. If so, there is no need to go on. If not, there are tools, like the profile module, that can identify the places in a program that take the most time.
+
+The other factor to consider is storage space. For example, using a histogram for the collection of suffixes might take less space because you only have to store each word once, no matter how many times 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 many applications, space is a secondary consideration after run time.
+
+One final thought: in this discussion, I have implied that we should use one data structure for both analysis and generation. But since these are separate phases, it would also be possible to use one structure for analysis and then convert to another structure for generation. This would be a net win if the time saved during generation exceeded the time spent in conversion.
+
+### 13.10 Debugging
+
+When you are debugging a program, and especially if you are working on a hard bug, there are four things to try:
+
+**reading:**: Examine your code, read it back to yourself, and check that it says what you meant to say.
+**running:**: Experiment by making changes and running different versions. Often if you display the right thing at the right place in the program, the problem becomes obvious, but sometimes you have to spend some time to build scaffolding.
+**running:**: Take some time to think! What kind of error is it: syntax, runtime, semantic? What information can you get from the error messages, or from the output of the program? What kind of error could cause the problem you're seeing? What did you change last, before the problem appeared?
+**retreating:**: At some point, the best thing to do is back off, undoing recent changes, until you get back to a program that works and that you understand. Then you can start rebuilding.
+
+Beginning programmers sometimes get stuck on one of these activities and forget the others. Each activity comes with its own failure mode.
+
+For example, reading your code might help if the problem is a typographical error, but not if the problem is a conceptual misunderstanding. If you don't understand what your program does, you can read it 100 times and never see the error, because the error is in your head.
+
+Running experiments can help, especially if you run small, simple tests. But if you run experiments without thinking or reading your code, you might fall into a pattern I call "random walk programming," which is the process of making random changes until the program does the right thing. Needless to say, random walk programming can take a long time.
+
+You have to take time to think. Debugging is like an experimental science. You should have at least one hypothesis about what the problem is. If there are two or more possibilities, try to think of a test that would eliminate one of them.
+
+Taking a break helps with the thinking. So does talking. If you explain the problem to someone else (or even yourself), you will sometimes find the answer before you finish asking the question.
+
+But even the best debugging techniques will fail if there are too many errors, or if the code you are trying to fix is too big and complicated. Sometimes the best option is to retreat, simplifying the program until you get to something that works and that you understand.
+
+Beginning programmers are often reluctant to retreat because they can't stand to delete a line of code (even if it's wrong). If it makes you feel better, copy your program into another file before you start stripping it down. Then you can paste the pieces back in a little bit at a time.
+
+Finding a hard bug requires reading, running, ruminating, and sometimes retreating. If you get stuck on one of these activities, try the others.
+
+### 13.11 Glossary
+
+**deterministic:**:
+
+Pertaining to a program that does the same thing each time it runs, given the same inputs.
+**pseudorandom:**:
+
+Pertaining to a sequence of numbers that appear to be random, but are generated by a deterministic program.
+**default value:**:
+
+The value given to an optional parameter if no argument is provided.
+**override:**:
+
+To replace a default value with an argument.
+**benchmarking:**:
+
+The process of choosing between data structures by implementing alternatives and testing them on a sample of the possible inputs.
+
+### 13.12 Exercises
+
+**Exercise 13.9**.: _The "rank" of a word is its position in a list of words sorted by frequency: the most common word has rank 1, the second most common has rank 2, etc._
+
+_Zipf's law describes a relationship between the ranks and frequencies of words in natural languages ([http://en.wikipedia.org/wiki/Zipf](http://en.wikipedia.org/wiki/Zipf)'s_law). Specifically, it predicts that the frequency, \(f\), of the word with rank \(r\) is:_
+
+\[f=cr^{-s}\]
+
+_where \(s\) and \(c\) are parameters that depend on the language and the text. If you take the logarithm of both sides of this equation, you get:_
+
+\[\log f=\log c-s\log r\]
+
+_So if you plot \(\log f\) versus \(\log r\), you should get a straight line with slope \(-s\) and intercept \(\log c\)._
+
+_Write a program that reads a text from a file, counts word frequencies, and prints one line for each word, in descending order of frequency, with \(\log f\) and \(\log r\). Use the graphing program of your choice to plot the results and check whether they form a straight line. Can you estimate the value of \(s\)?_
+
+_Solution:_[http://thinkpython.com/code/zipf.py_](http://thinkpython.com/code/zipf.py_). To make the plots, you might have to install matplotlib (see [http://matplotlib.sourceforge.net/](http://matplotlib.sourceforge.net/))._
+
+## Chapter 14 Files
+
+### 14.1 Persistence
+
+Most of the programs we have seen so far are transient in the sense that they run for a short time and produce some output, but when they end, their data disappears. If you run the program again, it starts with a clean slate.
+
+Other programs are **persistent**: they run for a long time (or all the time); they keep at least some of their data in permanent storage (a hard drive, for example); and if they shut down and restart, they pick up where they left off.
+
+Examples of persistent programs are operating systems, which run pretty much whenever a computer is on, and web servers, which run all the time, waiting for requests to come in on the network.
+
+One of the simplest ways for programs to maintain their data is by reading and writing text files. We have already seen programs that read text files; in this chapter we will see programs that write them.
+
+An alternative is to store the state of the program in a database. In this chapter I will present a simple database and a module, pickle, that makes it easy to store program data.
+
+### 14.2 Reading and writing
+
+A text file is a sequence of characters stored on a permanent medium like a hard drive, flash memory, or CD-ROM. We saw how to open and read a file in Section 9.1.
+
+To write a file, you have to open it with mode 'w' as a second parameter:
+
+>>> fout = open('output.txt', 'w')
+
+>>> print fout
+
+<open file 'output.txt', mode 'w' at 0xb7eb2410>
+
+If the file already exists, opening it in write mode clears out the old data and starts fresh, so be careful! If the file doesn't exist, a new one is created.
+
+The write method puts data into the file.
+
+#### 14.3 Format operator
+
+The argument of write has to be a string, so if we want to put other values in a file, we have to convert them to strings. The easiest way to do that is with str:
+
+>>> x = 52 >>> fout.write(str(x)) An alternative is to use the **format operator**, %. When applied to integers, % is the modulus operator. But when the first operand is a string, % is the format operator.
+
+The first operand is the **format string**, which contains one or more **format sequences**, which specify how the second operand is formatted. The result is a string.
+
+For example, the format sequence '%d' means that the second operand should be formatted as an integer (d stands for "decimal"):
+
+>>> camels = 42 >>> '%d' % camels '42' The result is the string '42', which is not to be confused with the integer value 42.
+
+A format sequence can appear anywhere in the string, so you can embed a value in a sentence:
+
+>>> 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. Each format sequence is matched with an element of the tuple, in order.
+
+The following example uses '%d' to format an integer, '%g' to format a floating-point number (don't ask why), and '%s' to format a string:
+
+>>> 'In %dy 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, the types of the elements have to match the format sequences:
+
+>>> '%d %d %d' % (1, 2) TypeError: not enough arguments for format string >>> '%d' % 'dollars' TypeError: illegal argument type for built-in operationIn the first example, there aren't enough elements; in the second, the element is the wrong type.
+
+The format operator is powerful, but it can be difficult to use. You can read more about it at [http://docs.python.org/2/library/stdtypes.html#string-formatting](http://docs.python.org/2/library/stdtypes.html#string-formatting).
+
+### 14.4 Filenames and paths
+
+Files are organized into **directories** (also called "folders"). Every running program has a "current directory," which is the default directory for most operations. For example, when you open a file for reading, Python looks for it in the current directory.
+
+The os module provides functions for working with files and directories ("os" stands for "operating system"). os.getcwd returns the name of the current directory:
+
+```
+>>>importos >>>cwd=os.getcwd() >>>printcwd /home/dinsdale
+```
+
+cwd stands for "current working directory." The result in this example is /home/dinsdale, which is the home directory of a user named dinsdale.
+
+A string like cwd that identifies a file is called a **path**. A **relative path** starts from the current directory; an **absolute path** starts from the topmost directory in the file system.
+
+The paths we have seen so far are simple filenames, so they are relative to the current directory. To find the absolute path to a file, you can use os.path.abspath:
+
+```
+>>>os.path.abspath('memo.txt' /home/dinsdale/memo.txt'
+```
+
+os.path.exists checks whether a file or directory exists:
+
+```
+>>>os.path.exists('memo.txt') True
+```
+
+If it exists, os.path.isdir checks whether it's a directory:
+
+```
+>>>os.path.isdir('memo.txt') False >>>os.path.isdir('music') True
+```
+
+Similarly, os.path.isfile checks whether it's a file.
+
+```
+os.listdir returns a list of the files (and other directories) in the given directory:
+``` >>>os.listdir(cwd) ['music', 'photos','memo.txt'] ```
+To demonstrate these functions, the following example "walks" through a directory, prints the names of all the files, and calls itself recursively on all the directories.
+``` defwalk(dirname):  fornameinos.listdir(dirname):  path=os.path.join(dirname, name)
+
+## Chapter 14 Files
+
+### 14.1 Files
+
+Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the F. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the Files. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F. The Files are the most common objects of the F.
+
+_If an error occurs while opening, reading, writing or closing files, your program should catch the exception, print an error message, and exit. Solution: [http://thinkpython.com/code/sed.py._](http://thinkpython.com/code/sed.py._)
+
+### 14.6 Databases
+
+A **database** is a file that is organized for storing data. Most databases are organized like a dictionary in the sense that they map from keys to values. The biggest difference is that the database is on disk (or other permanent storage), so it persists after the program ends.
+
+The module anydbm provides an interface for creating and updating database files. As an example, I'll create a database that contains captions for image files.
+
+Opening a database is similar to opening 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 a database object that can be used (for most operations) like a dictionary. If you create a new item, anydbm updates the database file.
+
+>>> db['cleese.png'] - 'Photo of John Cleese.' When you access one of the items, anydbm reads the file:
+
+>>> print db['cleese.png'] Photo of John Cleese. If you make another assignment to an existing key, anydbm replaces the old 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 iteration with a for statement.
+
+fork key in db:
+
+print key
+
+As with other files, you should close the database when you are done:
+
+>>> db.close()
+
+### 14.7 Pickling
+
+A limitation of anydbm is that the keys and values have to be strings. If you try to use any other type, you get an error.
+
+The pickle module can help. It translates almost any type of object into a string suitable for storage in a database, and then translates strings back into objects.
+
+pickle.dumps takes an object as a parameter and returns a string representation (dumps is short for "dump string"):8.1 The **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** **j**th** 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+
+**Algorithm 10** The _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of the _Maps_ of 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of the _Maps of the If you run this program, it reads itself and prints the number of lines in the file, which is 7. You can also import it like this:
+
+>>> import wc
+
+Now you have a module object wc:
+
+>>> print wc
+
+<module 'wc' from 'wc.py'>
+
+That provides a function called linecount:
+
+>>> wc.linecount('wc.py')
+
+So that's how you write modules in Python.
+
+The only problem with this example is that when you import the module it executes the test code at the bottom. Normally when you import a module, it defines new functions but it doesn't execute them.
+
+Programs that will be imported as modules often use the 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 a script, __name__ has the value __main__; in that case, the test code is executed. Otherwise, if the module is being imported, the test code is skipped.
+
+**Exercise 14.5**.: _Type this example into a file named wc.py and run it as a script. Then run the Python interpreter and import wc. What is the value of __name__ when the module is being imported?_
+
+_Warning: If you import a module that has already been imported, Python does nothing. It does not re-read the file, even if it has changed._
+
+_If you want to reload a module, you can use the built-in function reload, but it can be tricky, so the safest thing to do is restart the interpreter and then import the module again._
+
+### 14.10 Debugging
+
+When you are reading and writing files, you might run into problems with whitespace. These errors can be hard to debug because spaces, tabs and newlines are normally invisible:
+
+>>> s = '1 2\t 3\n 4'
+
+>>> prints
+
+1 2 3
+
+4
+
+The built-in function repr can help. It takes any object as an argument and returns a string representation of the object. For strings, it represents whitespace characters with backslash sequences:
+
+>>> print repr(s)
+
+'1 2\t 3\n 4'This can be helpful for debugging.
+
+One other problem you might run into is that different systems use different characters to indicate the end of a line. Some systems use a newline, represented n. Others use a return character, represented r. Some use both. If you move files between different systems, these inconsistencies might cause problems.
+
+For most systems, there are applications to convert from one format to another. You can find them (and read more about this issue) at [http://en.wikipedia.org/wiki/Newline](http://en.wikipedia.org/wiki/Newline). Or, of course, you could write one yourself.
+
+### 14.11 Glossary
+
+**persistent:**: Pertaining to a program that runs indefinitely and keeps at least some of its data in permanent storage.
+**format operator:**: An operator, X, that takes a format string and a tuple and generates a string that includes the elements of the tuple formatted as specified by the format string.
+**format string:**: A string, used with the format operator, that contains format sequences.
+**format sequence:**: A sequence of characters in a format string, like Xd, that specifies how a value should be formatted.
+**text file:**: A sequence of characters stored in permanent storage like a hard drive.
+**directory:**: A named collection of files, also called a folder.
+**path:**: A string that identifies a file.
+**relative path:**: A path that starts from the current directory.
+**absolute path:**: A path that starts from the topmost directory in the file system.
+**catch:**: To prevent an exception from terminating a program using the try and except statements.
+**database:**: A file whose contents are organized like a dictionary with keys that correspond to values.
+
+### 14.12 Exercises
+
+**Exercise 14.6**.: _The_ urllib _module provides methods for manipulating URLs and downloading information from the web. The following example downloads and prints a secret message from thinkpython.com: import urllib_
+
+conn = urllib.urlopen('[http://thinkpython.com/secret.html](http://thinkpython.com/secret.html)') for line in conn: print line.strip() _Run this code and follow the instructions you see there. Solution: [http://thinkpython.com/code/zip_code.py_](http://thinkpython.com/code/zip_code.py_).
+
+## Chapter 14 Files
+
+## Chapter 15 Classes and objects
+
+Code examples from this chapter are available from [http://thinkpython.com/code/Point1.py](http://thinkpython.com/code/Point1.py); solutions to the exercises are available from [http://thinkpython.com/code/Point1_soln.py](http://thinkpython.com/code/Point1_soln.py).
+
+### 15.1 User-defined types
+
+We have used many of Python's built-in types; now we are going to define a new type. As an example, we will create a type called Point that represents a point in two-dimensional space.
+
+In mathematical notation, points are often written in parentheses with a comma separating the coordinates. For example, \((0,0)\) represents the origin, and \((x,y)\) represents the point \(x\) units to the right and \(y\) units up from the origin.
+
+There are several ways we might represent points in Python:
+
+* We could store the coordinates separately in two variables, \(x\) and \(y\).
+* We could store the coordinates as elements in a list or tuple.
+* We could create a new type to represent points as objects.
+
+Creating a new type is (a little) more complicated than the other options, but it has advantages that will be apparent soon.
+
+A user-defined type is also called a **class**. A class definition looks like this:
+
+class Point(object):  """Reresents 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-in type.
+
+The body is a docstring that explains what the class is for. You can define variables and functions inside a class definition, but we will get back to that later.
+
+Defining a class named Point creates a class object.
+
+#### 15.2 Attributes
+
+You can assign values to an instance using dot notation:
+
+```
+>>>blank.x=3.0 >>>blank.y=4.0
+```
+
+This syntax is similar to the syntax for selecting a variable from a module, such as math.pi or string.whitespace. In this case, though, we are assigning values to named elements of an object. These elements are called **attributes**.
+
+As a noun, "AT-trip-ute" is pronounced with emphasis on the first syllable, as opposed to "a-TRIB-ute," which is a verb.
+
+The following diagram shows the result of these assignments. A state diagram that shows an object and its attributes is called an **object diagram**; see Figure 15.1.
+
+The variable blank refers to a Point object, which contains two attributes. Each attribute refers to a floating-point number.
+
+You can read the value of an attribute using the same syntax:
+
+```
+>>>printblank.y 4.0 >>>x=blank.x >>>printx 3.0
+```
+
+The expression blank.x means, "Go to the object blank refers to and get the value of x." In this case, we assign that value to a variable named x. There is no conflict between the variable x and the attribute x.
+
+You can use dot notation as part of any expression. For example:
+
+Figure 15.1: Object diagram.
+
+* 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ame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame={},frame=={},frame={box.corner = Point() box.corner.x = 0.0 box.corner.y = 0.0 The expression box.corner.x means, "Go to the object box refers to and select the attribute named corner; then go to that object and select the attribute named x."
+
+Figure 15.2 shows the state of this object. An object that is an attribute of another object is **embedded**.
+
+### 15.4 Instances as return values
+
+Functions can return instances. For example, find_center takes a Rectangle as an argument and returns a Point that contains the coordinates of the center of the Rectangle:
+
+def find_center(rect):  p = Point()  p.x = rect.corner.x + rect.width/2.0  p.y = rect.corner.y + rect.height/2.0  return p Here is an example that passes box as an argument and assigns the resulting Point to center:
+
+>>> center = find_center(box) >>> print_point(center) (50.0, 100.0)
+
+### 15.5 Objects are mutable
+
+You can change the state of an object by making an assignment to one of its attributes. For example, to change the size of a rectangle without changing its position, you can modify the values of width and height:
+
+box.width = box.width + 50 box.height = box.width + 100 You can also write functions that modify objects. For example, grow_rectangle takes a Rectangle object and two numbers, dwidth and dheight, and adds the numbers to the width and height of the rectangle:
+
+def grow_rectangle(rect, dwidth, dheight):  rect.width += dwidth  rect.height += dheight
+
+Figure 15.2: Object diagram.
+
+### 15.6 Copying
+
+Aliasing can make a program difficult to read because changes in one place might have unexpected effects in another place. It is hard to keep track of all the variables that might refer to a given object.
+
+Copying an object is often an alternative to aliasing. The copy module contains a function called copy that can duplicate any object:
+
+```
+>>> p1=Point() >>> p1.x=3.0 >>> p1.y=4.0 >>> importcopy >>>p2=copy.copy(p1) p1 and p2 contain the same data, but they are not the same Point. >>>print_point(p1) (3.0, 4.0) >>>print_point(p2) (3.0, 4.0) >>>p1isp2 False >>>p1==p2 False
+```
+
+The is operator indicates that p1 and p2 are not the same object, which is what we expected. But you 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 the same as the is operator; it checks object identity, not object equivalence. This behavior can be changed--we'll see how later.
+
+If you use copy.copy to duplicate a Rectangle, you will find that it copies the Rectangle object but not the embedded Point.
+
+#### 15.7 Debugging
+
+When you start working with objects, you are likely to encounter some new exceptions. If you try to access an attribute that doesn't exist, you get an AttributeError:
+
+```
+>>>p=Point() >>>printp.z AttributeError:Pointinstancehasnoattribute'z'
+```
+
+If you are not sure what type an object is, you can ask:
+
+```
+>>>type(p) <type'_main_Point'>
+```
+
+If you are not sure whether an object has a particular attribute, you can use the built-in function hasattr:
+
+```
+>>>hasattr(p,'x') True >>>hasattr(p,'z') False
+```
+
+Figure 15.3: Object diagram.
+
+The first argument can be any object; the second argument is a _string_ that contains the name of the attribute.
+
+### 15.8 Glossary
+
+**class:**: A user-defined type. A class definition creates a new class object.
+**class object:**: An object that contains information about a user-defined type. The class object can be used to create instances of the type.
+**instance:**: An object that belongs to a class.
+**attribute:**: One of the named values associated with an object.
+**embedded (object):**: An object that is stored as an attribute of another object.
+**shallow copy:**: To copy the contents of an object, including any references to embedded objects; implemented by the copy function in the copy module.
+**deep copy:**: To copy the contents of an object as well as any embedded objects, and any objects embedded in them, and so on; implemented by the deepcopy function in the copy module.
+**object diagram:**: A diagram that shows objects, their attributes, and the values of the attributes.
+
+### 15.9 Exercises
+
+**Exercise 15.4**.: _Swampy (see Chapter 4) provides a module named_ World_, which defines a user-defined type also called_ World_. You can import it like this:_
+
+from swamy.World import World
+
+_Or, depending on how you installed Swampy, like this:_
+
+from World import World
+
+_The following code creates a World object and calls the_ mainloop _method, which waits for the user._
+
+world = World()
+
+world.mainloop()
+
+_A window should appear with a title bar and an empty square. We will use this window to draw Points, Rectangles and other shapes. Add the following lines before calling_ mainloop _and run the program again._
+
+canvas = world.ca(width=500, height=500, background='white')
+
+bbox = [[-150,-100], [150, 100]]
+
+canvas.rectangle(bbox, outline='black', width=2, fill='green4')
+
+_You should see a green rectangle with a black outline. The first line creates a Canvas, which appears in the window as a white square. The Canvas object provides methods like_ rectangle _for drawing various shapes._
+
+bbox _is a list of lists that represents the "bounding box" of the rectangle. The first pair of coordinates is the lower-left corner of the rectangle; the second pair is the upper-right corner._
+
+_You can draw a circle like this:_
+
+## Chapter 15 Classes and objects
+
+### 15.1 Classes and objects
+
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+
+## Chapter 16 Classes and functions
+
+Code examples from this chapter are available from [http://thinkpython.com/code/Time1.py](http://thinkpython.com/code/Time1.py).
+
+### 16.1 Time
+
+As another example of a user-defined type, we'll define a class called Time that records the time of day. The class definition looks like this:
+
+```
+classTime(object): """Representsthetimeofday.
+``` attributes:hour,minute,second """ ```
+We can create a new Time object and assign attributes for hours, minutes, and seconds:
+``` time=Time() time.hour=11 time.minute=59 time.second=30 ```
+
+The state diagram for the Time object looks like Figure 16.1.
+
+**Exercise 16.1**.: _Write a function called print_time that takes a Time object and prints it in the form_ hour:minute:second. _Hint: the format sequence '%.2d' prints an integer using at least two digits, including a leading zero if necessary._
+
+**Exercise 16.2**.: _Write a boolean function called_ is_after _that takes two Time objects,_ t1 _and_ t2_, and returns_ True _if_ t1 _follows_ t2 _chronologically and_ False _otherwise. Challenge: don't use an_ if _statement._
+
+### 16.2 Pure functions
+
+In the next few sections, we'll write two functions that add time values. They demonstrate two kinds of functions: pure functions and modifiers. They also demonstrate a development plan I'll call **prototype and patch**, which is a way of tackling a complex problem by starting with a simple prototype and incrementally dealing with the complications.
+
+## Chapter 16 Classes and functions
+
+### 16.1 Classes and functions
+
+The class of functions is defined in the following way:
+
+```
+defadd_time(t1,t2): sum=Time() sum.hour=t1.hour+t2.hour sum.minute=t1.minute+t2.minute sum.second=t1.second+t2.second returnsum
+```
+
+The function creates a new Time object, initializes its attributes, and returns a reference to the new object. This is called a **pure function** because it does not modify any of the objects passed to it as arguments and it has no effect, like displaying a value or getting user input, other than returning a value.
+
+To test this function, I'll create two Time objects: start contains the start time of a movie, like _Monty Python and the Holy Grail_, and duration contains the run time of the movie, which is one hour 35 minutes.
+
+```
+add_timefiguresoutwhenthemoviewillbedone.
+``` >>>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)
+10:80:00 The result, 10:80:00 might not be what you were hoping for. The problem is that this function does not deal with cases where the number of seconds or minutes adds up to more than sixty. When that happens, we have to "carry" the extra seconds into the minute column or the extra minutes into the hour column.
+
+Here's an improved version:
+
+```
+defadd_time(t1,t2): sum=Time() sum.hour=t1.hour+t2.hour sum.minute=t1.minute+t2.minute sum.second=t1.second+t2.second
+```
+
+Figure 16.1: Object diagram.
+
+* **if** sum.second >= 60: **sum.second -= 60 **sum.minute += 1
+* **if** sum.minute >= 60: **sum.minute -= 60 **sum.hour += 1
+* **return** sum
+
+Although this function is correct, it is starting to get big. We will see a shorter alternative later.
+
+### 16.3 Modifiers
+
+Sometimes it is useful for a function to modify the objects it gets as parameters. In that case, the changes are visible to the caller. Functions that work this way are called **modifiers**.
+
+increment, which adds a given number of seconds to a Time object, can be written naturally as a modifier. Here is a rough draft:
+
+def increment(time, seconds): **time.second += seconds**
+
+ if time.second >= 60: **time.second -= 60**time.minute += 1
+
+ if time.minute >= 60: **time.minute -= 60**time.hour += 1
+
+The first line performs the basic operation; the remainder deals with the special cases we saw before.
+
+Is this function correct? What happens if the parameter seconds is much greater than sixty?
+
+In that case, it is not enough to carry once; we have to keep doing it until time.second is less than sixty. One solution is to replace the if statements with while statements. That would make the function correct, but not very efficient.
+
+**Exercise 16.3**.: _Write a correct version of increment that doesn't contain any loops._
+
+Anything that can be done with modifiers can also be done with pure functions. In fact, some programming languages only allow pure functions. There is some evidence that programs that use pure functions are faster to develop and less error-prone than programs that use modifiers. But modifiers are convenient at times, and functional programs tend to be less efficient.
+
+In general, I recommend that you write pure functions whenever it is reasonable and resort to modifiers only if there is a compelling advantage. This approach might be called a **functional programming style**.
+
+**Exercise 16.4**.: _Write a "pure" version of increment that creates and returns a new Time object rather than modifying the parameter._
+
+### 16.4 Prototyping versus planning
+
+The development plan I am demonstrating is called "prototype and patch." For each function, I wrote a prototype that performed the basic calculation and then tested it, patching errors along the way.
+
+This approach can be effective, especially if you don't yet have a deep understanding of the problem. But incremental corrections can generate code that is unnecessarily complicated--since it deals with many special cases--and unreliable--since it is hard to know if you have found all the errors.
+
+An alternative is **planned development**, in which high-level insight into the problem can make the programming much easier. In this case, the insight is that a Time object is really a three-digit number in base 60 (see [http://en.wikipedia.org/wiki/Sexagesimal](http://en.wikipedia.org/wiki/Sexagesimal).)! The second attribute is the "ones column," the minute attribute is the "sixties column," and the hour attribute is the "thirty-six hundreds column."
+
+When we wrote add_time and increment, we were effectively doing addition in base 60, which is why we had to carry from one column to the next.
+
+This observation suggests another approach to the whole problem--we can convert Time objects to integers and take advantage of the fact that the computer knows how to do integer arithmetic.
+
+Here is a function that converts Times to integers:
+
+```
+deftime_to_int(time): minutes=time.hour*60+time.minute seconds=minutes*60+time.second returnsseconds
+```
+
+And here is the function that converts integers to Times (recall that divmod divides the first argument by the second and returns the quotient and remainder as a tuple).
+
+```
+defint_to_time(seconds): time=Time() minutes,time.second=divmod(seconds,60) time.hour,time.minute=divmod(minutes,60) returntime
+```
+
+You might have to think a bit, and run some tests, to convince yourself that these functions are correct. One way to test them is to check that time_to_int(int_to_time(x)) == x for many values of x. This is an example of a consistency check.
+
+Once you are convinced they are correct, you can use them to rewrite add_time:
+
+```
+defadd_time(t1,t2): seconds=time_to_int(t1)+time_to_int(t2) returnint_to_time(seconds)
+```
+
+This version is shorter than the original, and easier to verify.
+
+**Exercise 16.5**.: _Rewrite_ increment _using_time_to_int _and_int_to_time.
+
+In some ways, converting from base 60 to base 10 and back is harder than just dealing with times. Base conversion is more abstract; our intuition for dealing with time values is better.
+
+But if we have the insight to treat times as base 60 numbers and make the investment of writing the conversion functions (time_to_int and int_to_time), we get a program that is shorter, easier to read and debug, and more reliable.
+
+### 16.5 Debugging
+
+It is also easier to add features later. For example, imagine subtracting two Times to find the duration between them. The naive approach would be to implement subtraction with borrowing. Using the conversion functions would be easier and more likely to be correct.
+
+Ironically, sometimes making a problem harder (or more general) makes it easier (because there are fewer special cases and fewer opportunities for error).
+
+### 16.5 Debugging
+
+A Time object is well-formed if the values of minute and second are between 0 and 60 (including 0 but not 60) and if hour is positive. hour and minute should be integral values, but we might allow second to have a fraction part.
+
+Requirements like these are called **invariants** because they should always be true. To put it a different way, if they are not true, then something has gone wrong.
+
+Writing code to check your invariants can help you detect errors and find their causes. For example, you might have a function like valid_time that takes a Time object and returns False if it violates an invariant:
+
+def valid_time(time) :  if time.hour < 0 or time.minute < 0 or time.second < 0:  return False  if time.minute >= 60 or time.second >= 60:  return False  return True Then at the beginning of each function you could check the arguments to make sure they are valid:
+
+def add_time(t1, t2) :  if not valid_time(t1) or not valid_time(t2) :  raise ValueErrorError('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 it fails:
+
+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 from code that checks for errors.
+
+### 16.6 Glossary
+
+**prototype and patch:**: A development plan that involves writing a rough draft of a program, testing, and correcting errors as they are found.
+**planned development:**: A development plan that involves high-level insight into the problem and more planning than incremental development or prototype development.
+
+## Chapter 16 Classes and functions
+
+## Chapter 17 Classes and methods
+
+Code examples from this chapter are available from [http://thinkpython.com/code/Time2.py](http://thinkpython.com/code/Time2.py).
+
+### 17.1 Object-oriented features
+
+Python is an **object-oriented programming language**, which means that it provides features that support 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 computation is expressed in terms of operations on objects.
+* Each object definition corresponds to some object or concept in the real world, and the functions that operate on that object correspond to the ways real-world objects interact.
+
+For example, the Time class defined in Chapter 16 corresponds to the way people record the time of 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 a rectangle.
+
+So far, we have not taken advantage of the features Python provides to support object-oriented programming. These features are not strictly necessary; most of them provide alternative syntax for things we have already done. But in many cases, the alternative is more concise and more accurately conveys the structure of the program.
+
+For example, in the Time program, there is no obvious connection between the class definition and the function definitions that follow. With some examination, it is apparent that every function takes at least one Time object as an argument.
+
+This observation is the motivation for **methods**; a method is a function that is associated with a particular class. We have seen methods for strings, lists, dictionaries and tuples. In this chapter, we will define methods for user-defined types.
+
+Methods are semantically the same as functions, but there are two syntactic differences:* Methods are defined inside a class definition in order to make the relationship between the class and the method explicit.
+* The syntax for invoking a method is different from the syntax for calling a function.
+
+In the next few sections, we will take the functions from the previous two chapters and transform them into methods. This transformation is purely mechanical; you can do it simply by following a sequence of steps. If you are comfortable converting from one form to another, you will be able to choose the best form for whatever you are doing.
+
+### 17.2 Printing objects
+
+In Chapter 16, we defined a class named Time and in Exercise 16.1, you wrote a function named print_time: class Time(object): """Represents the time of day."""
+
+def print_time(time):  print '%.2d:%.2d:%.2d' % (time.hour, time.minute, time.second) To call this function, you have to pass a Time object as an argument: >>> start = Time() >>> start.hour = 9 >>> start.minute = 45 >>> start.second = 00 >>> print_time(start) 09:45:00 To make print_time a method, all we have to do is move the function definition inside the class definition. Notice the change in indentation.
+
+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 function syntax: >>> Time.print_time(start) 09:45:00 In this use of dot notation, Time is the name of the class, and print_time is the name of the method. start is passed as a parameter.
+
+The second (and more concise) way is to use method syntax: >>> start.print_time() 09:45:00 In this use of dot notation, print_time is the name of the method (again), and start is the object the method is invoked on, which is called the **subject**. Just as the subject of a sentence is what the sentence is about, the subject of a method invocation is what the method is about.
+
+Inside the method, the subject is assigned to the first parameter, so in this case start is assigned to time.
+
+By convention, the first parameter of a method is called self, so it would be more common to write print_time like this:
+
+class Time(object):  def print_time(self):  print '%.2d:%.2d' % (self.hour, self.minute, self.second) The reason for this convention is an implicit metaphor:
+
+* The syntax for a function call, print_time(start), suggests that the function is the active agent. It says something like, "Hey print_time! Here's an object for you to print."
+* In object-oriented programming, the objects are the active agents. A method invocation like start.print_time() says "Hey start! Please print yourself."
+
+This change in perspective might be more polite, but it is not obvious that it is useful. In the examples we have seen so far, it may not be. But sometimes shifting responsibility from the functions onto the objects makes it possible to write more versatile functions, and makes it easier to maintain and reuse code.
+
+**Exercise 17.1**.: _Rewrite time_to_int (from Section 16.4) as a method. It is probably not appropriate to rewrite int_to_time as a method; what object you would invoke it on?_
+
+### 17.3 Another example
+
+Here's a version of increment (from Section 16.3) rewritten as a method:
+
+# 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 that it is a pure function, not a modifier.
+
+Here's how you would invoke increment:
+
+>>> start.print_time()
+
+09:45:00 >>> end = start.increment(1337) >>> end.print_time()
+
+10:07:17 The subject, start, gets assigned to the first parameter, self. The argument, 1337, gets assigned to the second parameter, seconds.
+
+This mechanism can be confusing, especially if you make an error. For example, if you invoke increment with two arguments, you get:
+
+>>> 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. But the subject is also considered an argument, so all together that's three.
+
+### 17.4 A more complicated example
+
+is_after (from Exercise 16.2) is slightly more complicated because it takes two Time objects as parameters. In this case it is conventional to name the first parameter self and the second parameter other:
+
+# inside class Time:
+
+ def is_after(self, other):  return self.time_to_int() > other.time_to_int() To use this method, you have to invoke it on one object and pass the other as an argument: >>> end.is_after(start) True One nice thing about this syntax is that it almost reads like English: "end is after start?"
+
+### 17.5 The init method
+
+The init method (short for "initialization") is a special method that gets invoked when an object is instantiated. Its full name is __init__ (two underscore characters, followed by init, and then two more underscores). An init method for the Time class might look like this:
+
+# inside class Time:
+
+ def __init__(self, hour=0, minute=0, second=0):  self.hour = hour  self.minute = minute  self.second = second It is common for the parameters of __init__ to have the same names as the attributes. The statement  self.hour = hour stores the value of the parameter hour as an attribute of self.
+
+The parameters are optional, so if you call Time with no arguments, you get the default values.
+
+>>> time = Time() >>> time.print_time()
+
+00:00:00
+
+If you provide one argument, it overrides hour:
+
+>>> time = Time (9) >>> time.print_time()
+
+09:00:00
+
+If you provide two arguments, they override hour and minute.
+
+>>> time = Time(9, 45) >>> time.print_time()
+
+09:45:00
+
+And if you provide three arguments, they override all three default values.
+
+**Exercise 17.2**.: _Write an init method for the Point class that takes x and y as optional parameters and assigns them to the corresponding attributes._
+
+### 17.6 The _str_ method
+
+__str__ is a special method, like __init__, that is supposed to return a string representation of an object.
+
+For example, here is a str method for Time objects:
+
+```
+#insideclassTime: def__str__(self): return'%.2d:%.2d:%.2d'%(self.hour,self.minute,self.second)
+```
+
+When you print an object, Python invokes the str method:
+
+```
+```
+```
+09:45:00 ```
+When I write a new class, I almost always start by writing __init__, which makes it easier to instantiate objects, and __str__, which is useful for debugging.
+
+**Exercise 17.3**.: _Write a str method for the Point class. Create a Point object and print it._
+
+### 17.7 Operator overloading
+
+By 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 + operator on Time objects.
+
+Here is what the definition might look like:
+```
+#insideclassTime: def__add__(self,other): seconds=self.time_to_int()+other.time_to_int() returnint_to_time(seconds) ```
+And here is how you could use it:
+```
+
+```
+```
+11:20:00
+```
+
+When you apply the + operator to Time objects, Python invokes __add__. When you print the result, Python invokes __str__. So there is quite a lot happening behind the scenes!
+
+Changing the behavior of an operator so that it works with user-defined types is called **operator overloading**. For every operator in Python there is a corresponding special method, like __add__. For more details, see [http://docs.python.org/2/reference/datamodel.html#specialnames](http://docs.python.org/2/reference/datamodel.html#specialnames).
+
+**Exercise 17.4**.: _Write an_add _method for the Point class._
+
+### 17.8 Type-based dispatch
+
+In the previous section we added two Time objects, but you also might want to add an integer to a Time object. The following is a version of __add__ that checks the type of other and invokes either add_time or increment:
+
+```
+#insideclassTime: def__add__(self,other): ifisinstance(other,Time): returnself.add_time(other) else: returnself.increment(other) defadd_time(self,other): seconds=self.time_to_int()+other.time_to_int() returnint_to_time(seconds) defincrement(self,seconds): seconds+=self.time_to_int() returnint_to_time(seconds)
+```
+
+The built-in function isinstance takes a value and a class object, and returns True if the value is an instance of the class.
+
+If other is a Time object, __add__invokes add_time. Otherwise it assumes that the parameter is a number and invokes increment. This operation is called a **type-based dispatch** because it dispatches the computation to different methods based on the type of the arguments.
+
+Here are examples that use the + operator with different types:
+
+```
+>>>start=Time(9,45) >>>duration=Time(1,35) >>>printstart+duration
+11:20:00 >>>printstart+1337
+10:07:17 Unfortunately, this implementation of addition is not commutative. If the integer is the first operand, you get
+``` >>>print1337+start TypeError:unsupportedoperandtype(s)for+:'int'and'instance' ```
+The problem is, instead of asking the Time object to add an integer, Python is asking an integer to add a Time object, and it doesn't know how to do that. But there is a clever solution for this problem: the special method __add__, which stands for "right-side add." This method is invoked when a Time object appears on the right side of the + operator. Here's the definition:
+```
+#insideclassTime: def__radd__(self,other): returnself.__add__(other) ```
+
+And here's how it's used:* [command={},frame={}
+
+### 17.10 Debugging
+
+It is legal to add attributes to objects at any point in the execution of a program, but if you are a stickler for type theory, it is a dubious practice to have objects of the same type with different attribute sets. It is usually a good idea to initialize all of an object's attributes in the init method.
+
+If you are not sure whether an object has a particular attribute, you can use the built-in function hasattr (see Section 15.7).
+
+Another way to access the attributes of an object is through the special attribute __dict__, which is a dictionary that maps attribute names (as strings) and values:
+
+>> p = Point(3, 4) >> print p.__dict__ {'y': 4, 'x': 3} For purposes of debugging, you might find it useful to keep this function handy:
+
+def print_attributes(obj) :  for attr in obj.__dict__:  print attr, getattr(obj, attr) print_attributes traverses the items in the object's dictionary and prints each attribute name and its corresponding value.
+
+The built-in function getattr takes an object and an attribute name (as a string) and returns the attribute's value.
+
+### 17.11 Interface and implementation
+
+One of the goals of object-oriented design is to make software more maintainable, which means that you can keep the program working when other parts of the system change, and modify the program to meet new requirements.
+
+A design principle that helps achieve that goal is to keep interfaces separate from implementations. For objects, that means that the methods a class provides should not depend on how the attributes are represented.
+
+For example, in this chapter we developed a class that represents a time of day. Methods provided by this class include time_to_int, is_after, and add_time.
+
+We could implement those methods in several ways. The details of the implementation depend on how we represent time. In this chapter, the attributes of a Time object are hour, minute, and second.
+
+As an alternative, we could replace these attributes with a single integer representing the number of seconds since midnight. This implementation would make some methods, like is_after, easier to write, but it makes some methods harder.
+
+After you deploy a new class, you might discover a better implementation. If other parts of the program are using your class, it might be time-consuming and error-prone to change the interface.
+
+But if you designed the interface carefully, you can change the implementation without changing the interface, which means that other parts of the program don't have to change.
+
+#### 17.1.2 Glossary
+
+**object-oriented language:**: A language that provides features, such as user-defined classes and method syntax, that facilitate object-oriented programming.
+**object-oriented programming:**: A style of programming in which data and the operations that manipulate it are organized into classes and methods.
+**method:**: A function that is defined inside a class definition and is invoked on instances of that class.
+**object:**: The object a method is invoked on.
+**operator overloading:**: Changing the behavior of an operator like + so it works with a user-defined type.
+**type-based dispatch:**: A programming pattern that checks the type of an operand and invokes different functions for different types.
+**polymorphic:**: Pertaining to a function that can work with more than one type.
+**information hiding:**: The principle that the interface provided by an object should not depend on its implementation, in particular the representation of its attributes.
+
+### 17.13 Exercises
+
+**Exercise 17.7**.: _This exercise is a cautionary tale about one of the most common, and difficult to find, errors in Python. Write a definition for a class named_Kangaroo _with the following methods:_
+
+1. _An_ __init__ _method that initializes an attribute named_ pouch_contents _to an empty list._
+2. _A method named_ put_in_pouch _that takes an object of any type and adds it to_ pouch_contents_._
+3. \(A\) __str__ _method that returns a string representation of the Kangaroo object and the contents of the pouch._
+
+_Test your code by creating two_Kangaroo _objects, assigning them to variables named_kanga _and_ roo_, and then adding_ roo _to the contents of_ kanga_'s pouch_._2.2 The \(\mathrm{RGB}
+
+## Chapter 18 Inheritance
+
+In this chapter I present classes to represent playing cards, decks of cards, and poker hands. If you don't play poker, you can read about it at [http://en.wikipedia.org/wiki/Poker](http://en.wikipedia.org/wiki/Poker), but you don't have to; I'll tell you what you need to know for the exercises. Code examples from this chapter are available from [http://thinkpython.com/code/Card.py](http://thinkpython.com/code/Card.py).
+
+If you are not familiar with Anglo-American playing cards, you can read about them at [http://en.wikipedia.org/wiki/Playing_cards](http://en.wikipedia.org/wiki/Playing_cards).
+
+### 18.1 Card objects
+
+There are fifty-two cards in a deck, each of which belongs to one of four suits and one of thirteen ranks. The suits are Spades, Hearts, Diamonds, and Clubs (in descending order in bridge). The ranks are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. Depending on the game that you are playing, an Ace may be higher than King or lower than 2.
+
+If we want to define a new object to represent a playing card, it is obvious what the attributes should be: rank and suit. It is not as obvious what type the attributes should be. One possibility is to use strings containing words like 'Spade' for suits and 'Queen' for ranks. One problem with this implementation is that it would not be easy to compare cards to see which had a higher rank or suit.
+
+An alternative is to use integers to **encode** the ranks and suits. In this context, "encode" means that we are going to define a mapping between numbers and suits, or between numbers and ranks. This kind of encoding is not meant to be a secret (that would be "encryption").
+
+For example, this table shows the suits and the corresponding integer codes:
+
+\begin{tabular}{l l l} Spades & \(\mapsto\) & 3 \\ Hearts & \(\mapsto\) & 2 \\ Diamonds & \(\mapsto\) & 1 \\ Clubs & \(\mapsto\) & 0 \\ \end{tabular} This code makes it easy to compare cards; because higher suits map to higher numbers, we can compare suits by comparing their codes.
+
+The mapping for ranks is fairly obvious; each of the numerical ranks maps to the corresponding integer, and for face cards:
+
+\begin{tabular}{l l l} Jack & \(\mapsto\) & 11 \\ Queen & \(\mapsto\) & 12 \\ King & \(\mapsto\) & 13 \\ \end{tabular}
+
+I am using the \(\mapsto\) symbol to make it clear that these mappings are not part of the Python program. They are part of the program design, but they don't appear explicitly in the code.
+
+The class definition for Card looks like this:
+
+class Card(object):  """Represents a standard playing card."""
+
+ def __init__(self, suit=0, rank=2):  self.suit = suit  self.rank = rank As usual, the init method takes an optional parameter for each attribute. The default card is the 2 of Clubs.
+
+To create a Card, you call Card with the suit and rank of the card you want.
+
+queen_of_diamonds = Card(1, 12)
+
+### 18.2 Class attributes
+
+In order to print Card objects in a way that people can easily read, we need a mapping from the integer codes to the corresponding ranks and suits. A natural way to do that is with lists of strings. We assign these lists to **class attributes**:
+
+```
+#insideclassCard:  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'%sof%%%(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 any method, are called class attributes because they are associated with the class object Card.
+
+This term distinguishes them from variables like suit and rank, which are called **instance attributes** because they are associated with a particular instance.
+
+Both kinds of attribute are accessed using dot notation. For example, in __str__, self is a Card object, and self.rank is its rank. Similarly, Card is a class object, and Card.rank_names is a list of strings associated with the class.
+
+Every card has its own suit and rank, but there is only one copy of suit_names and rank_names.
+
+#### 18.3 Comparing cards
+
+For built-in types, there are relational operators (<,>, --, etc.) that compare values and determine when one is greater than, less than, or equal to another. For user-defined types, we can override the behavior of the built-in operators by providing a method named __cmp__.
+
+__cmp__ takes two parameters, self and other, and returns a positive number if the first object is greater, a negative number if the second object is greater, and 0 if they are equal to each other.
+
+The correct ordering for cards is not obvious. For example, which is better, the 3 of Clubs or the 2 of Diamonds? One has a higher rank, but the other has a higher suit. In order to compare cards, you have to decide whether rank or suit is more important.
+
+The answer might depend on what game you are playing, but to keep things simple, we'll make the arbitrary choice that suit is more important, so all of the Spades outrank all of the Diamonds, and so on.
+
+With that decided, we can write __cmp__.
+
+Figure 18.1: Object diagram.
+
+## Chapter 18 Inheritance
+
+### 18.1 The _Cards_
+
+The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_ are the _Cards_ and _Cards_. The _Cards_ are the _Cards_ and _Cards_ are the
+
+### Printing the deck
+
+Here is a __str__ method for Deck:
+
+#inside class Deck:
+
+ def __str__(self):  res = []  for card in self.cards:  res.append(str(card))  return '\n'.join(res) This method demonstrates an efficient way to accumulate a large string: building a list of strings and then using join. The built-in function str invokes the __str__ method on each card and returns the string representation.
+
+Since we invoke join on a newline character, the cards are separated by newlines. Here's what the result looks like:
+
+>> deck = Deck() >> print deck Ace of Clubs
+2 of Clubs
+3 of Clubs...
+10 of Spades Jack of Spades Queen of Spades King of Spades
+
+Even though the result appears on 52 lines, it is one long string that contains newlines.
+
+### Add, remove, shuffle and sort
+
+To deal cards, we would like a method that removes a card from the deck and returns it. The list method pop provides a convenient way to do that:
+
+#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 life "bottom dealing" is frowned upon, but in this context it's ok.
+
+To add a card, we can use the list method append:
+
+#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 a **veneer**. The metaphor comes from woodworking, where it is common to glue a thin layer of good quality wood to the surface of a cheaper piece of wood.
+
+In this case we are defining a "thin" method that expresses a list operation in terms that are appropriate for decks.
+
+As another example, we can write a Deck method named shuffle using the function shuffle from the random module:
+
+```
+#insideclassDeck: defshuffle(self): random.shuffle(self.cards) Don't forget to importrandom. Exercise18.2. Write a Deck method named sort that uses the list method sort to sort the cards in a Deck. sort uses the__cmp__method we defined to determine sort order.
+```
+
+### 18.7 Inheritance
+
+The language feature most often associated with object-oriented programming is **inheritance**. Inheritance is the ability to define a new class that is a modified version of an existing class.
+
+It is called "inheritance" because the new class inherits the methods of the existing class. Extending this metaphor, the existing class is called the **parent** and the new class is called the **child**.
+
+As an example, let's say we want a class to represent a "hand," that is, the set of cards held by one player. A hand is similar to a deck: both are made up of a set of cards, and both require operations like adding and removing cards.
+
+A hand is also different from a deck; there are operations we want for hands that don't make sense for a deck. For example, in poker we might compare two hands to see which one wins. In bridge, we might compute a score for a hand in order to make a bid.
+
+This relationship between classes--similar, but different--lends itself to inheritance.
+
+The definition of a child class is like other class definitions, but the name of the parent class appears in parentheses:
+
+```
+classHand(Deck): """Representsahofplayingcards."""
+```
+
+This definition indicates that Hand inherits from Deck; that means we can use methods like pop_card and add_card for Hands as well as Decks.
+
+Hand also inherits__init__ from Deck, but it doesn't really do what we want: instead of populating the hand with 52 new cards, the init method for Hands should initialize cards with an empty list.
+
+If we provide an init method in the Hand class, it overrides the one in the Deck class:
+
+```
+#insideclassHand: def__init__(self,label='): self.cards=[] self.label=label
+
+So when you create a Hand, Python invokes this init method:
+
+```
+>>>hand=Hand('newhand') >>>printhand.cards [] >>>printhand.label newhand
+```
+
+But the other methods are inherited from Deck, so we can use pop_card and add_card to deal a card:
+
+```
+>>>decl=Deck() >>>card=deck.pop_card() >>>hand.add_card(card) >>>printhandKingofSpades
+```
+
+A natural next step is to encapsulate this code in a method called move_cards:
+
+```
+defmove_cards(self,hand,num):  foriinrange(num):  hand.add_card(self.pop_card()) move_cardstakestwoarguments,aHandobjectandthenumberofcardstodeal.Itmodifiesbothselfandhand,andreturnsNone.
+```
+
+In some games, cards are moved from one hand to another, or from a hand back to the deck. You can use move_cards for any of these operations: self can be either a Deck or a Hand, and hand, despite the name, can also be a Deck.
+
+**Exercise 18.3**.: _Write a Deck method called deal_hands that takes two parameters, the number of hands and the number of cards per hand, and that creates new Hand objects, deals the appropriate number of cards per hand, and returns a list of Hand objects._
+
+Inheritance is a useful feature. Some programs that would be repetitive without inheritance can be written more elegantly with it. Inheritance can facilitate code reuse, since you can customize the behavior of parent classes without having to modify them. In some cases, the inheritance structure reflects the natural structure of the problem, which makes the program easier to understand.
+
+On the other hand, inheritance can make programs difficult to read. When a method is invoked, it is sometimes not clear where to find its definition. The relevant code may be scattered among several modules. Also, many of the things that can be done using inheritance can be done as well or better without it.
+
+### 18.8 Class diagrams
+
+So far we have seen stack diagrams, which show the state of a program, and object diagrams, which show the attributes of an object and their values. These diagrams represent a snapshot in the execution of a program, so they change as the program runs.
+
+They are also highly detailed; for some purposes, too detailed. A class diagram is a more abstract representation of the structure of a program. Instead of showing individual objects, it shows classes and the relationships between them.
+
+There are several kinds of relationship between classes:
+
+* Objects in one class might contain references to objects in another class. For example, each Rectangle contains a reference to a Point, and each Deck contains references to many Cards. This kind of relationship is called **HAS-A**, as in, "a Rectangle has a Point."
+* One class might inherit from another. This relationship is called **IS-A**, as in, "a Hand is a kind of a Deck."
+* One class might depend on another in the sense that changes in one class would require changes in the other.
+
+A **class diagram** is a graphical representation of these relationships. For example, Figure 18.2 shows the relationships between Card, Deck and Hand.
+
+The arrow with a hollow triangle head represents an IS-A relationship; in this case it indicates that Hand inherits from Deck.
+
+The standard arrow head represents a HAS-A relationship; in this case a Deck has references to Card objects.
+
+The star (\(\ast\)) near the arrow head is a **multiplicity**; it indicates how many Cards a Deck has. A multiplicity can be a simple number, like 52, a range, like 5.7 or a star, which indicates that a Deck can have any number of Cards.
+
+A more detailed diagram might show that a Deck actually contains a _list_ of Cards, but built-in types like list and dict are usually not included in class diagrams.
+
+**Exercise 18.4**.: _Read_ TurtleWorld.py, World.py _and_ Gui.py _and draw a class diagram that shows the relationships among the classes defined there._
+
+### 18.9 Debugging
+
+Inheritance can make debugging a challenge because when you invoke a method on an object, you might not know which method will be invoked.
+
+Suppose you are writing a function that works with Hand objects. You would like it to work with all kinds of Hands, like PokerHands, BridgeHands, etc. If you invoke a method like shuffle, you might get the one defined in Deck, but if any of the subclasses override this method, you'll get that version instead.
+
+Any time you are unsure about the flow of execution through your program, the simplest solution is to add print statements at the beginning of the relevant methods. If
+
+Figure 18.2: Class diagram.
+
+## Chapter 18 Inheritance
+
+### 18.1 Glossary
+
+**encode:**: To represent one set of values using another set of values by constructing a mapping between them.
+**class attribute:**: An attribute associated with a class object. Class attributes are defined inside a class definition but outside any method.
+**instance attribute:**: An attribute associated with an instance of a class.
+**veneer:**: A method or function that provides a different interface to another function without doing much computation.
+**inheritance:**: The ability to define a new class that is a modified version of a previously defined class.
+
+**parent class:**: The class from which a child class inherits.
+**child class:**: A new class created by inheriting from an existing class; also called a "sub-class."
+**IS-A relationship:**: The relationship between a child class and its parent class.
+**HAS-A relationship:**: The relationship between two classes where instances of one class contain references to instances of the other.
+**class diagram:**: A diagram that shows the classes in a program and the relationships between them.
+**multiplicity:**: A notation in a class diagram that shows, for a HAS-A relationship, how many references there are to instances of another class.
+
+### 18.12 Exercises
+
+**Exercise 18.6**.: _The following are the possible hands in poker, in increasing order of value (and decreasing order of probability):_
+
+**pair:**: _two cards with the same rank_
+**two pair:**: _two pairs of cards with the same rank_
+**three of a kind:**: _three cards with the same rank_
+**straight:**: _five cards with ranks in sequence (aces can be high or low, so_ Acc-2-3-4-5 _is a straight and so_ is_ 10_-Jack-Queen-King-Ace,_ but_ Queen-King-Ace-2-3 _is not.)_
+**flush:**: _five cards with the same suit_
+**full house:**: _three cards with one rank, two cards with another_
+**four of a kind:**: _four cards with the same rank_
+**straight flush:**: _five cards in sequence (as defined above) and with the same suit_
+
+_The goal of these exercises is to estimate the probability of drawing these various hands._
+
+1. _Download the following files from_ [http://thinkpython.com/code:_](http://thinkpython.com/code:_) \(\mathtt{Card.py}\)__: _A complete version of the_ \(\mathtt{Card}\)_,_ \(\mathtt{Deck}\) _and_ \(\mathtt{Hand}\) _classes in this chapter._ \(\mathtt{PokerHand}\)_.py__: _An incomplete implementation of a class that represents a poker hand, and some code that tests it._
+2. _If you run_ \(\mathtt{PokerHand}\)_.py, it deals seven 7-card poker hands and checks to see if any of them contains a flush. Read this code carefully before you go on._
+3. _Add methods to_ \(\mathtt{PokerHand}\)_.py_ _named_ \(\mathtt{has_{pair}}\)_,_ \(\mathtt{has_{twopair}}\)_,_ \(\mathtt{etc}\)_. that return True or False according to whether or not the hand meets the relevant criteria. Your code should work correctly for "hands" that contain any number of cards (although_ \(5\) _and_ \(7\) _are the most common sizes)._
+4. _Write a method named_ classify _that figures out the highest-value classification for a hand and sets the_ label _attribute accordingly. For example, a 7-card hand might contain a flush and a pair; it should be labeled "flush"._* _When you are convinced that your classification methods are working, the next step is to estimate the probabilities of the various hands. Write a function in_ _PokerHand.py that shuffles a deck of cards, divides it into hands, classifies the hands, and counts the number of times various classifications appear._
+* _Print a table of the classifications and their probabilities. Run your program with larger and larger numbers of hands until the output values converge to a reasonable degree of accuracy. Compare your results to the values at_ [http://en.wikipedia.org/wiki/Hand_rankings_._](http://en.wikipedia.org/wiki/Hand_rankings_._)
+
+_Solution:_[http://thinkpython.com/code/PokerHandSoln.py_._](http://thinkpython.com/code/PokerHandSoln.py_._)
+
+**Exercise 18.7**.: _This exercise uses TurtleWorld from Chapter 4. You will write code that makes Turtles play tag. If you are not familiar with the rules of tag, see_ [http://en.wikipedia.org/wiki/Tag_](http://en.wikipedia.org/wiki/Tag_)(game)_._
+
+1. _Download_ [http://thinkpython.com/code/Wobbler.py](http://thinkpython.com/code/Wobbler.py) and run it. You should see a TurtleWorld with three Turtles. If you press the_ Run _button, the Turtles_ _wander at random._
+2. _Read the code and make sure you understand how it works. The_ _Wobbler class inherits from_ _Turtle_, which means that the_ _Turtle_ _methods_ _lt,_ rt,_ fd _and_ _bk _work on_ _Wobblers._ _The_ _step_ _method gets invoked by TurtleWorld. It invokes_ steer_, which turns the Turtle in the desired direction,_ wobble_, which makes a random turn in proportion to the Turtle's clumsiness, and_ move_, which moves forward a few pixels, depending on the Turtle's speed._
+3. _Create a file named_ _Tagger.py_. Import everything from_ Wobbler_, then define a class named_ _Tagger_ that inherits from_ Wobbler_. Call_ make_world _passing the_ Tagger _class object as an argument._
+4. _Add a_ steer _method to_ Tagger _to override the one in_ Wobbler_. As a starting place, write a version that always points the Turtle toward the origin. Hint: use the math function_ at an _and the Turtle attributes_ x_,_ y _and_ heading_._
+5. _Modify_ steer _so that the Turtles stay in bounds. For debugging, you might want to use the_ _Step_ _button, which invokes_ step _once on each Turtle._
+6. _Modify_ steer _so that each Turtle points toward its nearest neighbor. Hint: Turtles have an attribute,_ world_, that is a reference to the TurtleWorld they live in, and the TurtleWorld has an attribute,_ animals_, that is a list of all Turtles in the world._
+7. _Modify_ steer _so the Turtles play tag. You can add methods to_ Tagger _and you can override_ steer _and_ _init__, but you may not modify or override_ step_,_ wobble _or_ move_. Also,_ steer _is allowed to change the heading of the Turtle but not the position._ _Adjust the rules and your_ steer _method for good quality play; for example, it should be possible for the slow Turtle to tag the faster Turtles eventually._
+
+_Solution:_[http://thinkpython.com/code/Tagger.py_._](http://thinkpython.com/code/Tagger.py_._)
+
+## Chapter 19 Case study: Tkinter
+
+### 19.1 Gui
+
+Most of the programs we have seen so far are text-based, but many programs use **graphical user interfaces**, also known as **GUIs**.
+
+Python provides several choices for writing GUI-based programs, including wxPython, Tkinter, and Qt. Each has pros and cons, which is why Python has not converged on a standard.
+
+The one I will present in this chapter is Tkinter because I think it is the easiest to get started with. Most of the concepts in this chapter apply to the other GUI modules, too.
+
+There are several books and web pages about Tkinter. One of the best online resources is _An Introduction to Tkinter_ by Fredrik Lundh.
+
+I have written a module called Gui.py that comes with Swampy. It provides a simplified interface to the functions and classes in Tkinter. The examples in this chapter are based on this module.
+
+Here is a simple example that creates and displays a Gui:
+
+To create a GUI, you have to import Gui from Swampy:
+
+from swampy.Gui import *
+
+Or, depending on how you installed Swampy, like this:
+
+from Gui import *
+
+Then instantiate a Gui object:
+
+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
+
+#### 19.1.2 The **Frames**
+
+The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. The Frames are the **Frames** of the Frames. 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+
+The value of the command option is a function object, which is known as a **callback** because after you call bu to create the button, the flow of execution "calls back" when the user presses the button.
+
+This kind of flow is characteristic of **event-driven programming**. User actions, like button presses and key strokes, are called **events**. In event-driven programming, the flow of execution is determined by user actions rather than by the programmer.
+
+The challenge of event-driven programming is to construct a set of widgets and callbacks that work correctly (or at least generate appropriate error messages) for any sequence of user actions.
+
+**Exercise 19.1**.: _Write a program that creates a GII with a single button. When the button is pressed it should create a second button. When that button is pressed, it should create a label that says, "Nice job!"._
+
+_What happens if you press the buttons more than once? Solution: [http://thinkpython.com/code/button_demo.py_](http://thinkpython.com/code/button_demo.py_)
+
+### 19.3 Canvas widgets
+
+One of the most versatile widgets is the Canvas, which creates a region for drawing lines, circles and other shapes. If you did Exercise 15.4 you are already familiar with canvases.
+
+The method ca creates a new Canvas:
+
+canvas = g.ca(width=500, height=500) width and height are the dimensions of the canvas in pixels.
+
+After you create a widget, you can still change the values of the options with the config method. For example, the bg option changes the background 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 different implementations of Python, but all implementations provide at least:
+
+white black red green blue cyan yellow magenta
+
+Shapes on a Canvas are called **items**. For example, the Canvas method circle draws (you guessed it) a circle:
+
+item = canvas.circle([0,0], 100, fill='red') The first argument is a coordinate pair that specifies the center of the circle; the second is the radius.
+
+Gui.py provides a standard Cartesian coordinate system with the origin at the center of the Canvas and the positive \(y\) axis pointing up. This is different from some other graphics systems where the origin is in the upper left corner, with the \(y\) axis pointing down.
+
+The fill option specifies that the circle should be filled in with red.
+
+The return value from circle is an Item object that provides methods for modifying the item on the canvas. For example, you can use config to change any of the circle's options:* **The \(\mathtt{get}\) method returns the contents of the Entry (which may have been changed by the user):**
+
+```
+>>entry.get() 'Defaulttext.'
+```
+
+**tecreates a Text widget:**
+
+``` text=g.te(width=100,height=5) widthandheightarethedimensionsofthewidgetincharactersandlines.insertputstextEND is a special index that indicates the last character in the Text widget.
+
+You can also specify a character using a dotted index, like 1.1, which has the line number before the dot and the column number after. The following example adds the letters 'nother' after the first character of the first line.
+
+>>> text.insert(1.1, 'nother')
+
+The get method reads the text in the widget; it takes a start and end index as arguments. The following example returns all the text in the widget, including the newline 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 first two characters:
+
+>>> 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 it to change the fill color of the circle. Use config to modify the existing circle; don't create a new one._
+
+_Your program should handle the case where the user tries to change the color of a circle that hasn't been created, and the case where the color name is invalid._
+
+_You can see my solution at [http://thinkpython.com/code/circle_demo.py._](http://thinkpython.com/code/circle_demo.py._)
+
+### 19.6 Packing widgets
+
+So far we have been stacking widgets in a single column, but in most GUIs the layout is more complicated. For example, Figure 19.1 shows a simplified version of TurtleWorld (see Chapter 4).
+
+This section presents the code that creates this GUI, broken into a series of steps. You can download the complete example from [http://thinkpython.com/code/SimpleTurtleWorld.py](http://thinkpython.com/code/SimpleTurtleWorld.py).
+
+At the top level, this GUI contains two widgets--a Canvas and a Frame--arranged in a row. So the first step is to create the row.
+
+class SimpleTurtleWorld(TurtleWorld):  """This class is identical to TurtleWorld, but the code that  lays 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 called **packing**.
+
+row creates a row Frame and makes it the "current Frame." Until this Frame is closed or another Frame is created, all subsequent widgets are packed in a row.
+
+Here is the code that creates the Canvas and the column Frame that hold the other widgets:self.canvas = self.ca(width=400, height=400, bg='white') self.col() The first widget in the column is a grid Frame, which contains four buttons arranged two-by-two:
+
+ self.gr(cols=2)  self.bu(text='Print canvas', command=self.canvas.dump)  self.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-to-right, top-to-bottom.
+
+The first button uses self.canvas.dump as a callback; the second uses self.quit. These are **bound methods**, which means they are associated with a particular object. When they are invoked, they are invoked on the object.
+
+The next widget in the column is a row Frame that contains a Button and an Entry:
+
+ self.row([0,1], paddy=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 between widgets. The list [0,1] means that all extra space is allocated to the second widget, which is the Entry. If you run this code and resize the window, you will see that the Entry grows and the Button doesn't.
+
+The option paddy "pads" this row in the \(y\) direction, adding 30 pixels of space above and below.
+
+Figure 19.1: TurtleWorld after running the snowflake code.
+
+endrow ends this row of widgets, so subsequent widgets are packed in the column Frame. Gui.py keeps a stack of Frames:
+
+* When you use row, col or gr to create a Frame, it goes on top of the stack and becomes the current Frame.
+* When you use endrow, endcol or endgr to close a Frame, it gets popped off the stack and the previous Frame on the stack becomes the current Frame.
+
+The method run_file reads the contents of the Entry, uses it as a filename, reads the contents and passes it to run_code. self_inter is an Interpreter object that knows how to take a string and execute it as Python code.
+
+ def run_file(self):  filename = self.en_file.get()  fp = open(filename)  source = fp.read()  self.inter.run_code(source, filename) The last two widgets are a Text widget and a Button:  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 to run_file except that it takes the code from the Text widget instead of from a file:  def run_text(self):  source = self.te_code.get(1.0, END)  self.inter.run_code(source, 'user-provided code>') Unfortunately, the details of widget layout are different in other languages, and in different Python modules. Tkinter alone provides three different mechanisms for arranging widgets. These mechanisms are called **geometry managers**. The one I demonstrated in this section is the "grid" geometry manager; the others are called "pack" and "place".
+
+Fortunately, most of the concepts in this section apply to other GUI modules and other languages.
+
+### 19.7 Menus and Callables
+
+A Menubbutton is a widget that looks like a button, but when pressed it pops up a menu. After the user selects an item, the menu disappears.
+
+Here is code that creates a color selection Menubbutton (you can download it from [http://thinkpython.com/code/menubutton_demo.py](http://thinkpython.com/code/menubutton_demo.py)):
+
+g = Gui() g.la('Selectacolor:')  colors = ['red', 'green', 'blue']  mb = g.mb(text=colors[0])
+
+## Chapter 19 Case study: Tkinter
+
+The first experiment is the first experiment. The second experiment is the first experiment. The second experiment is the first experiment.
+
+The Event object contains information about the type of event and details like the coordinates of the 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. The method canvas_coords translates them to "Canvas coordinates," which are compatible with Canvas methods like circle.
+
+For Entry widgets, it is common to bind the <Return> event, which is triggered when the user presses the Return or Enter key. For example, the following code creates a Button and an Entry.
+
+```
+bu=g.bu('Maketextitem:',make_text) en=g.en() en.bind('Return>',make_text) make_text is called when the Button is pressed or when the user hits Return while typing in the Entry. To make this work, we need a function that can be called as a command (with no arguments) or as an event handler (with an Event as an argument): defmake_text(event=None): text=en.get() item=ca.text([0,0],text) make_text gets the contents of the Entry and displays it as a Text item in the Canvas.
+
+It is also possible to create bindings for Canvas items. The following is a class definition for Draggable, which is a child class of Item that provides bindings that implement drag-and-drop capability.
+``` classDraggable(Item): def__init__(self,item): self.canvas=item.canvas self.tag=item.tag self.bind('<Button-3>',self.select) self.bind('<B3-Motion>',self.drag) self.bind('<Release-3>',self.drop) ```
+The init method takes an Item as a parameter. It copies the attributes of the Item and then creates bindings for three events: a button press, button motion, and button release.
+
+The event handler select stores the coordinates of the current event and the original color of the item, then changes the color to yellow:
+``` defselect(self,event): self.dragx=event.x self.dragy=event.y self.fill=self.cget('fill') self.config(fill='yellow') ```
+cget stands for "get configuration;" it takes the name of an option as a string and returns the current value 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.
+``` defdrag(self,event): dx=event.x-self.dragx* ```
+
+### 19.4 The _Catalog_
+
+The _Catalog_ is a _Catalog_. The _Catalog_ is a _Catalog_.
+
+As the number of widgets grows, it is increasingly difficult to imagine all possible sequences of events. One way to manage this complexity is to encapsulate the state of the system in an object and then consider:
+
+* What are the possible states? In the Circle example, we might consider two states: before and after the user creates the first 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 two buttons, there are four state-event pairs to consider.
+* What can cause a transition from one state to another? In this case, there is a transition when the user creates the first circle.
+
+You might also find it useful to define, and check, invariants that should hold regardless of the sequence of events.
+
+This approach to GUI programming can help you write correct code without taking the time to test every possible sequence of user events!
+
+### 19.10 Glossary
+
+**GUI:**: A graphical user interface.
+**widget:**: One of the elements that makes up a GUI, including buttons, menus, text entry fields, etc.
+**option:**: A value that controls the appearance or function of a widget.
+**keyword argument:**: An argument that indicates the parameter name as part of the function call.
+**callback:**: A function associated with a widget that is called when the user performs an action.
+**bound method:**: A method associated with a particular instance.
+**event-driven programming:**: A style of programming in which the flow of execution is determined by user actions.
+**event:**: A user action, like a mouse click or key press, that causes a GUI to respond.
+**event loop:**: An infinite loop that waits for user actions and responds.
+**item:**: A graphical element on a Canvas widget.
+**bounding box:**: A rectangle that encloses a set of items, usually specified by two opposing corners.
+**pack:**: To arrange and display the elements of a GUI.
+**geometry manager:**: A system for packing widgets.
+**binding:**: An association between a widget, an event, and an event handler. The event handler is called when the event occurs in the widget.
+
+## Chapter 19 Case study: Tkinter
+
+### 19.11 Exercises
+
+**Exercise 19.4**.: _For this exercise, you will write an image viewer. Here is a simple example:_
+
+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.image _puts 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 Python Imaging Library (PIL) to read other files._
+
+_The name of the PIL module is_ Image_, but Tkinter defines an object with the same name. To avoid the conflict, you can use_ import...as _like this:_
+
+import Image as PIL import ImageTk_
+
+_The first line imports_ Image _and gives it the local name_ PIL_. The second line imports_ ImageTk_, which can translate a PIL image into a Tkinter PhotolImage. Here's an example:_
+
+image = PIL.open('allen.png') photo2 = ImageTk.PhotoImage(image) g.la(image=photo2)
+
+1. _Download_image_demo.py, danger.gif _and_ allen.png _from_ http://thinkpython. com/code. Run image_demo.py_. You might have to install_ PIL _and_ ImageTk_. They are probably in your software repository, but if not you can get them from_ [http://pythonware.com/products/pii_._](http://pythonware.com/products/pii_._)
+2. _In_ image_demo.py _change the name of the second_ PhotolImage _from_ photo2 _to_ photo _and run the program again. You should see the second_ PhotolImage _but not the first._ _The problem is that when you reassign_ photo _it overwrites the reference to the first PhotolImage, which then disappears. The same thing happens if you assign a_ PhotolImage _to a local variable; it disappears when the function ends._ _To avoid this problem, you have to store a reference to each_ PhotolImage _you want to keep. You can use a global variable, or store_ PhotolImages _in a data structure or as an attribute of an object._ _This behavior can be frustrating, which is why I am warning you (and why the example image says "Danger!")._
+3. _Starting with this example, write a program that takes the name of a directory and loops through all the files, displaying any files that PIL recognizes as images. You can use a_ try _statement to catch the files_ PIL _doesn't recognize._ _When the user clicks on the image, the program should display the next one._* _PIL provides a variety of methods for manipulating images. You can read about them at_ [http://pythonware.com/library/pi/handbook_](http://pythonware.com/library/pi/handbook_). As a challenge, choose a few of these methods and provide a GUI for applying them to images._
+
+_Solution:_[http://thinkpython.com/code/ImageBrowser.py_._](http://thinkpython.com/code/ImageBrowser.py_._)
+
+**Exercise 19.5**.: _A vector graphics editor is a program that allows users to draw and edit shapes on the screen and generate output files in vector graphics formats like Postscript and SVG._
+
+_Write a simple vector graphics editor using Tkinter. At a minimum, it should allow users to draw lines, circles and rectangles, and it should use_ Canvas.dump _to generate a Postscript description of the contents of the Canvas._
+
+_As a challenge, you could allow users to select and resize items on the Canvas._
+
+**Exercise 19.6**.: _Use Tkinter to write a basic web browser. It should have a Text widget where the user can enter a URL and a Canvas to display the contents of the page._
+
+_You can use the_ urllib _module to download files (see Exercise 14.6) and the_ HTMLparser _module to parse the HTML tags (see_ [http://docs.python.org/2/library/htmlparser.html_](http://docs.python.org/2/library/htmlparser.html_))._
+
+_At a minimum your browser should handle plain text and hyperlinks. As a challenge you could handle background colors, text formatting tags and images._
+
+## Chapter 19 Case study: Tkinter
+
+## Appendix A Debugging
+
+Different kinds of errors can occur in a program, and it is useful to distinguish among them in order to track them down more quickly:
+
+* Syntax errors are produced by Python when it is translating the source code into byte code. They usually indicate that there is something wrong with the syntax of the program. Example: Omitting the colon at the end of a def statement yields the somewhat redundant message SyntaxError: invalid syntax.
+* Runtime errors are produced by the interpreter if something goes wrong while the program is running. Most runtime error messages include information about where the error occurred and what functions were executing. Example: An infinite recursion eventually causes the runtime error "maximum recursion depth exceeded."
+* Semantic errors are problems with a program that runs without producing error messages but doesn't do the right thing. Example: An expression may not be evaluated in the order you expect, yielding an incorrect result.
+
+The first step in debugging is to figure out which kind of error you are dealing with. Although the following sections are organized by error type, some techniques are applicable in more than one situation.
+
+### Syntax errors
+
+Syntax errors are usually easy to fix once you figure out what they are. Unfortunately, the error messages are often not helpful. The most common messages are SyntaxError: invalid syntax and SyntaxError: invalid token, neither of which is very informative.
+
+On the other hand, the message does tell you where in the program the problem occurred. Actually, it tells you where Python noticed a problem, which is not necessarily where the error is. Sometimes the error is prior to the location of the error message, often on the preceding line.
+
+If you are building the program incrementally, you should have a good idea about where the error is. It will be in the last line you added.
+
+If you are copying code from a book, start by comparing your code to the book's code very carefully. Check every character. At the same time, remember that the book might be wrong, so if you see something that looks like a syntax error, it might be.
+
+Here are some ways to avoid the most common syntax errors:
+
+1. Make sure you are not using a Python keyword for a variable name.
+2. Check that you have a colon at the end of the header of every compound statement, including for, while, if, and def statements.
+3. Make sure that any strings in the code have matching quotation marks.
+4. If you have multiline strings with triple quotes (single or double), make sure you have terminated the string properly. An unterminated string may cause an invalid token error at the end of your program, or it may treat the following part of the program as a string until it comes to the next string. In the second case, it might not produce an error message at all!
+5. An unclosed opening operator--(,, or [--makes Python continue with the next line as part of the current statement. Generally, an error occurs almost immediately in the next line.
+6. Check for the classic - instead of -- inside a conditional.
+7. Check the indentation to make sure it lines up the way it is supposed to. Python can handle space and tabs, but if you mix them it can cause problems. The best way to avoid this problem is to use a text editor that knows about Python and generates consistent indentation.
+
+If nothing works, move on to the next section...
+
+#### I keep making changes and it makes no difference.
+
+If the interpreter says there is an error and you don't see it, that might be because you and the interpreter are not looking at the same code. Check your programming environment to make sure that the program you are editing is the one Python is trying to run.
+
+If you are not sure, try putting an obvious and deliberate syntax error at the beginning of the program. Now run it again. If the interpreter doesn't find the new error, you are not running the new code.
+
+There are a few likely culprits:
+
+* You edited the file and forgot to save the changes before running it again. Some programming environments do this for you, but some don't.
+* You changed the name of the file, but you are still running the old name.
+* Something in your development environment is configured incorrectly.
+
+* If you are writing a module and using import, make sure you don't give your module the same name as one of the standard Python modules.
+* If you are using import to read a module, remember that you have to restart the interpreter or use reload to read a modified file. If you import the module again, it doesn'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 new program like "Hello, World!," and make sure you can get a known program to run. Then gradually add the pieces of the original program to the new one.
+
+### A.2 Runtime errors
+
+Once your program is syntactically correct, Python can compile it and at least start running it. What could possibly go wrong?
+
+#### A.2.1 My program does absolutely nothing.
+
+This problem is most common when your file consists of functions and classes but does not actually invoke anything to start execution. This may be intentional if you only plan to import this module to supply classes and functions.
+
+If it is not intentional, make sure that you are invoking a function to start execution, or execute one from the interactive prompt. Also see the "Flow of Execution" section below.
+
+#### A.2.2 My program hangs.
+
+If a program stops and seems to be doing nothing, it is "hanging." Often that means that it is caught in an infinite loop or infinite recursion.
+
+* If there is a particular loop that you suspect is the problem, add a print statement immediately before the loop that says "entering the loop" and another immediately after that says "exiting the loop." Run the program. If you get the first message and not the second, you've got an infinite loop. Go to the "Infinite Loop" section below.
+* Most of the time, an infinite recursion will cause the program to run for a while and then produce a "RuntimeError: Maximum recursion depth exceeded" error. If that happens, go to the "Infinite Recursion" section below. If you are not getting this error but you suspect there is a problem with a recursive method or function, you can still use the techniques in the "Infinite Recursion" section.
+* If neither of those steps works, start testing other loops and other recursive functions and methods.
+* If that doesn't work, then it is possible that you don't understand the flow of execution in your program. Go to the "Flow of Execution" section below.
+
+## Appendix A Debugging
+
+### Infinite Loop
+
+If 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 condition and the value of the condition.
+
+For example:
+
+```
+whilex>0andy<0:  #dosomethingtox  #dosomethingtoy
+``` print"x:",x  print"y:",y  print"condition:",(x>0andy<0) ```
+
+Now 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 be able to see the values of x and y, and you might figure out why they are not being updated correctly.
+
+### Infinite Recursion
+
+Most of the time, an infinite recursion will cause the program to run for a while and then produce a Maximum recursion depth exceeded error.
+
+If you suspect that a function or method is causing an infinite recursion, start by checking to make sure that there is a base case. In other words, there should be some condition that will cause the function or method to return without making a recursive invocation. If not, then you need to rethink the algorithm and identify a base case.
+
+If there is a base case but the program doesn't seem to be reaching it, add a print statement at the beginning of the function or method that prints the parameters. Now when you run the program, you will see a few lines of output every time the function or method is invoked, and you will see the parameters. If the parameters are not moving toward the base case, you will get some ideas about why not.
+
+### Flow of Execution
+
+If you are not sure how the flow of execution is moving through your program, add print statements to the beginning of each function with a message like "entering function foo," where foo is the name of the function.
+
+Now when you run the program, it will print a trace of each function as it is invoked.
+
+#### When I run the program I get an exception.
+
+If something goes wrong during runtime, Python prints a message that includes the name of the exception, the line of the program where the problem occurred, and a traceback.
+
+The traceback identifies the function that is currently running, and then the function that invoked it, and then the function that invoked _that_, and so on. In other words, it traces thesequence of function invocations that got you to where you are. It also includes the line number in your file where each of these calls occurs.
+
+The first step is to examine the place in the program where the error occurred and see if you can figure out what happened. These are some of the most common runtime errors:
+
+**NameError:**: You are trying to use a variable that doesn't exist in the current environment. Remember that local variables are local. You cannot refer to them from outside the function where they are defined.
+**TypeError:**: There are several possible causes:
+
+You are trying to use a value improperly. Example: indexing a string, list, or tuple with something other than an integer.
+
+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 invalid conversion is called for.
+
+You are passing the wrong number of arguments to a function or method. For methods, look at the method definition and check that the first parameter is self. Then look at the method invocation; make sure you are invoking the method on an object with the right type and providing the other arguments correctly.
+**KeyError:**: You are trying to access an element of a dictionary using a key that the dictionary does not contain.
+**AttributeError:**: You are trying to access an attribute or method that does not exist. Check the spelling! You can use dir to list the attributes that do exist.
+
+If an AttributeError indicates that an object has NoneType, that means that it is None. One common cause is forgetting to return a value from a function; if you get to the end of a function without hitting a return statement, it returns None. Another common cause is using the result from a list method, like sort, that returns None.
+**IndexError:**: The index you are using to access a list, string, or tuple is greater than its length minus one. Immediately before the site of the error, add a print statement to display the value of the index and the length of the array. Is the array the right size? Is the index the right value?
+
+The Python debugger (pdb) is useful for tracking down Exceptions because it allows you to examine the state of the program immediately before the error. You can read about pdb at [http://docs.python.org/2/library/pdb.html](http://docs.python.org/2/library/pdb.html).
+
+#### I added so many print statements I get inundated with output.
+
+One of the problems with using print statements for debugging is that you can end up buried in output. There are two ways to proceed: simplify the output or simplify the program.
+
+To simplify the output, you can remove or comment out print statements that aren't helping, or combine them, or format the output so it is easier to understand.
+
+To simplify the program, there are several things you can do. First, scale down the problem the program is working on. For example, if you are searching a list, search a _small_ list. If the program takes input from the user, give it the simplest input that causes the problem.
+
+Second, clean up the program. Remove dead code and reorganize the program to make it as easy to read as possible. For example, if you suspect that the problem is in a deeply nested part of the program, try rewriting that part with simpler structure. If you suspect a large function, try splitting it into smaller functions and testing them separately.
+
+Often the process of finding the minimal test case leads you to the bug. If you find that a program works in one situation but not in another, that gives you a clue about what is going on.
+
+Similarly, rewriting a piece of code can help you find subtle bugs. If you make a change that you think shouldn't affect the program, and it does, that can tip you off.
+
+### Appendix A.3 Semantic errors
+
+In some ways, semantic errors are the hardest to debug, because the interpreter provides no information about what is wrong. Only you know what the program is supposed to do.
+
+The 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 that hard is that computers run so fast.
+
+You will often wish that you could slow the program down to human speed, and with some debuggers you can. But the time it takes to insert a few well-placed print statements is often short compared to setting up the debugger, inserting and removing breakpoints, and "stepping" the program to where the error is occurring.
+
+#### My program doesn't work.
+
+You should ask yourself these questions:
+
+* Is there something the program was supposed to do but which doesn't seem to be happening? Find the section of the code that performs that function and make sure it is executing when you think it should.
+* Is something happening that shouldn't? Find code in your program that performs that function and see if it is executing when it shouldn't.
+* Is a section of code producing an effect that is not what you expected? Make sure that you understand the code in question, especially if it involves invocations to functions or methods in other Python modules. Read the documentation for the functions you invoke. Try them out by writing simple test cases and checking the results.
+
+In order to program, you need to have a mental model of how programs work. If you write a program that doesn't do what you expect, very often the problem is not in the program; it's in your mental model.
+
+### Semantic errors
+
+The best way to correct your mental model is to break the program into its components (usually the functions and methods) and test each component independently. Once you find the discrepancy between your model and reality, you can solve the problem.
+
+Of course, you should be building and testing components as you develop the program. If you encounter a problem, there should be only a small amount of new code that is not known to be correct.
+
+#### i.3.2 I've got a big hairy expression and it doesn't do what I expect.
+
+Writing complex expressions is fine as long as they are readable, but they can be hard to debug. It is often a good idea to break a complex expression into a series of assignments to temporary variables.
+
+For example:
+
+self.hands[i].addCard(self.hands[self.findNeighbor(i)].popCard())
+
+This can be rewritten as:
+
+neighbor = self.findNeighbor(i) pickedCard = self.hands[neighbor].popCard() self.hands[i].addCard(pickedCard)
+
+The 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 display their values.
+
+Another problem that can occur with big expressions is that the order of evaluation may not be what you expect. For example, if you are translating the expression \(\frac{x}{2\pi}\) into Python, you might write:
+
+y = x / 2 * math.pi That is not correct because multiplication and division have the same precedence and are evaluated from left to right. So this expression computes \(x\pi/2\).
+
+A good way to debug expressions is to add parentheses to make the order of evaluation explicit:
+
+y = x / (2 * math.pi) Whenever you are not sure of the order of evaluation, use parentheses. Not only will the program be correct (in the sense of doing what you intended), it will also be more readable for other people who haven't memorized the rules of precedence.
+
+#### i.3.3 I've got a function or method that doesn't return what I expect.
+
+If you have a return statement with a complex expression, you don't have a chance to print the return value before returning. Again, you can use a temporary variable. For example, instead of:
+
+return self.hands[i].removeMatches() you could write:
+
+count = self.hands[i].removeMatches() returncount Now you have the opportunity to display the value of count before returning.
+
+#### I'm really, really stuck and I need help.
+
+First, try getting away from the computer for a few minutes. Computers emit waves that affect the brain, causing these symptoms:
+
+* Frustration and rage.
+* Superstitious beliefs ("the computer hates me") and magical thinking ("the program only works when I wear my hat backward").
+* Random walk programming (the attempt to program by writing every possible program and choosing the one that does the right thing).
+
+If you find yourself suffering from any of these symptoms, get up and go for a walk. When you are calm, think about the program. What is it doing? What are some possible causes of that behavior? When was the last time you had a working program, and what did you do next?
+
+Sometimes it just takes time to find a bug. I often find bugs when I am away from the computer and let my mind wander. Some of the best places to find bugs are trains, showers, and in bed, just before you fall asleep.
+
+#### No, I really need help.
+
+It happens. Even the best programmers occasionally get stuck. Sometimes you work on a program so long that you can't see the error. A fresh pair of eyes is just the thing.
+
+Before you bring someone else in, make sure you are prepared. Your program should be as simple as possible, and you should be working on the smallest input that causes the error. You should have print statements in the appropriate places (and the output they produce should be comprehensible). You should understand the problem well enough to describe it concisely.
+
+When you bring someone in to help, be sure to give them the information they need:
+
+* If there is an error message, what is it and what part of the program does it indicate?
+* What was the last thing you did before this error occurred? What were the last lines of code that you wrote, or what is the new test case that fails?
+* What have you tried so far, and what have you learned?
+
+When you find the bug, take a second to think about what you could have done to find it faster. Next time you see something similar, you will be able to find the bug more quickly.
+
+Remember, the goal is not just to make the program work. The goal is to learn how to make the program work.
+
+## Appendix B Analysis of Algorithms
+
+This appendix is an edited excerpt from _Think Complexity_, by Allen B. Downey, also published by O'Reilly Media (2011). When you are done with this book, you might want to move on to that one.
+
+**Analysis of algorithms** is a branch of computer science that studies the performance of algorithms, especially their run time and space requirements. See [http://en.wikipedia.org/wiki/Analysis_of_algorithms](http://en.wikipedia.org/wiki/Analysis_of_algorithms).
+
+The practical goal of algorithm analysis is to predict the performance of different algorithms in order to guide design decisions.
+
+During the 2008 United States Presidential Campaign, candidate Barack Obama was asked to perform an impromptu analysis when he visited Google. Chief executive Eric Schmidt jokingly asked him for "the most efficient way to sort a million 32-bit integers." Obama had apparently been tipped off, because he quickly replied, "I think the bubble sort would be the wrong way to go." See [http://www.youtube.com/watch?v=k4RRi_ntQc8](http://www.youtube.com/watch?v=k4RRi_ntQc8).
+
+This is true: bubble sort is conceptually simple but slow for large datasets. The answer Schmidt was probably looking for is "radix sort" ([http://en.wikipedia.org/wiki/Radix_sort](http://en.wikipedia.org/wiki/Radix_sort))1.
+
+Footnote 1: But if you get a question like this in an interview, I think a better answer is, “The fastest way to sort a million integers is to use whatever sort function is provided by the language I’m using. Its performance is good enough for the vast majority of applications, but if it turned out that my application was too slow, I would use a profiler to see where the time was being spent. If it looked like a faster sort algorithm would have a significant effect on performance, then I would look around for a good implementation of radix sort.”
+
+The goal of algorithm analysis is to make meaningful comparisons between algorithms, but there are some problems:
+
+* The relative performance of the algorithms might depend on characteristics of the hardware, so one algorithm might be faster on Machine A, another on Machine B. The general solution to this problem is to specify a **machine model** and analyze the number of steps, or operations, an algorithm requires under a given model.
+* Relative performance might depend on the details of the dataset. For example, some sorting algorithms run faster if the data are already partially sorted; other algorithmsrun slower in this case. A common way to avoid this problem is to analyze the **worst case** scenario. It is sometimes useful to analyze average case performance, but that's usually harder, and it might not be obvious what set of cases to average over.
+* Relative performance also depends on the size of the problem. A sorting algorithm that is fast for small lists might be slow for long lists. The usual solution to this problem is to express run time (or number of operations) as a function of problem size, and to compare the functions **asymptotically** as the problem size increases.
+
+The good thing about this kind of comparison that it lends itself to simple classification of algorithms. For example, if I know that the run time of Algorithm A tends to be proportional to the size of the input, \(n\), and Algorithm B tends to be proportional to \(n^{2}\), then I expect A to be faster than B for large values of \(n\).
+
+This kind of analysis comes with some caveats, but we'll get to that later.
+
+### Order of growth
+
+Suppose you have analyzed two algorithms and expressed their run times in terms of the size of the input: Algorithm A takes \(100n+1\) steps to solve a problem with size \(n\); Algorithm B takes \(n^{2}+n+1\) steps.
+
+The following table shows the run time of these algorithms for different problem sizes:
+
+\begin{tabular}{|r|r|r|} \hline Input & Run time of & Run time of \\ size & Algorithm A & Algorithm B \\ \hline
+10 & 1 001 & 111 \\
+100 & 10 001 & 10 101 \\
+1 000 & 100 001 & 1 001 001 \\
+10 000 & 1 000 001 & \(>10^{10}\) \\ \hline \end{tabular}
+
+At \(n=10\), Algorithm A looks pretty bad; it takes almost 10 times longer than Algorithm B. But for \(n=100\) they are about the same, and for larger values A is much better.
+
+The fundamental reason is that for large values of \(n\), any function that contains an \(n^{2}\) term will grow faster than a function whose leading term is \(n\). The **leading term** is the term with the highest exponent.
+
+For Algorithm A, the leading term has a large coefficient, 100, which is why B does better than A for small \(n\). But regardless of the coefficients, there will always be some value of \(n\) where \(an^{2}>bn\).
+
+The same argument applies to the non-leading terms. Even if the run time of Algorithm A were \(n+100000\), it would still be better than Algorithm B for sufficiently large \(n\).
+
+In general, we expect an algorithm with a smaller leading term to be a better algorithm for large problems, but for smaller problems, there may be a **crossover point** where another algorithm is better. The location of the crossover point depends on the details of the algorithms, the inputs, and the hardware, so it is usually ignored for purposes of algorithmic analysis. But that doesn't mean you can forget about it.
+
+If two algorithms have the same leading order term, it is hard to say which is better; again, the answer depends on the details. So for algorithmic analysis, functions with the same leading term are considered equivalent, even if they have different coefficients.
+
+**Definition 1.1**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.2**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.3**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.4**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.5**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.6**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.7**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.8**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.9**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.10**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.11**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.12**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.13**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.14**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.15**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices. Then \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices.
+
+**Definition 1.16**.: _Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices._
+
+Proof.: Let \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) be a graph with \(n\) vertices and \(\mathcal{G}\) is a graph with \(n\) vertices
+
+## Appendix B Analysis of Algorithms
+
+### Analysis of basic Python operations
+
+Most arithmetic operations are constant time; multiplication usually takes longer than addition and subtraction, and division takes even longer, but these run times don't depend on the magnitude of the operands. Very large integers are an exception; in that case the run time increases with the number of digits.
+
+Indexing operations--reading or writing elements in a sequence or dictionary--are also constant time, regardless of the size of the data structure.
+
+A for loop that traverses a sequence or dictionary is usually linear, as long as all of the operations in the body of the loop are constant time. For example, adding up the elements of a list is linear:
+
+ total = 0  for x int t:  total += x The built-in function sum is also linear because it does the same thing, but it tends to be faster because it is a more efficient implementation; in the language of algorithmic analysis, it has a smaller leading coefficient.
+
+If you use the same loop to "add" a list of strings, the run time is quadratic because string concatenation is linear.
+
+The string method join is usually faster because it is linear in the total length of the strings.
+
+As a rule of thumb, if the body of a loop is in \(O(n^{a})\) then the whole loop is in \(O(n^{a+1})\). The exception is if you can show that the loop exits after a constant number of iterations. If a loop runs \(k\) times regardless of \(n\), then the loop is in \(O(n^{a})\), even for large \(k\).
+
+Multiplying by \(k\) doesn't change the order of growth, but neither does dividing. So if the body of a loop is in \(O(n^{a})\) and it runs \(n/k\) times, the loop is in \(O(n^{a+1})\), even for large \(k\).
+
+Most string and tuple operations are linear, except indexing and len, which are constant time. The built-in functions min and max are linear. The run-time of a slice operation is proportional to the length of the output, but independent of the size of the input.
+
+All string methods are linear, but if the lengths of the strings are bounded by a constant--for example, operations on single characters--they are considered constant time.
+
+Most list methods are linear, but there are some exceptions:
+
+* Adding an element to the end of a list is constant time on average; when it runs out of room it occasionally gets copied to a bigger location, but the total time for \(n\) operations is \(O(n)\), so we say that the "amortized" time for one operation is \(O(1)\).
+* Removing an element from the end of a list is constant time.
+* Sorting is \(O(n\log n)\).
+
+Most dictionary operations and methods are constant time, but there are some exceptions:
+
+* The run time of copy is proportional to the number of elements, but not the size of the elements (it copies references, not the elements themselves).
+
+* The run time of update is proportional to the size of the dictionary passed as a parameter, not the dictionary being updated.
+* keys, values and items are linear because they return new lists; iterkeys, itervalues and iteritems are constant time because they return iterators. But if you loop through the iterators, the loop will be linear. Using the "iter" functions saves some overhead, but it doesn't change the order of growth unless the number of items you access is bounded.
+
+The performance of dictionaries is one of the minor miracles of computer science. We will see how they work in Section B.4.
+
+**Exercise B.2**.: _Read the Wikipedia page on sorting algorithms at [http://en.wikipedia.org/wiki/Sorting_algorithm](http://en.wikipedia.org/wiki/Sorting_algorithm) and answer the following questions:_
+
+1. _What is a "comparison sort?" What is the best worst-case order of growth for a comparison sort? What is the best worst-case order of growth for any sort algorithm?_
+2. _What is the order of growth of bubble sort, and why does Barack Obama think it is "the wrong way to go?"_
+3. _What is the order of growth of radix sort? What preconditions do we need to use it?_
+4. _What is a stable sort and why might it matter in practice?_
+5. _What is the worst sorting algorithm (that has a name)?_
+6. _What sort algorithm does the C library use? What sort algorithm does Python use? Are these algorithms stable? You might have to Google around to find these answers._
+7. _Many of the non-comparison sorts are linear, so why does does Python use an_ \(O(n\log n)\) _comparison sort?_
+
+### Analysis of search algorithms
+
+A **search** is an algorithm that takes a collection and a target item and determines whether the target is in the collection, often returning the index of the target.
+
+The simplest search algorithm is a "linear search," which traverses the items of the collection in order, stopping if it finds the target. In the worst case it has to traverse the entire collection, so the run time is linear.
+
+The in operator for sequences uses a linear search; so do string methods like find and count.
+
+If the elements of the sequence are in order, you can use a **bisection search**, which is \(O(\log n)\). Bisection search is similar to the algorithm you probably use to look a word up in a dictionary (a real dictionary, not the data structure). Instead of starting at the beginning and checking each item in order, you start with the item in the middle and check whether the word you are looking for comes before or after. If it comes before, then you search the first half of the sequence. Otherwise you search the second half. Either way, you cut the number of remaining items in half.
+
+If the sequence has 1,000,000 items, it will take about 20 steps to find the word or conclude that it's not there. So that's about 50,000 times faster than a linear search.
+
+**Exercise B.3**.: _Write a function called_ bisection _that takes a sorted list and a target value and returns the index of the value in the list, if it's there, or_ None _if it's not._
+
+_Or you could read the documentation of the_ bisect _module and use that!_
+
+Bisection search can be much faster than linear search, but it requires the sequence to be in order, which might require extra work.
+
+There is another data structure, called a **hashtable** that is even faster--it can do a search in constant time--and it doesn't require the items to be sorted. Python dictionaries are implemented using hashtables, which is why most dictionary operations, including the in operator, are constant time.
+
+### Hashtables
+
+To explain how hashtables work and why their performance is so good, I start with a simple implementation of a map and gradually improve it until it's a hashtable.
+
+I use Python to demonstrate these implementations, but in real life you wouldn't write code like this in Python; you would just use a dictionary! So for the rest of this chapter, you have to imagine that dictionaries don't exist and you want to implement a data structure that maps from keys to values. The operations you have to implement are:
+
+add(k, v): Add a new item that maps from key k to value v. With a Python dictionary, d, this operation is written d[k] = v.
+
+get(target): Look up and return the value that corresponds to key target. With a Python dictionary, d, this operation is written d[target] or d.get(target).
+
+For now, I assume that each key only appears once. The simplest implementation of this interface uses a list of tuples, where each tuple is a key-value pair.
+
+class LinearMap(object):
+
+ def __init__(self):  self.items = []
+
+ def add(self, k, v):  self.items.append((k, v))
+
+ def get(self, k):  for key, val in self.items:  if key == k:  return val  raise KeyError
+
+add appends a key-value tuple to the list of items, which takes constant time.
+
+get uses a f or loop to search the list: if it finds the target key it returns the corresponding value; otherwise it raises a KeyError. So get is linear.
+
+An alternative is to keep the list sorted by key. Then get could use a bisection search, which is \(O(\log n)\). But inserting a new item in the middle of a list is linear, so this mightnot be the best option. There are other data structures (see [http://en.wikipedia.org/wiki/Red-black_tree](http://en.wikipedia.org/wiki/Red-black_tree)) that can implement add and get in log time, but that's still not as good as constant time, so let's move on.
+
+One way to improve LinearMap is to break the list of key-value pairs into smaller lists. Here's an implementation called BetterMap, which is a list of 100 LinearMaps. As we'll see in a second, the order of growth for get is still linear, but BetterMap is a step on the path toward hashtables:
+
+class BetterMap(object):
+
+ def __init__(self, n=100):  self.maps = []  for i in range(n):  self.maps.append(LinearMap())
+
+ def find_map(self, k):  index = hash(k) % len(self.maps)  return self.maps[index]
+
+ def add(self, k, v):  m = self.find_map(k)  m.add(k, v)
+
+ def get(self, k):  m = self.find_map(k)  return m.get(k)
+
+__init__ makes a list of n LinearMaps.
+
+find_map is used by add and get to figure out which map to put the new item in, or which map to search.
+
+find_map uses the built-in function hash, which takes almost any Python object and returns an integer. A limitation of this implementation is that it only works with hashable keys. Mutable types like lists and dictionaries are unhashable.
+
+Hashable objects that are considered equal return the same hash value, but the converse is not necessarily true: two different objects can return the same hash value.
+
+find_map uses the modulus operator to wrap the hash values into the range from 0 to len(self.maps), so the result is a legal index into the list. Of course, this means that many different hash values will wrap onto the same index. But if the hash function spreads things out pretty evenly (which is what hash functions are designed to do), then we expect \(n/100\) items per LinearMap.
+
+Since the run time of LinearMap.get is proportional to the number of items, we expect BetterMap to be about 100 times faster than LinearMap. The order of growth is still linear, but the leading coefficient is smaller. That's nice, but still not as good as a hashtable.
+
+Here (finally) is the crucial idea that makes hashtables fast: if you can keep the maximum length of the LinearMaps bounded, LinearMap.get is constant time. All you have to do is keep track of the number of items and when the number of items per LinearMap exceeds a threshold, resize the hashtable by adding more LinearMaps.
+
+Here is an implementation of a hashtable:
+
+## Appendix B Analysis of Algorithms
+
+```
+classHashMap(object): def__init__(self): self.maps=BetterMap(2) self.num=0 defget(self,k): returnsself.maps.get(k) defadd(self,k,v): ifself.num==len(self.maps.maps): self.resize() self.maps.add(k,v) self.num+=1 defresize(self): new_maps=BetterMap(self.num*2) forminself.maps.maps: fork,vinn.items: new_maps.add(k,v) self.maps=new_maps
+```
+
+Each HashMap contains a BetterMap;__init__starts with just 2 LinearMaps and initializes num, which keeps track of the number of items.
+
+get just dispatches to BetterMap. The real work happens in add, which checks the number of items and the size of the BetterMap: if they are equal, the average number of items per LinearMap is 1, so it callsresize.
+
+resize make a new BetterMap, twice as big as the previous one, and then "rehashes" the items from the old map to the new.
+
+Rehashing is necessary because changing the number of LinearMaps changes the denominator of the modulus operator in find_map. That means that some objects that used to wrap into the same LinearMap will get split up (which is what we wanted, right?).
+
+Rehashing is linear, soresize is linear, which might seem bad, since I promised that add would be constant time. But remember that we don't have to resize every time, so add is usually constant time and only occasionally linear. The total amount of work to run add\(n\) times is proportional to \(n\), so the average time of each add is constant time!
+
+To see how this works, think about starting with an empty HashTable and adding a sequence of items. We start with 2 LinearMaps, so the first 2 adds are fast (no resizing required). Let's say that they take one unit of work each. The next add requires a resize, so we have to rehash the first two items (let's call that 2 more units of work) and then add the third item (one more unit). Adding the next item costs 1 unit, so the total so far is 6 units of work for 4 items.
+
+The next add costs 5 units, but the next three are only one unit each, so the total is 14 units for the first 8 adds.
+
+The next add costs 9 units, but then we can add 7 more before the next resize, so the total is 30 units for the first 16 adds.
+
+After 32 adds, the total cost is 62 units, and I hope you are starting to see a pattern. After \(n\) adds, where \(n\) is a power of two, the total cost is \(2n-2\) units, so the average work per add is a little less than 2 units. When \(n\) is a power of two, that's the best case; for other values of \(n\) the average work is a little higher, but that's not important. The important thing is that it is \(O(1)\).
+
+Figure B.1 shows how this works graphically. Each block represents a unit of work. The columns show the total work for each add in order from left to right: the first two adds cost 1 units, the third costs 3 units, etc.
+
+The extra work of rehashing appears as a sequence of increasingly tall towers with increasing space between them. Now if you knock over the towers, amortizing the cost of resizing over all adds, you can see graphically that the total cost after \(n\) adds is \(2n-2\).
+
+An important feature of this algorithm is that when we resize the HashTable it grows geometrically; that is, we multiply the size by a constant. If you increase the size arithmetically--adding a fixed number each time--the average time per add is linear.
+
+You can download my implementation of HashMap from http://thinkpython/code/Map.py, but remember that there is no reason to use it; if you want a map, just use a Python dictionary.
+
+Figure B.1: The cost of a hashtable add.
+
+## Appendix B Analysis of Algorithms
+
+## Appendix C
+
+### 1.1 Luminy
+
+Throughout the book, I have used diagrams to represent the state of running programs.
+
+In Section 2.2, we used a state diagram to show the names and values of variables. In Section 3.10 I introduced a stack diagram, which shows one frame for each function call. Each frame shows the parameters and local variables for the function or method. Stack diagrams for recursive functions appear in Section 5.9 and Section 6.5.
+
+Section 10.2 shows what a list looks like in a state diagram, Section 11.4 shows what a dictionary looks like, and Section 12.6 shows two ways to represent tuples.
+
+Section 15.2 introduces object diagrams, which show the state of an object's attributes, and their attributes, and so on. Section 15.3 has object diagrams for Rectangles and their embedded Points. Section 16.1 shows the state of a Time object. Section 18.2 has a diagram that includes a class object and an instance, each with their own attributes.
+
+Finally, Section 18.8 introduces class diagrams, which show the classes that make up a program and the relationships between them.
+
+These diagrams are based on the Unified Modeling Language (UML), which is a standardized graphical language used by software engineers to communicate about program design, especially for object-oriented programs.
+
+UML is a rich language with many kinds of diagrams that represent many kinds of relationship between objects and classes. What I presented in this book is a small subset of the language, but it is the subset most commonly used in practice.
+
+The purpose of this appendix is to review the diagrams presented in the previous chapters, and to introduce Lumpy. Lumpy, which stands for "UML in Python," with some of the letters rearranged, is part of Swamy, which you already installed if you worked on the case study in Chapter 4 or Chapter 19, or if you did Exercise 15.4,
+
+Lumpy uses Python's inspect module to examine the state of a running program and generate object diagrams (including stack diagrams) and class diagrams.
+
+### 1.2 State diagram
+
+Here's an example that uses Lumpy to generate a state diagram.
+
+* [15] M. C. Cacciari, G. P. Salam, and G. Soyez, "The anti-jet clustering algorithm", _JHEP_ **04** (2008) 063, doi:10.1088/1126-6708/2008/04/063, arXiv:0802.1189.
+
+[MISSING_PAGE_POST]
+
+numbers = [17, 123] empty = []
+
+lumpy.object_diagram() Figure C.3 shows the result. Lists are represented by a box that shows the indices mapping to the elements. This representation is slightly misleading, since indices are not actually part of the list, but I think they make the diagram easier to read. The empty list is represented by an empty box.
+
+And here's an example showing the dictionaries from Section 11.4. You can download it from [http://thinkpython.com/code/lumpy_demo4.py](http://thinkpython.com/code/lumpy_demo4.py).
+
+from swampy.Lumpy import Lumpy
+
+lumpy = Lumpy() lumpy.make_reference()
+
+hist = histogram('parrot') inverse = invert_dict(hist)
+
+lumpy.object_diagram() Figure C.4 shows the result. hist is a dictionary that maps from characters (single-letter strings) to integers; inverse maps from integers to lists of strings.
+
+This example generates an object diagram for Point and Rectangle objects, as in Section 15.6. You can download it from [http://thinkpython.com/code/lumpy_demo5.py](http://thinkpython.com/code/lumpy_demo5.py).
+
+import copy from swampy.Lumpy import Lumpy
+
+Figure C.4: Object diagram.
+
+* [15] M. C. C.
+
+But if you are passing functions and classes as parameters, you might want them to appear. This example shows what that looks like; you can download it from [http://thinkpython.com/code/lumpy_demo6.py](http://thinkpython.com/code/lumpy_demo6.py).
+
+import copy from swamy.Lumpy import Lumpy
+
+lumpy = Lumpy() lumpy.make_reference()
+
+class Point(object):  """Represents a point in 2-D space."""
+
+class Rectangle(object):  """Represents arectangle."""
+
+def instantiate(constructor):  """Instantiates a new object."""  obj = constructor()  lumpy.object_diagram()  return obj
+
+point = instantiate(Point)
+
+Figure C.6 shows the result. Since we invoke object_diagram inside a function, we get a stack diagram with a frame for the module-level variables and for the invocation of instantiate.
+
+At the module level, Point and Rectangle refer to class objects (which have type type); instantiate refers to a function object.
+
+This diagram might clarify two points of common confusion: (1) the difference between the class object, Point, and the instance of Point, obj, and (2) the difference between the function object created when instantiate is defined, and the frame created with it is called.
+
+### Class Diagrams
+
+Although I distinguish between state diagrams, stack diagrams and object diagrams, they are mostly the same thing: they show the state of a running program at a point in time.
+
+Class diagrams are different. They show the classes that make up a program and the relationships between them. They are timeless in the sense that they describe the program as a whole, not any particular point in time. For example, if an instance of Class A generally contains a reference to an instance of Class B, we say there is a "HAS-A relationship" between those classes.
+
+Here's an example that shows a HAS-A relationship. You can download it from [http://thinkpython.com/code/lumpy_demo7.py](http://thinkpython.com/code/lumpy_demo7.py).
+
+from swamy.lumpy import Lumpy
+
+lumpy = Lumpy()
+
+lumpy.make_reference()
+
+box = Rectangle() box.width = 100.0 box.height = 200.0 box.corner = Point() box.corner.x = 0.0 box.corner.y = 0.0
+
+lumpy.class_diagram()
+
+Figure C.7 shows the result. Each class is represented with a box that contains the name of the class, any methods the class provides, any class variables, and any instance variables. In this example, Rectangle and Point have instance variables, but no methods or class variables.
+
+The arrow from Rectangle to Point shows that Rectangles contain an embedded Point. In addition, Rectangle and Point both inherit from object, which is represented in the diagram with a triangle-headed arrow.
+
+Figure C.8: Class diagram.
+
+Here's a more complex example using my solution to Exercise 18.6. You can download the code from [http://thinkpython.com/code/lumpy_demo8.py](http://thinkpython.com/code/lumpy_demo8.py); you will also need [http://thinkpython.com/code/PokerHand.py](http://thinkpython.com/code/PokerHand.py).
+
+from swamy.Lumpy import Lumpy
+
+from PokerHand import *
+
+lumpy = Lumpy()
+
+lumpy.make_reference()
+
+deck = Deck()
+
+hand = PokerHand()
+
+deck.move_cards(hand, 7)
+
+lumpy.class_diagram()
+
+Figure C.8 shows the result. PokerHand inherits from Hand, which inherits from Deck. Both Deck and PokerHand have Cards.
+
+This diagram does not show that Hand also has cards, because in the program there are no instances of Hand. This example demonstrates a limitation of Lumpy; it only knows about the attributes and HAS-A relationships of objects that are instantiated.
\ No newline at end of file