How to Think Like a Computer Scientist - Learning with Python, 2008a

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Appendix B Creating a new data type Object-oriented programming languages allow programmers to create new data types that behave much like built-in data types. We will explore this capability by building a Fraction class that works very much like the built-in numeric types: integers, longs and floats. Fractions, also known as rational numbers, are values that can be expressed as a ratio of whole numbers, such as 5/6. The top number is called the numerator and the bottom number is called the denominator. We start by defining a Fraction class with an initialization method that provides the numerator and denominator as integers:
232 Creating a new data type class Fraction: def __init__(self, numerator, denominator=1): self.numerator = numerator self.denominator = denominator The denominator is optional. A Fraction with just one parameter represents a whole number. If the numerator is n, we build the Fraction n/1. Thenextstepistowritea str method that displays fractions in a way that makes sense. The form “numerator/denominator” is natural here: class Fraction: ... def __str__(self): return "%d/%d" % (self.numerator, self.denominator) To test what we have so far, we put it in a file named Fraction.py and import it into the Python interpreter. Then we create a fraction object and print it. >>> from Fraction import Fraction >>> spam = Fraction(5,6) >>> print "The fraction is", spam The fraction is 5/6 As usual, the print command invokes the str method implicitly. B.1 Fraction multiplication We would like to be able to apply the normal addition, subtraction, multiplication, and division operations to fractions. To do this, we can overload the mathematical operators for Fraction objects. We’ll start with multiplication because it is the easiest to implement. To multiply fractions, we create a new fraction with a numerator that is the product of the original numerators and a denominator that is a product of the original denominators. mul is the name Python uses for a method that overloads the * operator: class Fraction: ... def __mul__(self, other): return Fraction(self.numerator*other.numerator, self.denominator*other.denominator) We can test this method by computing the product of two fractions:
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How to Think Like a Computer Scient
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How to Think Like a Computer Scient
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Foreword By David Beazley As an edu
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Preface By Jeff Elkner This book ow
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make instant changes whenever someo
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call (type) out its name.” Parame
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Contributor List To paraphrase the
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• Paul Sleigh found an error in C
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xvii • Roger Sperberg pointed out
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Contents Foreword v Preface vii Con
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Contents xxi 4.7 Nested conditional
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Contents xxiii 8.15 Matrices . . .
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Contents xxv 14.4 A more complicate
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Contents xxvii 19.4 Improved Linked
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Chapter 1 The way of the program Th
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1.2 What is a program? 3 $ python P
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1.3 What is debugging? 5 1.3.2 Runt
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1.4 Formal and natural languages 7
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1.6 Glossary 9 source code: A progr
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Chapter 2 Variables, expressions an
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2.3 Variable names and keywords 13
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2.4 Statements 15 >>> 76trombones =
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2.6 Operators and operands 17 2.6 O
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2.9 Composition 19 On one hand, thi
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2.11 Glossary 21 state diagram: A g
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Chapter 3 Functions 3.1 Function ca
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3.4 Math functions 25 >>> minute =
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3.6 Adding new functions 27 problem
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3.7 Definitions and use 29 3.7 Defi
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3.10 Variables and parameters are l
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3.12 Functions with results 33 The
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3.13 Glossary 35 local variable: A
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Chapter 4 Conditionals and recursio
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4.4 Conditional execution 39 In gen
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4.7 Nested conditionals 41 Each con
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4.9 Recursion 43 countdown expects
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4.11 Infinite recursion 45 4.11 Inf
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4.13 Glossary 47 block: A group of
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Chapter 5 Fruitful functions 5.1 Re
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5.2 Program development 51 avoid lo
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5.3 Composition 53 3. Once the prog
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5.5 More recursion 55 But the extra
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5.6 Leap of faith 57 __main__ facto
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5.8 Checking types 59 >>> factorial
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Chapter 6 Iteration 6.1 Multiple as
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6.2 The while statement 63 1. Evalu
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6.3 Tables 65 1.0 0.0 2.0 0.6931471
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6.5 Encapsulation and generalizatio
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6.7 Local variables 69 6.7 Local va
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6.9 Functions 71 the function is ca
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Chapter 7 Strings 7.1 A compound da
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7.3 Traversal and the for loop 75 T
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7.6 Strings are immutable 77 Other
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7.9 The string module 79 As an exer
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7.11 Glossary 81 There are other us
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Chapter 8 Lists A list is an ordere
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8.3 List length 85 If you try to re
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8.6 List operations 87 for VARIABLE
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8.9 List deletion 89 >>> list = [
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8.10 Objects and values 91 8.10 Obj
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8.13 List parameters 93 >>> b[0] =
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8.16 Strings and lists 95 might be
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Chapter 9 Tuples 9.1 Mutability and
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9.3 Tuples as return values 99 9.3
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9.6 Counting 101 >>> randomList(8)
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9.7 Many buckets 103 bucketWidth =
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9.9 Glossary 105 9.9 Glossary Assig
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Chapter 10 Dictionaries The compoun
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10.2 Dictionary methods 109 10.2 Di
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10.5 Hints 111 An alternative is to
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10.6 Long integers 113 Using this v
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10.8 Glossary 115 overflow: A numer
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Chapter 11 Files and exceptions Whi
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11.1 Text files 119 The following f
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11.2 Writing variables 121 the str
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11.3 Directories 123 11.3 Directori
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11.5 Exceptions 125 Or trying to op
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11.6 Glossary 127 format sequence:
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Chapter 12 Classes and objects 12.1
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12.3 Instances as arguments 131 con
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12.5 Rectangles 133 >>> p1 = Point(
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12.8 Copying 135 The variables dwid
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12.9 Glossary 137 12.9 Glossary cla
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Chapter 13 Classes and functions 13
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13.3 Modifiers 141 The output of th
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13.5 Prototype development versus p
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13.8 Glossary 145 Similarly, the te
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Chapter 14 Classes and methods 14.1
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14.3 Another example 149 class Time
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14.5 Optional arguments 151 if done
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14.7 Points revisited 153 >>> curre
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14.9 Polymorphism 155 def __mul__(s
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14.10 Glossary 157 Of course, we in
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Chapter 15 Sets of objects 15.1 Com
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15.3 Class attributes and the str m
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15.5 Decks 163 def __cmp__(self, ot
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15.7 Shuffling the deck 165 >>> dec
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15.9 Glossary 167 class Deck: ... d
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Chapter 16 Inheritance 16.1 Inherit
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16.3 Dealing cards 171 16.3 Dealing
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16.6 OldMaidHand class 173 class Ca
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16.7 OldMaidGame class 175 Hand fra
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16.7 OldMaidGame class 177 class Ol
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16.8 Glossary 179 Hand Allen picked
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Page 222 and 223: 18.4 Pushing and popping 193 def po
Page 224 and 225: 18.7 Evaluating postfix 195 Python
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Page 228 and 229: Chapter 19 Queues This chapter pres
Page 230 and 231: 19.3 Performance characteristics 20
Page 232 and 233: 19.5 Priority queue 203 and it is m
Page 234 and 235: 19.6 The Golfer class 205 19.6 The
Page 236 and 237: Chapter 20 Trees Like linked lists,
Page 238 and 239: 20.2 Traversing trees 209 20.2 Trav
Page 240 and 241: 20.4 Tree traversal 211 def printTr
Page 242 and 243: 20.5 Building an expression tree 21
Page 244 and 245: 20.5 Building an expression tree 21
Page 246 and 247: 20.7 The animal tree 217 Are you th
Page 248 and 249: 20.8 Glossary 219 def yes(ques): fr
Page 250 and 251: Appendix A Debugging Different kind
Page 252 and 253: A.2 Runtime errors 223 A.1.1 I can
Page 254 and 255: A.2 Runtime errors 225 If there is
Page 256 and 257: A.3 Semantic errors 227 A.3 Semanti
Page 258 and 259: A.3 Semantic errors 229 return self
Page 262 and 263: B.1 Fraction multiplication 233 >>>
Page 264 and 265: B.4 Comparing fractions 235 This re
Page 266 and 267: B.6 Glossary 237 reduce: To change
Page 268 and 269: Appendix C Recommendations for furt
Page 270 and 271: C.2 Recommended general computer sc
Page 272 and 273: Index Make Way for Ducklings, 75 Py
Page 274 and 275: Index 245 element, 83, 96 embedded
Page 276 and 277: Index 247 well-formed, 189 list del
Page 278 and 279: Index 249 redundancy, 7 reference,
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