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

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Chapter 20 Trees Like linked lists, trees are made up of nodes. A common kind of tree is a binary tree, in which each node contains a reference to two other nodes (possibly null). These references are referred to as the left and right subtrees. Like list nodes, tree nodes also contain cargo. A state diagram for a tree looks like this: tree cargo 1 left right cargo 2 cargo 3 left right left right None None None None To avoid cluttering up the picture, we often omit the Nones. Thetopofthetree(thenodetree refers to) is called the root. In keeping with the tree metaphor, the other nodes are called branches and the nodes at the tips with null references are called leaves. It may seem odd that we draw the picture with the root at the top and the leaves at the bottom, but that is not the strangest thing. To make things worse, computer scientists mix in another metaphor—the family tree. The top node is sometimes called a parent and the nodes it refers to are its children. Nodes with the same parent are called siblings.
208 Trees Finally, there is a geometric vocabulary for talking about trees. We already mentioned left and right, but there is also “up” (toward the parent/root) and “down” (toward the children/leaves). Also, all of the nodes that are the same distance from the root comprise a level of the tree. We probably don’t need three metaphors for talking about trees, but there they are. Like linked lists, trees are recursive data structures because they are defined recursively. A tree is either: • the empty tree, represented by None, or • a node that contains an object reference and two tree references. 20.1 Building trees The process of assembling a tree is similar to the process of assembling a linked list. Each constructor invocation builds a single node. class Tree: def __init__(self, cargo, left=None, right=None): self.cargo = cargo self.left = left self.right = right def __str__(self): return str(self.cargo) The cargo can be any type, but the arguments for left and right should be tree nodes. left and right are optional; the default value is None. To print a node, we just print the cargo. One way to build a tree is from the bottom up. Allocate the child nodes first: left = Tree(2) right = Tree(3) Then create the parent node and link it to the children: tree = Tree(1, left, right); We can write this code more concisely by nesting constructor invocations: >>> tree = Tree(1, Tree(2), Tree(3)) Either way, the result is the tree at the beginning of the chapter.
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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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Page 188 and 189: Chapter 15 Sets of objects 15.1 Com
Page 190 and 191: 15.3 Class attributes and the str m
Page 192 and 193: 15.5 Decks 163 def __cmp__(self, ot
Page 194 and 195: 15.7 Shuffling the deck 165 >>> dec
Page 196 and 197: 15.9 Glossary 167 class Deck: ... d
Page 198 and 199: Chapter 16 Inheritance 16.1 Inherit
Page 200 and 201: 16.3 Dealing cards 171 16.3 Dealing
Page 202 and 203: 16.6 OldMaidHand class 173 class Ca
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Page 212 and 213: 17.3 Lists as collections 183 node1
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Page 216 and 217: 17.8 Wrappers and helpers 187 def r
Page 218 and 219: 17.10 Invariants 189 tail = self.ne
Page 220 and 221: Chapter 18 Stacks 18.1 Abstract dat
Page 222 and 223: 18.4 Pushing and popping 193 def po
Page 224 and 225: 18.7 Evaluating postfix 195 Python
Page 226 and 227: 18.9 Glossary 197 18.9 Glossary abs
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 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 260 and 261: Appendix B Creating a new data type
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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