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44 CHAPTER 1 ■ Fundamentals In this book, we use StdDraw for data analysis and for creating visual representations of algorithms in operation. The table at on the opposite page indicates some possiblities; we will consider many more examples in the text and the exercises throughout the book. The library also supports animation—of course, this topic is treated primarily on the booksite.
1.1 ■ Basic Programming Model 45 data plot implementation (code fragment) result function values int N = 100; StdDraw.setXscale(0, N); StdDraw.setYscale(0, N*N); StdDraw.setPenRadius(.01); for (int i = 1; i
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Many of the designations used by ma
Page 8 and 9: CONTENTS Preface . . . . . . . . .
Page 10 and 11: PREFACE This book is intended to su
Page 12 and 13: Booksite An important feature of th
Page 14 and 15: Acknowledgments This book has been
Page 16 and 17: ONE Fundamentals 1.1 Basic Programm
Page 18 and 19: 4 CHAPTER 1 ■ Fundamentals Algor
Page 20 and 21: 6 CHAPTER 1 ■ Fundamentals of the
Page 22 and 23: 1.1 BASIC PROGRAMMING MODEL Our stu
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Page 26 and 27: 12 CHAPTER 1 ■ Fundamentals To de
Page 28 and 29: 14 CHAPTER 1 ■ Fundamentals State
Page 30 and 31: 16 CHAPTER 1 ■ Fundamentals Short
Page 32 and 33: 18 CHAPTER 1 ■ Fundamentals Ar r
Page 34 and 35: 20 CHAPTER 1 ■ Fundamentals doubl
Page 36 and 37: 22 CHAPTER 1 ■ Fundamentals signa
Page 38 and 39: 24 CHAPTER 1 ■ Fundamentals P ro
Page 40 and 41: 26 CHAPTER 1 ■ Fundamentals Basic
Page 42 and 43: 28 CHAPTER 1 ■ Fundamentals APIs
Page 44 and 45: 30 CHAPTER 1 ■ Fundamentals Our s
Page 46 and 47: 32 CHAPTER 1 ■ Fundamentals inten
Page 48 and 49: 34 CHAPTER 1 ■ Fundamentals St r
Page 50 and 51: 36 CHAPTER 1 ■ Fundamentals stand
Page 52 and 53: 38 CHAPTER 1 ■ Fundamentals conve
Page 54 and 55: 40 CHAPTER 1 ■ Fundamentals Re di
Page 56 and 57: 42 CHAPTER 1 ■ Fundamentals Stand
Page 60 and 61: 46 CHAPTER 1 ■ Fundamentals Binar
Page 62 and 63: 48 CHAPTER 1 ■ Fundamentals White
Page 64 and 65: 50 CHAPTER 1 ■ Fundamentals Persp
Page 66 and 67: 52 CHAPTER 1 ■ Fundamentals Q&A (
Page 68 and 69: 54 CHAPTER 1 ■ Fundamentals EXERC
Page 74 and 75: 60 CHAPTER 1 ■ Fundamentals CREAT
Page 76 and 77: 62 CHAPTER 1 ■ Fundamentals EXPER
Page 78 and 79: 1.2 DATA ABSTRACTION A data type is
Page 80 and 81: 66 CHAPTER 1 ■ Fundamentals ■ I
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Page 86 and 87: 72 CHAPTER 1 ■ Fundamentals Ar ra
Page 88 and 89: 74 CHAPTER 1 ■ Fundamentals Examp
Page 90 and 91: 76 CHAPTER 1 ■ Fundamentals Ge o
Page 92 and 93: 78 CHAPTER 1 ■ Fundamentals Infor
Page 94 and 95: 80 CHAPTER 1 ■ Fundamentals St r
Page 96 and 97: 82 CHAPTER 1 ■ Fundamentals as th
Page 98 and 99: 84 CHAPTER 1 ■ Fundamentals Imple
Page 100 and 101: 86 CHAPTER 1 ■ Fundamentals impli
Page 102 and 103: 88 CHAPTER 1 ■ Fundamentals API,
Page 104 and 105: 90 CHAPTER 1 ■ Fundamentals More
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94 CHAPTER 1 ■ Fundamentals Visua
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96 CHAPTER 1 ■ Fundamentals Data-
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98 CHAPTER 1 ■ Fundamentals Algor
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100 CHAPTER 1 ■ Fundamentals Int
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102 CHAPTER 1 ■ Fundamentals St r
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104 CHAPTER 1 ■ Fundamentals Me m
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106 CHAPTER 1 ■ Fundamentals you
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108 CHAPTER 1 ■ Fundamentals an i
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110 CHAPTER 1 ■ Fundamentals Q &
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114 CHAPTER 1 ■ Fundamentals EXER
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118 CHAPTER 1 ■ Fundamentals CREA
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1.3 BAGS, QUEUES, AND STACKS Severa
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122 CHAPTER 1 ■ Fundamentals Ge n
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124 CHAPTER 1 ■ Fundamentals Bags
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126 CHAPTER 1 ■ Fundamentals enqu
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128 CHAPTER 1 ■ Fundamentals Ar i
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130 CHAPTER 1 ■ Fundamentals is e
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132 CHAPTER 1 ■ Fundamentals StdI
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134 CHAPTER 1 ■ Fundamentals Ge n
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136 CHAPTER 1 ■ Fundamentals Arra
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138 CHAPTER 1 ■ Fundamentals Ite
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140 CHAPTER 1 ■ Fundamentals deta
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142 CHAPTER 1 ■ Fundamentals Link
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144 CHAPTER 1 ■ Fundamentals When
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146 CHAPTER 1 ■ Fundamentals Othe
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148 CHAPTER 1 ■ Fundamentals StdI
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150 CHAPTER 1 ■ Fundamentals Queu
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to be to or be to null null null or
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154 CHAPTER 1 ■ Fundamentals B ag
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156 CHAPTER 1 ■ Fundamentals Over
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158 CHAPTER 1 ■ Fundamentals Q&A
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164 CHAPTER 1 ■ Fundamentals LINK
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166 CHAPTER 1 ■ Fundamentals LINK
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1.4 ANALYSIS OF ALGORITHMS AS peopl
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174 CHAPTER 1 ■ Fundamentals % mo
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176 CHAPTER 1 ■ Fundamentals Anal
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178 CHAPTER 1 ■ Fundamentals So f
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180 CHAPTER 1 ■ Fundamentals Appr
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182 CHAPTER 1 ■ Fundamentals prog
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184 CHAPTER 1 ■ Fundamentals Summ
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186 CHAPTER 1 ■ Fundamentals Orde
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188 CHAPTER 1 ■ Fundamentals stan
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190 CHAPTER 1 ■ Fundamentals prop
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192 CHAPTER 1 ■ Fundamentals Doub
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194 CHAPTER 1 ■ Fundamentals so t
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196 CHAPTER 1 ■ Fundamentals some
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198 CHAPTER 1 ■ Fundamentals run
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200 CHAPTER 1 ■ Fundamentals type
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202 CHAPTER 1 ■ Fundamentals Ar r
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204 CHAPTER 1 ■ Fundamentals Stri
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214 CHAPTER 1 ■ Fundamentals EXPE
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1.5 CASE STUDY: UNION-FIND To illus
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218 CHAPTER 1 ■ Fundamentals conn
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220 CHAPTER 1 ■ Fundamentals data
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222 CHAPTER 1 ■ Fundamentals Impl
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224 CHAPTER 1 ■ Fundamentals 0 Q
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226 CHAPTER 1 ■ Fundamentals Quic
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228 CHAPTER 2 ■ Fundamentals ALGO
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230 CHAPTER 1 ■ Fundamentals quic
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232 CHAPTER 1 ■ Fundamentals quic
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240 CHAPTER 1 ■ Fundamentals EXPE
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TWO Sor t i ng 2.1 Elementary Sorts
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2.1 ELEMENTARY SORTS For our first
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246 CHAPTER 2 ■ Sorting Ce r t if
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248 CHAPTER 2 ■ Sorting Select io
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250 CHAPTER 2 ■ Sorting Inser t i
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252 CHAPTER 2 ■ Sorting More gene
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254 CHAPTER 2 ■ Sorting Comparing
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256 CHAPTER 2 ■ Sorting Co m p a
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258 CHAPTER 2 ■ Sorting h = 4 L E
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260 CHAPTER 2 ■ Sorting input 13-
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262 CHAPTER 2 ■ Sorting can break
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264 CHAPTER 2 ■ Sorting EXERCISES
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266 CHAPTER 2 ■ Sorting CREATIVE
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268 CHAPTER 2 ■ Sorting EXPERIMEN
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2.2 MERGESORT The algorithms that w
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272 CHAPTER 2 ■ Sorting Top-dow n
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274 CHAPTER 2 ■ Sorting term is t
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276 CHAPTER 2 ■ Sorting first sub
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278 CHAPTER 2 ■ Sorting Bottom-up
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280 CHAPTER 2 ■ Sorting Propositi
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282 CHAPTER 2 ■ Sorting than ~ N
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2.3 QUICKSORT The subject of this s
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290 CHAPTER 2 ■ Sorting before du
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292 CHAPTER 2 ■ Sorting Partition
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294 CHAPTER 2 ■ Sorting C N = N
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296 CHAPTER 2 ■ Sorting If your s
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298 CHAPTER 2 ■ Sorting One strai
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300 CHAPTER 2 ■ Sorting equal to
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302 CHAPTER 2 ■ Sorting Q & A Q.
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2.4 PRIORITY QUEUES Many applicatio
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310 CHAPTER 2 ■ Sorting A priorit
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312 CHAPTER 2 ■ Sorting data stru
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314 CHAPTER 2 ■ Sorting Definitio
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316 CHAPTER 2 ■ Sorting violates
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318 CHAPTER 2 ■ Sorting ALGORITHM
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320 CHAPTER 2 ■ Sorting Ar ray re
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322 CHAPTER 2 ■ Sorting M u lti w
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324 CHAPTER 2 ■ Sorting ALGORITHM
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326 CHAPTER 2 ■ Sorting input hea
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328 CHAPTER 2 ■ Sorting Q&A Q. I
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2.5 APPLICATIONS Sorting algorithms
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338 CHAPTER 2 ■ Sorting Pointer s
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340 CHAPTER 2 ■ Sorting Priority
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342 CHAPTER 2 ■ Sorting Which sor
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344 CHAPTER 2 ■ Sorting ■ A dif
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346 CHAPTER 2 ■ Sorting statistic
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348 CHAPTER 2 ■ Sorting A brief s
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350 CHAPTER 2 ■ Sorting example,
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352 CHAPTER 2 ■ Sorting Q & A Q.
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358 CHAPTER 2 ■ Sorting EXPERIMEN
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THREE Se a rch i ng 3.1 Symbol Tabl
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3.1 SYMBOL TABLES The primary purpo
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364 CHAPTER 3 ■ Searching entries
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366 CHAPTER 3 ■ Searching Ordered
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368 CHAPTER 3 ■ Searching Range q
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370 CHAPTER 3 ■ Searching keys va
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372 CHAPTER 3 ■ Searching A symbo
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374 CHAPTER 3 ■ Searching Sequent
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376 CHAPTER 3 ■ Searching charact
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378 CHAPTER 3 ■ Searching Binar y
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380 CHAPTER 3 ■ Searching public
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382 CHAPTER 3 ■ Searching A LG O
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384 CHAPTER 3 ■ Searching method
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386 CHAPTER 3 ■ Searching quickly
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388 CHAPTER 3 ■ Searching Q&A (co
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390 CHAPTER 3 ■ Searching EXERCIS
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392 CHAPTER 3 ■ Searching CREATIV
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394 CHAPTER 3 ■ Searching EXPERIM
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3.2 BINARY SEARCH TREES a subtree I
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398 CHAPTER 3 ■ Searching ALGORIT
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400 CHAPTER 3 ■ Searching success
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402 CHAPTER 3 ■ Searching key val
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404 CHAPTER 3 ■ Searching Proposi
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406 CHAPTER 3 ■ Searching Order-b
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408 CHAPTER 3 ■ Searching go left
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410 CHAPTER 3 ■ Searching availab
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412 CHAPTER 3 ■ Searching Range q
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414 CHAPTER 3 ■ Searching in loga
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3.3 BALANCED SEARCH TREES The algor
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426 CHAPTER 3 ■ Searching inserti
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428 CHAPTER 3 ■ Searching links c
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430 CHAPTER 3 ■ Searching insert
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432 CHAPTER 3 ■ Searching Re d-bl
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434 CHAPTER 3 ■ Searching h less
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436 CHAPTER 3 ■ Searching ■ ■
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438 CHAPTER 3 ■ Searching In summ
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440 CHAPTER 3 ■ Searching insert
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442 CHAPTER 3 ■ Searching Remarka
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444 CHAPTER 3 ■ Searching Propert
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446 CHAPTER 3 ■ Searching 20 comp
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448 CHAPTER 3 ■ Searching Q&A Q.
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3.4 HASH TABLES key hash value a 2
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460 CHAPTER 3 ■ Searching M - 1.
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462 CHAPTER 3 ■ Searching public
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464 CHAPTER 3 ■ Searching key has
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468 CHAPTER 3 ■ Searching 125 = 1
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470 CHAPTER 3 ■ Searching ALGORIT
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472 CHAPTER 3 ■ Searching before
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476 CHAPTER 3 ■ Searching The plo
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3.5 APPLICATIONS From the early day
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488 CHAPTER 3 ■ Searching Our sym
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490 CHAPTER 3 ■ Searching Extendi
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492 CHAPTER 3 ■ Searching Diction
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494 CHAPTER 3 ■ Searching % more
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496 CHAPTER 3 ■ Searching of thin
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498 CHAPTER 3 ■ Searching Inv e r
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500 CHAPTER 3 ■ Searching FileInd
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502 CHAPTER 3 ■ Searching Sparse
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504 CHAPTER 3 ■ Searching array o
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FOUR Graphs 4.1 Undirected Graphs .
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516 CHAPTER 4 ■ Graphs Maps. A pe
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4.1 UNDIRECTED GRAPHS Our stARting
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520 CHAPTER 4 ■ Graphs An acyclic
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522 CHAPTER 4 ■ Graphs Undirected
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524 CHAPTER 4 ■ Graphs Re pres e
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526 CHAPTER 4 ■ Graphs Graph data
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528 CHAPTER 4 ■ Graphs Design pat
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530 CHAPTER 4 ■ Graphs maze graph
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532 CHAPTER 4 ■ Graphs tinyCG.txt
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534 CHAPTER 4 ■ Graphs This basic
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536 CHAPTER 4 ■ Graphs ALGORITHM
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538 CHAPTER 4 ■ Graphs Breadth-fi
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542 CHAPTER 4 ■ Graphs 20% 40% 60
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546 CHAPTER 4 ■ Graphs connected(
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548 CHAPTER 4 ■ Graphs routes.txt
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550 CHAPTER 4 ■ Graphs public sta
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552 CHAPTER 4 ■ Graphs Sy m bo l
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554 CHAPTER 4 ■ Graphs friends ab
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556 CHAPTER 4 ■ Graphs Summary In
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558 CHAPTER 4 ■ Graphs EXERCISES
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562 CHAPTER 4 ■ Graphs CREATIVE P
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564 CHAPTER 4 ■ Graphs EXPERIMENT
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4.2 DIRECTED GRAPHS In directed gra
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568 CHAPTER 4 ■ Graphs Digraph da
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570 CHAPTER 4 ■ Graphs Re achabil
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572 CHAPTER 4 ■ Graphs dfs(0) dfs
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574 CHAPTER 4 ■ Graphs Cycles and
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576 CHAPTER 4 ■ Graphs Cycles in
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578 CHAPTER 4 ■ Graphs When execu
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580 CHAPTER 4 ■ Graphs D e pth- f
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582 CHAPTER 4 ■ Graphs Propositio
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584 CHAPTER 4 ■ Graphs St rong co
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586 CHAPTER 4 ■ Graphs Accordingl
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588 CHAPTER 4 ■ Graphs Kosaraju
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590 CHAPTER 4 ■ Graphs A larger e
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592 CHAPTER 4 ■ Graphs understand
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594 CHAPTER 4 ■ Graphs Summary In
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4.3 MINIMUM SPANNING TREES V tinyEW
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606 CHAPTER 4 ■ Graphs Underlying
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608 CHAPTER 4 ■ Graphs Edge-weigh
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610 CHAPTER 4 ■ Graphs We ighte d
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612 CHAPTER 4 ■ Graphs Compar ing
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614 CHAPTER 4 ■ Graphs Test data.
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616 CHAPTER 4 ■ Graphs ineligible
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618 CHAPTER 4 ■ Graphs After havi
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620 CHAPTER 4 ■ Graphs E ager ver
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624 CHAPTER 4 ■ Graphs next MST e
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626 CHAPTER 4 ■ Graphs 20% The fi
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628 CHAPTER 4 ■ Graphs Perspectiv
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630 CHAPTER 4 ■ Graphs Q&A Q. Do
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4.4 SHORTEST PATHS edge-weighted di
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640 CHAPTER 4 ■ Graphs 0 6->0 1 n
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642 CHAPTER 4 ■ Graphs D i rec te
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644 CHAPTER 4 ■ Graphs V tinyEWD.
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646 CHAPTER 4 ■ Graphs Data struc
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648 CHAPTER 4 ■ Graphs Ve r tex r
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650 CHAPTER 4 ■ Graphs Theoretica
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652 CHAPTER 4 ■ Graphs Dijkst r a
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654 CHAPTER 4 ■ Graphs The implem
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656 CHAPTER 4 ■ Graphs Source-sin
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658 CHAPTER 4 ■ Graphs Acyclic ed
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662 CHAPTER 4 ■ Graphs The figure
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664 CHAPTER 4 ■ Graphs job start
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666 CHAPTER 4 ■ Graphs original j
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668 CHAPTER 4 ■ Graphs V tinyEWDn
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670 CHAPTER 4 ■ Graphs Strawman I
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672 CHAPTER 4 ■ Graphs Queue-base
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676 CHAPTER 4 ■ Graphs tinyEWDn.t
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678 CHAPTER 4 ■ Graphs The exampl
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680 CHAPTER 4 ■ Graphs A r bitra
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682 CHAPTER 4 ■ Graphs Perspectiv
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684 CHAPTER 4 ■ Graphs Q&A Q. Why
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FIVE St r i ngs 5.1 String Sorts .
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696 CHAPTER 5 ■ Strings The plan
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698 CHAPTER 5 ■ Strings We primar
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700 CHAPTER 5 ■ Strings access. W
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5.1 STRING SORTS For many sorting a
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704 CHAPTER 5 ■ Strings i 0 1 2 3
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706 CHAPTER 5 ■ Strings LSD st r
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708 CHAPTER 5 ■ Strings J 6 A
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710 CHAPTER 5 ■ Strings J 6 A
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712 CHAPTER 5 ■ Strings ALGORITHM
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714 CHAPTER 5 ■ Strings input she
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716 CHAPTER 5 ■ Strings Extra spa
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718 CHAPTER 5 ■ Strings When N is
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722 CHAPTER 5 ■ Strings Randomiza
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724 CHAPTER 5 ■ Strings Which str
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726 CHAPTER 5 ■ Strings EXERCISES
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728 CHAPTER 5 ■ Strings EXPERIMEN
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5.2 TRIES As with sorting, we can t
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732 CHAPTER 5 ■ Strings Tr ies In
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734 CHAPTER 5 ■ Strings In s e r
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736 CHAPTER 5 ■ Strings Keys in t
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738 CHAPTER 5 ■ Strings Col l e c
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740 CHAPTER 5 ■ Strings "she" pub
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742 CHAPTER 5 ■ Strings The code
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744 CHAPTER 5 ■ Strings tions is
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746 CHAPTER 5 ■ Strings get("sea"
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748 CHAPTER 5 ■ Strings TST and i
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750 CHAPTER 5 ■ Strings and searc
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752 CHAPTER 5 ■ Strings Which str
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756 CHAPTER 5 ■ Strings CREATIVE
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5.3 SUBSTRING SEARCH A fundamental
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760 CHAPTER 5 ■ Strings public st
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762 CHAPTER 5 ■ Strings text afte
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764 CHAPTER 5 ■ Strings DFA simul
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766 CHAPTER 5 ■ Strings 1 2 3 4 5
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770 CHAPTER 5 ■ Strings Boyer-Mo
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774 CHAPTER 5 ■ Strings Rabin-Kar
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776 CHAPTER 5 ■ Strings Implement
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778 CHAPTER 5 ■ Strings same valu
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780 CHAPTER 5 ■ Strings Q&A Q. Th
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786 CHAPTER 5 ■ Strings EXPERIMEN
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5.4 REGULAR EXPRESSIONS IN many app
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790 CHAPTER 5 ■ Strings Regular e
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792 CHAPTER 5 ■ Strings REs in ap
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794 CHAPTER 5 ■ Strings Nondeter
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796 CHAPTER 5 ■ Strings A A A 0 1
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798 CHAPTER 5 ■ Strings 0 1 2 3 4
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800 CHAPTER 5 ■ Strings Building
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804 CHAPTER 5 ■ Strings Propositi
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5.5 DATA COMPRESSION The world is a
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812 CHAPTER 5 ■ Strings Binary in
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814 CHAPTER 5 ■ Strings public cl
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816 CHAPTER 5 ■ Strings Limitatio
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818 CHAPTER 5 ■ Strings The pract
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820 CHAPTER 5 ■ Strings The same
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822 CHAPTER 5 ■ Strings Run-lengt
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824 CHAPTER 5 ■ Strings public st
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826 CHAPTER 5 ■ Strings Huffman c
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828 CHAPTER 5 ■ Strings private s
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830 CHAPTER 5 ■ Strings Trie cons
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832 CHAPTER 5 ■ Strings trie repr
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834 CHAPTER 5 ■ Strings leaves A
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838 CHAPTER 5 ■ Strings One reaso
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840 CHAPTER 5 ■ Strings input LZW
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844 CHAPTER 5 ■ Strings A LG O R
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846 CHAPTER 5 ■ Strings Q&A Q. Wh
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SIX Context
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854 CONTEXT several advanced contex
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856 CONTEXT advance time to t + dt
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858 CONTEXT resolution (at time t +
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860 CONTEXT Particles. Exercise 6.1
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862 CONTEXT A second twist in the i
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864 CONTEXT Event- b a s e d s i m
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866 CONTEXT B-t re es In Chapter 3,
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868 CONTEXT any. It is convenient t
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870 CONTEXT Representation. As just
Page 886 and 887:
872 CONTEXT ALGORITHM 6.12 B-tree s
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874 CONTEXT this book) that the ave
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876 CONTEXT brute-force solution im
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878 CONTEXT accessed web page. Agai
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880 CONTEXT public class LRS { publ
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882 CONTEXT Implementation. The cod
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884 CONTEXT Improved implementation
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886 CONTEXT Ne twor k-flow algor it
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888 CONTEXT but our discussion appl
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890 CONTEXT public class FlowEdge F
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892 CONTEXT Ford-Fulkerson maxflow
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894 CONTEXT Proposition F. ( Maxflo
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896 CONTEXT Fl ow e d g e d a t a t
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898 CONTEXT ALGORITHM 6.14 Ford-Ful
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900 CONTEXT Shortest augmenting pat
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902 CONTEXT The practical applicati
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904 CONTEXT end up costing linearit
Page 920 and 921:
906 CONTEXT Proposition J. The foll
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908 CONTEXT Proposition K. The foll
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910 CONTEXT Int r actabilit y The a
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912 CONTEXT The crux of the matter
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914 CONTEXT Easy search problems. T
Page 930 and 931:
916 CONTEXT The main question. Nond
Page 932 and 933:
918 CONTEXT Definition. A search pr
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920 CONTEXT Boolean satisfiability.
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922 CONTEXT EXERCISES on collision
Page 938 and 939:
924 CONTEXT EXERCISES on B-Trees 6.
Page 940 and 941:
926 CONTEXT EXERCISES on suffix arr
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928 CONTEXT EXERCISES on maxflow 6.
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930 CONTEXT EXERCISES on reductions
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Index
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934 INDEX cost model 182 divide-and
Page 950 and 951:
936 INDEX Center of a graph 559 Cer
Page 952 and 953:
938 INDEX adjacency-lists represent
Page 954 and 955:
940 INDEX Huffman encoding 830 mini
Page 956 and 957:
942 INDEX using objects 69 variable
Page 958 and 959:
944 INDEX See Mincut problem Minota
Page 960 and 961:
946 INDEX Cycle 547 Date 91, 103, 2
Page 962 and 963:
948 INDEX defined 432 delete the ma
Page 964 and 965:
950 INDEX Draw 82-83 In 41, 82-83 O
Page 966 and 967:
952 INDEX odd cycle detection 562 p
Page 968 and 969:
ALGORITHMS Fundamentals 1.1 Pushdow
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Algorithms

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