Algorithms: A Functional Programming Approach

247 Pages·1999·3.67 MB·English

by  Fethi A. Rabhi

Algorithms: a
functional
•
programm1ng
approach
Secoenddi tion
FethRia bhi
Guy Lapalme
•
TT
Addison-Wesley
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Contents
Preface ix
1 Introduction 1
1.1 Algorithms 1
1.2 Functiolnaanlg uages 5
1.3 Bibliogranpohtiecsa l 10
2 Functiopnraolg rammiinngH askell 11
2.1 Aboutth el anguage 11
2.2 Equatiaonndsf unctions 12
2.3 Basitcy peasn dc onstructypteesd 15
2.4 Lists 18
2.5 Higher-ofrudnecrt ipornoaglr ammitnegc hniques 27
2.6 Algebrtyapiecsa ndp olymorphism 33
2.7 Arrays 40
2.8 Typec lasasnedsc lamsest hods 43
Exercises 48
2.9 Bibliogranpohtiecsa l 51
3 Thee fficienocffy u nctionparlo grams 52
3.1 Reductoirodne r 52
3.2 Analyztihneeg ff icieonfcp yr ograms 56
3.3 Progratmr ansformation 65
3.4 Conclusion 69
Exercises 69
3.5 Bibliogranpohtiecsa l 70
vi Contents
4 Concredtaet tyap es 71
4.1 Lists 71
4.2 Trees 77
4.3 Arrays 82
Exercises 84
4.4 Bibliogranpohtiecsa l 85
5 Abstradcatt tay pes 86
5.1 Introduction 86
5.2 Stacks 87
5.3 Queues 90
5.4 Priorqiuteyu es 92
5.5 Sets 93
5.6 Tables 97
5.7 Binasreya rch trees 99
5.8 Heaps 103
5.9 AVLt reest 107
Exercises 112
5.10B ibliogranpohtiecsa l 113
6 Sorting 114
6.1 Introduction 114
6.2 Comparison-sboarsteidn g 115
6.3 Bassiocr tianlgg orithms 118
6.4 Tree-bassoerdt ing 122
6.5 Efficioefcn ocmyp arison-ablagsoerdi thmst 123
6.6 Representatiosno-rbtaisnegd 129
Exercises 132
6.7 Bibliogranpohtiecsa l 133
7 Grapha lgorithms 135
7.1 Definitainodtn esr minology 135
7.2 The grapAhD T 136
7.3 Depth-fainrdbs rte adth-sfeiarrscth 140
7.4 Topologsiocratl 144
7.5 Minimusmp annitnrge e 146
7.6 Depth-fsierasrttc rhe aesn df orestst 149
7.7 Conclusion 152
Exercises 153
7.8 Bibliogranpohtiecsa l 154
8 Top-dowdne sigtne chniques 155
8.1 Divide-and-conquer 155
8.2 Backtracskeianrgc h 159
8.3 Prioritsye-africrhs t 167
8.4 Greedayl gorithms 170
Contentvsi i
Exercises 174
8.5 Bibliogranpohtiecsa l 176
9 Dynamipcr ogramming 178
9.1 Introduction 178
9.2 Thed ynamipcr ogrammihnigg her-ofrudnecrt ion 180
9.3 Chainmeadt rmiuxl tiplications 181
9.4 Optimbailn asreya rtcrhe es 184
9.5 All-psahiorrst peastth 188
9.6 Thet ravelsianlge sperson 191
9.7 Conclusion 194
Exercises 194
9.8 Bibliogranpohtiecsa l 196
10A dvancetdo pics 197
101. Procensestw orks 197
10.2M onads 202
10 .3 Paralalleglo rithms 207
10 .4 Bibliogranpohtiecsa l 216
Bibliography 218
A Haskeilmlp lementations 227
B Mathematibcaaclk ground 228
B.1 Notation 228
B.2 Logarithms 228
B.3 Summatifoonr mulas 229
B.4 Solvirnegc urreenqcuea tions 229
Index 230

Preface
........................................................................ ..................................................... ....
Puproseg/o als
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widrea nogfea lgoritthhbemo soa,kl sdoi scutshsleei sm itations sotfy lfuen citni onal
dealwiintgh certain problems.
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x Preface
Apporach
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Prefacxei
Ovevriew
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