Artificial Intelligence and Problem Solving

372 Pages·2016·7.39 MB·English

by  Danny Kopec

Artificial
Intelligence
and
Problem Solving
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Artificial
Intelligence
and
Problem Solving
Dr. Danny Kopec
Christopher Pileggi
David Ungar
Shweta Shetty
Mercury Learning and Information
Dulles, Virginia
Boston, Massachusetts
New Delhi
Copyright ©2017 by Mercury Learning and Information LLC. All rights reserved.
Portions of this book appeared in Artificial Intelligence Problems and Their Solutions
(978-1-938549-83-0). ©Copyright 2014. Mercury Learning and Information LLC.
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D. Kopec, C. Pileggi, D. Ungar, & S. Shetty. Artificial Intelligence and Problem Solving.
ISBN: 978-1-944534-58-5
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C
ontents
Preface ������������������������������������������������������������������������������xiii
List of Figures and Tables ��������������������������������������������������xv
Chapter 1: Introduction ���������������������������������������������1
1.1 Goals and Purpose of This Book .........................................1
1.2 Background and Previous Work ..........................................4
1.3 Contributions of This Book .................................................5
1.4 References............................................................................5
Part I: Problem Solving and Traditional Artificial
Intelligence Problems ������������������������������������������������7
Chapter 2: Problem Solving ���������������������������������������9
2.1 Polya’s Five Steps for Problem Solving ...............................9
2.2 Problem-Solving Techniques.............................................14
2.2.1 Heuristics ................................................................22
2.2.2 Additional Heuristics for Problem Solving ...........24
2.3 The Human Window .........................................................25
2.4 Human Window Criteria and Ranking of Solutions .........28
2.5 Classification ......................................................................31
2.6 References..........................................................................33
vi • Artificial Intelligence and Problem Solving
Chapter 3: The Missionaries and
Cannibals Problem ���������������������������������������������������35
3.1 Background ........................................................................35
3.2 Choosing an Appropriate Representation ........................37
3.3 Solution ..............................................................................40
3.4 Human Problem Solving ...................................................42
3.5 Human Window Analysis of Solutions ..............................47
3.5.1 The Most Human Window–Compatible
Solution ...................................................................48
3.5.2 The Least Human Window–Compatible
Solution ...................................................................50
3.6 Best Machine Solution ......................................................52
3.7 Related Problems ...............................................................53
3.8 Playable Program ...............................................................54
3.9 References..........................................................................55
Chapter 4: The 12 Coins Problem ���������������������������57
4.1 Background ........................................................................57
4.2 Solving a Smaller Problem ................................................58
4.3 Solution ..............................................................................62
4.4 Human Problem Solving ...................................................68
4.5 Human Window Analysis of Solutions ..............................69
4.5.1 The Most Human Window–Compatible
Solution ...................................................................71
4.5.2 The Least Human Window–Compatible
Solution ...................................................................71
4.6 Best Machine Solution ......................................................74
4.7 Playable Program ...............................................................75
4.8 References..........................................................................75
Chapter 5: Cryptarithms ������������������������������������������77
5.1 Background ........................................................................77
5.2 Problem-Solving Techniques.............................................78
5.3 Solution ..............................................................................79
5.4 Human Problem Solving ...................................................91
5.5 Human Window Analysis of Solutions ..............................92
5.5.1 The Most Human Window–Compatible
Solution ...................................................................94
Contents • vii
5.5.2 The Least Human Window–Compatible
Solution ...................................................................95
5.6 Best Machine Solution ......................................................96
5.7 Related Problems ...............................................................97
5.8 Playable Program ...............................................................98
5.9 References........................................................................100
Chapter 6: The Red Donkey Puzzle ����������������������101
6.1 Background ......................................................................101
6.2 Solution ............................................................................103
6.2.1 Bidirectional Search .............................................106
6.3 Human Problem Solving .................................................107
6.4 Human Window Analysis of Solutions ............................108
6.4.1 The Most Human Window–Compatible
Solution .................................................................109
6.4.2 The Least Human Window–Compatible
Solution .................................................................112
6.5 Best Machine Solution ....................................................114
6.6 Related Problems .............................................................115
6.7 Playable Program .............................................................115
6.8 References........................................................................116
Chapter 7: The 15 Puzzle ���������������������������������������117
7.1 Background ......................................................................117
7.2 Problem-Solving Techniques...........................................118
7.3 Solution ............................................................................119
7.3.1 Solving the First Row ...........................................120
7.3.2 The Corner Technique.........................................124
7.3.3 Solving the Second Row ......................................126
7.3.4 Solving the Third Row .........................................127
7.3.5 Solving the Fourth Row .......................................130
7.4 Human Window Analysis of Solutions ............................132
7.4.1 The Most Human Window–Compatible
Solution .................................................................134
7.4.2 The Least Human Window–Compatible
Solution .................................................................134
7.5 Best Machine Solution ....................................................136
7.6 Related Problems .............................................................138
7.7 Playable Program .............................................................139
7.8 References........................................................................139
viii • Artificial Intelligence and Problem Solving
Chapter 8: The Knight’s Tour Problem �����������������141
8.1 Background ......................................................................141
8.2 Problem-Solving Techniques...........................................142
8.3 Solution ............................................................................143
8.4 Human Problem Solving .................................................152
8.5 Human Window Analysis of Solutions ............................152
8.5.1 The Most Human Window–Compatible
Solution .................................................................155
8.5.2 The Least Human Window–Compatible
Solution .................................................................156
8.6 Best Machine Solution ....................................................158
8.7 Related Problems .............................................................160
8.8 Playable Program .............................................................160
8.9 References........................................................................161
Chapter 9: Mastermind ������������������������������������������163
9.1 Background ......................................................................163
9.2 Problem-Solving Techniques...........................................164
9.3 Solution ............................................................................165
9.3.1 Example 1 .............................................................166
9.3.2 Example 2 .............................................................168
9.3.3 Example 3 .............................................................170
9.3.4 Example 4 .............................................................173
9.4 Human Problem Solving .................................................174
9.5 Human Window Analysis of Solutions ............................175
9.6 Best Machine Solution ....................................................176
9.7 Related Problems .............................................................177
9.8 Playable Program .............................................................177
9.9 References........................................................................178
Chapter 10: The Monty Hall Problem �������������������179
10.1 Background ......................................................................179
10.2 Problem-Solving Techniques...........................................180
10.3 Solution ............................................................................182
10.4 Human Problem Solving .................................................182
10.5 Related Problems .............................................................183
10.6 References........................................................................184
Contents • ix
Chapter 11: Rubik’s Cube ��������������������������������������185
11.1 Background ......................................................................185
11.2 Problem-Solving Techniques...........................................186
11.3 Solution ............................................................................187
11.3.1 Cube Components ..............................................188
11.3.2 Subgoal 1: The Top Cross ...................................193
11.3.3 Subgoal 2: The Top Corners...............................194
11.3.4 Subgoal 4: The New Top Cross ..........................198
11.3.5 Subgoal 5: The New Top’s Corners ....................200
11.3.6 Subgoal 6: Correct Corner Positioning ..............201
11.3.7 Subgoal 7: The Top Edges ..................................203
11.4 Human Problem Solving .................................................205
11.5 Human Window Analysis of Solutions ............................206
11.5.1 The Most Human Window–Compatible
Solution ...............................................................208
11.5.2 The Least Human Window–Compatible
Solution ...............................................................209
11.6 Best Machine Solution ....................................................212
11.7 Playable Program .............................................................214
11.8 References........................................................................215
Chapter 12: The Prisoner’s Dilemma ��������������������217
12.1 The Traditional Problem* ................................................217
12.2 The Iterated Prisoner’s Dilemma ....................................220
12.3 Applications in Diverse Areas .........................................220
12.4 Related Problems .............................................................223
12.5 References........................................................................223
Part II: Problems Requiring Computer
Solutions �����������������������������������������������������������������225
Chapter 13: Sudoku ������������������������������������������������227
13.1 Background ......................................................................228
13.2 Mathematical Analysis .....................................................230
13.3 Problem Solving Techniques and Strategies ...................235
13.4 A Real Life Experiment ...................................................240
13.5 Algorithms for Computer Solutions ................................244