Table Of Content

Lee_662-5FRONT.fm Page i Friday, February 17, 2006 7:26 PM Programming Sudoku ■ ■ ■ Wei-Meng Lee Lee_662-5FRONT.fm Page ii Friday, February 17, 2006 7:26 PM Programming Sudoku Copyright © 2006 by Wei-Meng Lee All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval system, without the prior written permission of the copyright owner and the publisher. ISBN-13 (pbk): 978-1-59059-662-3 ISBN-10 (pbk): 1-59059-662-5 Printed and bound in the United States of America 9 8 7 6 5 4 3 2 1 Trademarked names may appear in this book. Rather than use a trademark symbol with every occurrence of a trademarked name, we use the names only in an editorial fashion and to the benefit of the trademark owner, with no intention of infringement of the trademark. Lead Editor: Dominic Shakeshaft Technical Reviewer: Andy Olsen Editorial Board: Steve Anglin, Dan Appleman, Ewan Buckingham, Gary Cornell, Jason Gilmore, Jonathan Hassell, James Huddleston, Chris Mills, Matthew Moodie, Dominic Shakeshaft, Jim Sumser, Keir Thomas, Matt Wade Project Manager and Production Director: Grace Wong Copy Edit Manager: Nicole LeClerc Copy Editor: Bill McManus Assistant Production Director: Kari Brooks-Copony Production Editor: Katie Stence Compositor: Susan Glinert Proofreader: Lori Bring Indexer: Carol Burbo Artist: April Milne Cover Designer: Kurt Krames Manufacturing Director: Tom Debolski Distributed to the book trade worldwide by Springer-Verlag New York, Inc., 233 Spring Street, 6th Floor, New York, NY 10013. Phone 1-800-SPRINGER, fax 201-348-4505, e-mail [email protected], or visit http://www.springeronline.com. For information on translations, please contact Apress directly at 2560 Ninth Street, Suite 219, Berkeley, CA 94710. Phone 510-549-5930, fax 510-549-5939, e-mail [email protected], or visit http://www.apress.com. The information in this book is distributed on an “as is” basis, without warranty. Although every precaution has been taken in the preparation of this work, neither the author(s) nor Apress shall have any liability to any person or entity with respect to any loss or damage caused or alleged to be caused directly or indirectly by the information contained in this work. The source code for this book is available to readers at http://www.apress.com in the Source Code section. You will need to answer questions pertaining to this book in order to successfully download the code. Lee_662-5FRONT.fm Page iii Friday, February 17, 2006 7:26 PM Contents at a Glance About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ix About the Technical Reviewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiii ■ CHAPTER 1 What Is Sudoku? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ■ CHAPTER 2 Creating the Sudoku Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 ■ CHAPTER 3 Basic Sudoku Solving Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 ■ CHAPTER 4 Intermediate Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 ■ CHAPTER 5 Advanced Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 ■ CHAPTER 6 Generating Sudoku Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 ■ CHAPTER 7 How to Play Kakuro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 ■ APPENDIX The SudokuPuzzle Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 ■ INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 iii Lee_662-5FRONT.fm Page iv Friday, February 17, 2006 7:26 PM Lee_662-5FRONT.fm Page v Friday, February 17, 2006 7:26 PM CCoonntteennttss About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ix About the Technical Reviewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiii ■ CHAPTER 1 What Is Sudoku? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Rules of Sudoku . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Sudoku Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 It’s Just Logic! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Variants of Sudoku . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Let’s Play Sudoku! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 ■ CHAPTER 2 Creating the Sudoku Application . . . . . . . . . . . . . . . . . . . . . . . . . 11 Creating the Sudoku Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Creating the User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Declaring the Member Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Representing Values in the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Generating the Grid Dynamically. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Starting a New Game. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Selecting the Numbers to Insert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Handling Click Events on the Label Controls. . . . . . . . . . . . . . . . . . . 30 Undoing and Redoing a Move . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Saving a Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Opening a Saved Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Ending the Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Testing the Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 v Lee_662-5FRONT.fm Page vi Friday, February 17, 2006 7:26 PM vi ■ CONTENTS ■ CHAPTER 3 Basic Sudoku Solving Technique . . . . . . . . . . . . . . . . . . . . . . . . . 47 Elimination Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Column, Row, and Minigrid Elimination. . . . . . . . . . . . . . . . . . . . . . . 48 Usefulness of the CRME Technique . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Exception Scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Implementing the CRME Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Adding Member Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Modifying the SetCell() Subroutine. . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Adding a ToolTip Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Calculating the Possible Values for a Cell . . . . . . . . . . . . . . . . . . . . . 61 Scanning the Grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Wiring the Controls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Testing It Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 ■ CHAPTER 4 Intermediate Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Lone Rangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Lone Rangers in a Minigrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Lone Rangers in a Row . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Lone Rangers in a Column. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Implementing the Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Looking for Lone Rangers in Minigrids. . . . . . . . . . . . . . . . . . . . . . . . 77 Looking for Lone Rangers in Rows. . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Looking for Lone Rangers in Columns. . . . . . . . . . . . . . . . . . . . . . . . 81 Modifying the SolvePuzzle() Function. . . . . . . . . . . . . . . . . . . . . . . . . 83 Testing Out the Lone Ranger Technique . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 ■ CHAPTER 5 Advanced Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Looking for Twins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Looking for Triplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Variants of Triplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Brute-Force Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Lee_662-5FRONT.fm Page vii Friday, February 17, 2006 7:26 PM ■ CONTENTS vii Implementing the Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Looking for Twins in Minigrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Looking for Twins in Rows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Looking for Twins in Columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Looking for Triplets in Minigrids. . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Looking for Triplets in Rows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Looking for Triplets in Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Modifying the SolvePuzzle() Function. . . . . . . . . . . . . . . . . . . . . . . . 127 Using Brute-Force Elimination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Modifying the Code Behind for the Solve Puzzle Button . . . . . . . . 133 Testing the Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 ■ CHAPTER 6 Generating Sudoku Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Determining the Level of Difficulty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Steps to Generate a Sudoku Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Determining the Locations of Empty Cells. . . . . . . . . . . . . . . . . . . . 144 Single-Solution Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Implementing the Puzzle-Generating Algorithm . . . . . . . . . . . . . . . . . . . 148 Creating the Class. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Randomizing the List of Possible Values . . . . . . . . . . . . . . . . . . . . . 150 Generating a New Puzzle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Creating Empty Cells in the Grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Vacating Another Pair of Cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Exposing the GetPuzzle() Function . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Wiring Up the Logic with the User Interface . . . . . . . . . . . . . . . . . . . . . . 162 Testing the Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Easy Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Medium Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Difficult Puzzles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Extremely Difficult Puzzles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Lee_662-5FRONT.fm Page viii Friday, February 17, 2006 7:26 PM viii ■ CONTENTS ■ CHAPTER 7 How to Play Kakuro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 The Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Solving a Kakuro Puzzle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Tips for Solving Kakuro Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 ■ APPENDIX The SudokuPuzzle Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 ■ INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Lee_662-5FRONT.fm Page ix Friday, February 17, 2006 7:26 PM About the Author ■ WEI-MENG LEE is a technologist and founder of Developer Learning Solutions, a technology company that specializes in hands-on training in the latest Microsoft technologies. Wei-Meng speaks regularly at international conferences and has authored and coauthored numerous books on .NET, XML, and wireless technologies, including ASP.NET 2.0: A Developer’s Notebook and Visual Basic 2005 Jumpstart (both from O’Reilly Media). He is also the coauthor of the Apress title XML Programming Using the Microsoft XML Parser. Find out about the latest books and articles by Wei-Meng at his blog: http://weimenglee.blogspot.com/. ix