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 * Created on 31-Aug-2005
 * Copyright (c)- 2005 - Bronstee.com Software & Services and others.
 * All rights reserved.   This program and the accompanying materials
 * are made available under the terms of the 
 * GNU General Public License (GPL) Version 2, June 1991, 
 * which accompanies this distribution, and is available at: 
 * http://www.opensource.org/licenses/gpl-license.php
 * Contributors:
 * Ghica van Emde Boas - original author, Sept 2005
 * <contributor2> - <description of contribution>
 *     ...
  <title>Help for PHP Sudoku Solver</title>
  <link rel="stylesheet" type="text/css" href="sudoku.css" />
<h2>The Sudoku Puzzle Solver</h2>
From <a href="http://en.wikipedia.org/wiki/Sudoku" target="_blank">Wikipedia</a>, the free encyclopedia:
A <b>Sudoku</b> puzzle (Sudoku is Japanese for <i>unique number</i>), 
sometimes spelled Su Doku, is a placement puzzle, also known as <i>Number Place</i>
in the United States. 
The aim of the puzzle is to enter a numeral from 1 through 9 in each cell of a grid, 
most frequently a 9×9 grid made up of 3×3 subgrids (called "regions"), 
starting with various numerals given in some cells (the "givens"). 
Each row, column and region must contain only one instance of each numeral. 
Completing the puzzle requires patience and logical ability. 
Its grid layout is reminiscent of other newspaper puzzles like crosswords and chess problems. 
Sudoku initially became popular in Japan in 1986 and attained international popularity in 2005.
<h3>How to start the Solver</h3>
Start the solver by typing something like <b>http://your-url/sudoku/sudolu.php</b>
in the addressbar of your browser. You should see something like:
<br/><img src="su-init.jpg" width=600><br/>
<h3>Example Sudoku's</h3>
There is an abundance of sudoku's in many newspapers, magazines and on the web.
Most of them are copyrighted and therefore I cannot include them here.
<br/>A very good website about Sudoku's (<a href="http://www.puzzle.jp/" target="_blank">http://www.puzzle.jp/</a>)
has some free samples, and you can subscribe for daily new puzzles.
<p>I found also a site that generates Sudoku's for you, 
<a href="http://www.opensky.ca/~jdhildeb/software/sudokugen/" target="blank">http://www.opensky.ca/~jdhildeb/software/sudokugen/<a>, 
where the software behind it is 
<a href="http://sourceforge.net/projects/gnome-sudoku/" target="blank">http://sourceforge.net/projects/gnome-sudoku/<a>.
These are open source, and therefore I could include an easy and a hard Sudoku for you.
<h4>Sudoku saved file format</h4>
The Sudoku's can be defined as a comma-separated file, either be exporting a spreadsheet as .csv file
or by entering the puzzle in the Solver grid and press the <i>show csv</i> button.
<h3>Upload a Sudoku</h3>

    <li>Press the <i>Browse...</i> Button.
    <li>Choose a local file that contains a Sudoku definition in comma-separated format and press open.
    <li>Press the <i>upload</i> button.
<br/><img src="screenshot1.jpg" width=600><br/>  
<h3>Enter a Sudoku</h3>
You can enter the Sudoku values directly into the grid.
<br/>Save your work by pressing the <i>show csv</i> button, and copy-paste the
comma-separated Sudoku values (highlight, press Ctrl-c, create a text file, open it, paste with Ctrl-v and save).
<h3>Solve a Sudoku</h3>
The objective of this Sudoku solver is to follow as much as possible the human way of reasoning. 
We did not implement any brute-force or tree waliking algorithms. You can also edit the Sudoku values or the set
of possible values after each step and continue the solution.
<h4>The Value-Check Action</h4>
This action is useful if you would like to solve the Sudoku yourself, but you would like to avoid the pain
of finding all possible values for each field. 
<br/>This action iterates over each field and calculates the possible values. If this is a single value, that will
lead to updatting the possible values already found. The Solver makes only one pass and does no recursion
after having found a value. 
Newly found values are shown in red.
<br/><img src="screenshot2.jpg" width=600><br/>  
<h4>The Unique-Check Action</h4>
The solver performs first the value-check action, and then it looks at every row, column or block
to find values that occur only once in the possible value sets. 
Newly found values are shown in red. By repeatedly pressing this button you can solve most
Sudoku's found in newspapers.
<h4>The RC-Check Action</h4>
This action first performs the Unique-check action and then checks in each block whether
there are values that occur only in one row or one column. In this case this value cannot appear in the 
same row or column in the other two blocks that contain part of the row/column. 
The possible values are adjusted accordingly.
<br/><img src="screenshot3.jpg" width=600><br/>  
<h4>The Pair-Check Action</h4>
This action first performs the Unique-check action and then checks in each row, column or block, whether
there are two pairs of the same possible values. In this case these values cannot appear in the 
other fields of the same row, column or block. 
The possible values are adjusted accordingly.
<h4>What if the Sudoku cannot be solved with these rules?</h4>
There are Sudoku's that cannot be solved with these rules. the included "very hard" example 
is of that kind. After you have applied all rules until you can find no new values, you could try
brute force. Take away one value for a pair (you have 50% chance that it works) and try again.
If it fails, you can reload the sudoku and try the other value.
<br/>A check is not implemented yet to see if a solution is valid, therefore you should do this check
<h3>The Clear, Reset and Undo Buttons</h3>
<i>Clear</i> clears the Sudoku matrix.
<br/><i>Reset</i> sets the fields in the Sudoku matrix to the values they had after the latest file upload.
<br/><i>Undo</i> restores the state to the state before the last action-button press.
There are some things left to do:
    <li>Implement the <i>brute force</i> rule.
    <li>Implement a finish check to see if a solution is valid</li>
    <li>If someone finds a rule that could be implemented to solve a "very hard" Sudoku, please
let me know (or better, send me the implementation).

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