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moodle-mod_game/sudoku/class.Sudoku.php

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<?php
//
// Edit History:
//
// Dick Munroe (munroe@csworks.com) 02-Nov-2005
// Initial version created.
//
// Dick Munroe (munroe@csworks.com) 12-Nov-2005
// Allow initialzePuzzle to accept a file name in addition
// to a resource. Windows doesn't do file redirection properly
// so the examples have to be able to handle a file NAME as
// input as well as a redirected file.
// Allow initializePuzzle to accept a string of 81 characters.
//
// Dick Munroe (munroe@csworks.com) 13-Nov-2005
// It appears that getBoardAsString screws up somehow. Rewrite it.
//
// Dick Munroe (munroe@csworks.com) 16-Nov-2005
// Add a "pair" inference.
//
// Dick Munroe (munroe@csworks.com) 17-Nov-2005
// Add comments to input files.
// There was a bug in _applyTuple that caused premature exiting of the inference
// engine.
// If SDD isn't present, don't display error.
//
// Dick Munroe (munroe@csworks.com) 19-Nov-2005
// Add a new tuple inference.
// Do a ground up ObjectS oriented redesign to make the addition of arbitrary
// inferences MUCH easier.
// Get the printing during solving right.
// Somehow array_equal developed a "bug".
//
// Dick Munroe (munroe@csworks.com) 22-Nov-2005
// Add n,n+1 tuple recognition for n=2.
// Restructure inference engine to get maximum benefit out of each pass.
//
// Dick Munroe (munroe@csworks.com) 28-Nov-2005
// Attempt to build harder Sudoku by implementing a coupling coefficient
// attempting to distribute clues more optimally.
//
@include_once "SDD/class.SDD.php" ;
/**
* @author Dick Munroe <munroe@csworks.com>
* @copyright copyright @ 2005 by Dick Munroe, Cottage Software Works, Inc.
* @license http://www.csworks.com/publications/ModifiedNetBSD.html
* @version 2.2.0
* @package Sudoku
*/
/**
* Basic functionality needed for ObjectSs in the Sudoku solver.
*
* Technically speaking these aren't restricted to the Sudoku classes
* and are of use generally.
*
* @package Sudoku
*/
class ObjectS
{
/**
* @desc Are two array's equal (have the same contents).
* @param array
* @param array
* @return boolean
*/
function array_equal($theArray1, $theArray2)
{
if (!(is_array($theArray1) && is_array($theArray2)))
{
return false ;
}
if (count($theArray1) != count($theArray2))
{
return false ;
}
$xxx = array_diff($theArray1, $theArray2) ;
return (count($xxx) == 0) ;
}
/**
* Deep copy anything.
*
* @access public
* @param array $theArray [optional] Something to be deep copied. [Default is the current
* ObjectS.
* @return mixed The deep copy of the input. All references embedded within
* the array have been resolved into copies allowing things like the
* board array to be copied.
*/
function deepCopy($theArray = NULL)
{
if ($theArray === NULL)
{
return unserialize(serialize($this)) ;
}
else
{
return unserialize(serialize($theArray)) ;
}
}
/**
* @desc Debugging output interface.
* @access public
* @param mixed $theValue The "thing" to be pretty printed.
* @param boolean $theHTMLFlag True if the output will be seen in a browser, false otherwise.
*/
function print_d(&$theValue, $theHTMLFlag = true)
{
print SDD::dump($theValue, $theHTMLFlag) ;
}
}
/**
* The individual cell on the Sudoku board.
*
* These cells aren't restricted to 9x9 Sudoku (although pretty much everything else
* at the moment). This class provides the state manipulation and searching capabilities
* needed by the inference engine (class RCS).
*
* @package Sudoku
*/
class Cell extends ObjectS
{
var $r ;
var $c ;
var $state = array() ;
var $applied = false ;
/**
* @desc Constructor
* @param integer $r row address of this cell (not used, primarily for debugging purposes).
* @param integer $c column address of this cell (ditto).
* @param integer $nStates The number of states each cell can have. Looking forward to
* implementing Super-doku.
*/
function Cell($r, $c, $nStates = 9)
{
$this->r = $r ;
$this->c = $c ;
for ($i = 1; $i <= $nStates; $i++)
{
$this->state[$i] = $i ;
}
}
/**
* @desc This cell has been "applied", i.e., solved, to the board.
*/
function applied()
{
$this->applied = true ;
}
/**
* Only those cells which are not subsets of the tuple have the
* contents of the tuple removed.
*
* @desc apply a 23Tuple to a cell.
* @access public
* @param array $aTuple the tuple to be eliminated.
*/
function apply23Tuple($aTuple)
{
if (is_array($this->state))
{
$xxx = array_intersect($this->state, $aTuple) ;
if ((count($xxx) > 0) && (count($xxx) != count($this->state)))
{
return $this->un_set($aTuple) ;
}
else
{
return false ;
}
}
else
{
return false ;
}
}
/**
* For more details on the pair tuple algorithm, see RCS::_pairSolution.
*
* @desc Remove all values in the tuple, but only if the cell is a superset.
* @access public
* @param array A tuple to be eliminated from the cell's state.
*/
function applyTuple($aTuple)
{
if (is_array($this->state))
{
if (!$this->array_equal($aTuple, $this->state))
{
return $this->un_set($aTuple) ;
}
}
return false ;
}
/**
* @desc Return the string representation of the cell.
* @access public
* @param boolean $theFlag true if the intermediate states of the cell are to be visible.
* @return string
*/
function asString($theFlag = false)
{
if (is_array($this->state))
{
if (($theFlag) || (count($this->state) == 1))
{
return implode(", ", $this->state) ;
}
else
{
return " " ;
}
}
else
{
return $this->state ;
}
}
/**
* Used to make sure that solved positions show up at print time.
* The value is used as a candidate for "slicing and dicing" by elimination in
* Sudoku::_newSolvedPosition.
*
* @desc Assert pending solution.
* @access public
* @param integer $value The value for the solved position.
*/
function flagSolvedPosition($value)
{
$this->state = array($value => $value) ;
}
/**
* @desc return the state of a cell.
* @access protected
* @return mixed Either solved state or array of state pending solution.
*/
function &getState()
{
return $this->state ;
}
/**
* @desc Has the state of this cell been applied to the board.
* @access public
* @return boolean True if it has, false otherwise. Implies that IsSolved is true as well.
*/
function IsApplied()
{
return $this->applied ;
}
/**
* @desc Has this cell been solved?
* @access public
* @return boolean True if this cell has hit a single state.
*/
function IsSolved()
{
return !is_array($this->state) ;
}
/**
* This is used primarily by the pretty printer, but has other applications
* in the code.
*
* @desc Return information about the state of a cell.
* @access public
* @return integer 0 => the cell has been solved.
* 1 => the cell has been solved but not seen a solved.
* 2 => the cell has not been solved.
*/
function solvedState()
{
if (is_array($this->state))
{
if (count($this->state) == 1)
{
return 1 ;
}
else
{
return 2 ;
}
}
else
{
return 0 ;
}
}
/**
* This is the negative inference of Sudoku. By eliminating values the
* cells approach solutions. Once a cell has been completely eliminated,
* the value causing the complete elimination must be the solution and the
* cell is promoted into the solved state.
*
* @desc Eliminate one or more values from the state information of the cell.
* @access public
* @param mixed The value or values to be removed from the cell state.
* @return boolean True if the cell state was modified, false otherwise.
*/
function un_set($theValues)
{
if (is_array($theValues))
{
$theReturn = FALSE ;
foreach ($theValues as $theValue)
{
$theReturn |= $this->un_set($theValue) ;
}
return $theReturn ;
}
if (is_array($this->state))
{
$theReturn = isset($this->state[$theValues]) ;
unset($this->state[$theValues]) ;
if (count($this->state) == 0)
{
$this->state = $theValues ;
}
return $theReturn ;
}
else
{
return false ;
}
}
}
/**
* The individual row column or square on the Sudoku board.
*
* @package Sudoku
*/
class RCS extends ObjectS
{
var $theIndex ;
var $theRow = array() ;
var $theHeader = "" ;
var $theTag = "" ;
/**
* This
* @desc Constructor
* @access public
* @param string $theTag "Row", "Column", "Square", used primarily in debugging.
* @param integer $theIndex 1..9, where is this on the board. Square are numbered top
* left, ending bottom right
* @param ObjectS $a1..9 of class Cell. The cells comprising this entity. This interface is what
* limts things to 9x9 Sudoku currently.
*/
function RCS($theTag, $theIndex, &$a1, &$a2, &$a3, &$a4, &$a5, &$a6, &$a7, &$a8, &$a9)
{
$this->theTag = $theTag ;
$this->theIndex = $theIndex ;
$this->theRow[1] = &$a1 ;
$this->theRow[2] = &$a2 ;
$this->theRow[3] = &$a3 ;
$this->theRow[4] = &$a4 ;
$this->theRow[5] = &$a5 ;
$this->theRow[6] = &$a6 ;
$this->theRow[7] = &$a7 ;
$this->theRow[8] = &$a8 ;
$this->theRow[9] = &$a9 ;
}
/**
* There is a special case that comes up a lot in Sudoku. If there
* are values i, j, k and cells of the form (i, j), (j, k), (i, j, k)
* the the values i, j, and k cannot appear in any other cells. The
* proof is a simple "by contradiction" proof. Assume that the values
* do occur elsewhere and you always get a contradiction for these
* three cells. I'm pretty sure that this is a general rule, but for
* 9x9 Sudoku, they probably aren't of interested.
*
* @desc
* @access private
* @return boolean True if a 23 solution exists and has been applied.
*/
function _23Solution()
{
$theCounts = array() ;
$theTuples = array() ;
$theUnsolved = 0 ;
for ($i = 1; $i <= 9; $i++)
{
$j = count($this->theRow[$i]->getState());
$theCounts[ $j][] = $i ;
$theUnsolved++ ;
}
if( array_key_exists( 2, $theCounts) and array_key_exists( 3, $theCounts))
{
if ((count($theCounts[2]) < 2) || (count($theCounts[3]) < 1))
return false ;
}
/*
* Look at each pair of 2 tuples and see if their union exists in the 3 tuples.
* If so, eliminate everything from the set and bail.
*/
$the2Tuples = &$theCounts[2] ;
$the3Tuples = &$theCounts[3] ;
$theCount2 = count($the2Tuples) ;
$theCount3 = count($the3Tuples) ;
for ($i = 0; $i < $theCount2 - 1; $i++)
{
for ($j = $i + 1; $j < $theCount2; $j++)
{
$xxx = array_unique(array_merge($this->theRow[$the2Tuples[$i]]->getState(),
$this->theRow[$the2Tuples[$j]]->getState())) ;
for ($k = 0; $k < $theCount3; $k++)
{
if ($this->array_equal($xxx, $this->theRow[$the3Tuples[$k]]->getState()))
{
$theTuples[] = $xxx ;
break ;
}
}
}
}
/*
* Since it takes 3 cells to construct the 23 tuple, unless there are more than 3
* unsolved cells, further work doesn't make any sense.
*/
$theReturn = false ;
if ((count($theTuples) != 0) && ($theUnsolved > 3))
{
foreach ($theTuples as $aTuple)
{
foreach($this->theRow as $theCell)
{
$theReturn |= $theCell->apply23Tuple($aTuple) ;
}
}
}
if ($theReturn)
{
$this->theHeader[] = sprintf("<br />Apply %s[%d] 23 Tuple Inference:", $this->theTag, $this->theIndex) ;
}
return $theReturn ;
}
/**
* @desc apply a tuple to exclude items from within the row/column/square.
* @param array $aTuple the tuple to be excluded.
* @access private
* @return boolean true if anything changes.
*/
function _applyTuple(&$aTuple)
{
$theReturn = FALSE ;
for ($i = 1; $i <=9; $i++)
{
$theReturn |= $this->theRow[$i]->applyTuple($aTuple) ;
}
return $theReturn ;
}
/**
* This is a placeholder to be overridden to calculate the "coupling" for
* a cell. Coupling is defined to be the sum of the sizes of the intersection
* between this cell and all others in the row/column/square. This provides
* a metric for deciding placement of clues within puzzles. In effect, this
* forces the puzzle generator to select places for new clues depending upon
* how little information is changed by altering the state of a cell. The larger
* the number returned by the coupling, function, the less information is currently
* available for the state of the cell. By selecting areas with the least information
* the clue sets are substantially smaller than simple random placement.
*
* @desc Calculate the coupling for a cell within the row/column/square.
* @access abstract
* @param integer $theRow the row coordinate on the board of the cell.
* @param integer $theColumn the column coordinate on the board of the cell.
* @return integer the degree of coupling between the cell and the rest of the cells
* within the row/column/square.
*/
function coupling($theRow, $theColumn)
{
return 0 ;
}
/**
* I think that the goal of the inference engine is to eliminate
* as much "junk" state as possible on each pass. Therefore the
* order of the inferences should be 23 tuple, pair, unique because
* the 23 tuple allows you to eliminate 3 values (if it works), and the
* pair (generally) only 2. The unique solution adds no new information.
*
* @desc Run the inference engine for a row/column/square.
* @access public
* @param array theRow A row/column/square data structure.
* @param string theType A string merged with the standard headers during
* intermediate solution printing.
* @return boolean True when at least one inference has succeeded.
*/
function doAnInference()
{
$this->theHeader = NULL ;
$theReturn = $this->_23Solution() ;
$theReturn |= $this->_pairSolution() ;
$theReturn |= $this->_uniqueSolution() ;
return $theReturn ;
}
/**
* @desc Find all tuples with the same contents.
* @param array Array of n size tuples.
* @returns array of tuples that appear the same number of times as the size of the contents
*/
function _findTuples(&$theArray)
{
$theReturn = array() ;
for ($i = 0; $i < count($theArray); $i++)
{
$theCount = 1 ;
for ($j = $i + 1; $j < count($theArray); $j++)
{
$s1 = &$this->theRow[$theArray[$i]] ;
$s1 =& $s1->getState() ;
$s2 = &$this->theRow[$theArray[$j]] ;
$s2 =& $s2->getState() ;
$aCount = count($s1) ;
if ($this->array_equal($s1, $s2))
{
$theCount++ ;
if ($theCount == $aCount)
{
$theReturn[] = $s1 ;
break ;
}
}
}
}
return $theReturn ;
}
/**
* @desc Get a reference to the specified cell.
* @access public
* @return reference to ObjectS of class Cell.
*/
function &getCell($i)
{
return $this->theRow[$i] ;
}
/**
* @desc Get the header set by the last call to doAnInference.
*
*/
function getHeader()
{
return $this->theHeader ;
}
/**
* Turns out if you every find a position of n squares which can only contain
* the same values, then those values cannot appear elsewhere in the structure.
* This is a second positive inference that provides additional negative information.
* Thanks to Ghica van Emde Boas (also an author of a Sudoku class) for convincing
* me that these situations really occurred.
*
* @desc Eliminate tuple-locked alternatives.
* @access private
* @return boolean True if something changed.
*/
function _pairSolution()
{
$theCounts = array() ;
$theTuples = array() ;
for ($i = 1; $i <= 9; $i++)
{
$c = &$this->theRow[$i] ;
$theCounts[count($c->getState())][] = $i ;
}
unset($theCounts[1]) ;
/*
** Get rid of any set of counts which cannot possibly meet the
** requirements.
*/
$thePossibilities = $theCounts ;
foreach ($theCounts as $theKey => $theValue)
{
if (count($theValue) < $theKey)
{
unset($thePossibilities[$theKey]) ;
}
}
if (count($thePossibilities) == 0)
{
return false ;
}
/*
* At this point there are 1 or more tuples which MAY satisfy the conditions.
*/
$theReturn = false ;
foreach ($thePossibilities as $theValue)
{
$theTuples = $this->_findTuples($theValue) ;
if (count($theTuples) != 0)
{
foreach ($theTuples as $aTuple)
{
$theReturn |= $this->_applyTuple($aTuple) ;
}
}
}
if ($theReturn)
{
$this->theHeader[] = sprintf("<br />Apply %s[%d] Pair Inference:", $this->theTag, $this->theIndex) ;
}
return $theReturn ;
}
function un_set($theValues)
{
$theReturn = false ;
for ($i = 1; $i <= 9; $i++)
{
$c = &$this->theRow[$i] ;
$theReturn |= $c->un_set($theValues) ;
}
return $theReturn ;
}
/**
* Find a solution to a row/column/square.
*
* Find any unique numbers within the row/column/square under consideration.
* Look through a row structure for a value that appears in only one cell.
* When you find one, that's a solution for that cell.
*
* There is a second inference that can be taken. Given "n" cells in a row/column/square
* and whose values can only consist of a set of size "n", then those values may obtain
* there and ONLY there and may be eliminated from consideration in the rest of the set.
* For example, if two cells must contain the values 5 or 6, then no other cell in that
* row/column/square may contain those values, similarly for 3 cells, etc.
*
* @access private
* @return boolean True if one or more values in the RCS has changed state.
*/
function _uniqueSolution()
{
$theSet = array() ;
for ($i = 1; $i <= 9; $i++)
{
$c = &$this->theRow[$i] ;
if (!$c->IsSolved())
{
foreach ($c->getState() as $theValue)
{
$theSet[$theValue][] = $i ;
}
}
}
/*
* If there were no unsolved positions, then we're done and nothing has
* changed.
*/
if (count($theSet) == 0)
{
return false ;
}
/*
* Pull out all those keys having only one occurrance in the RCS.
*/
foreach ($theSet as $theKey => $theValues)
{
if (count($theValues) != 1)
{
unset($theSet[$theKey]) ;
}
}
/*
* If there aren't any unique values, we're done.
*/
if (count($theSet) == 0)
{
return false ;
}
foreach ($theSet as $theValue => $theIndex)
{
$this->theRow[$theIndex[0]]->flagSolvedPosition($theValue) ;
}
$this->theHeader[] = sprintf("<br />Apply %s[%d] Unique Inference:", $this->theTag, $this->theIndex) ;
return true ;
}
/**
* @desc Check to see if the RCS contains a valid state.
* @access public
* @return boolean True if the state of the RCS could be part of a valid
* solution, false otherwise.
*/
function validateSolution()
{
$theNewSet = array() ;
foreach ($this->theRow as $theCell)
{
if ($theCell->solvedState() == 0)
{
$theNewSet[] = $theCell->getState() ;
}
}
$xxx = array_unique($theNewSet) ;
return (count($xxx) == count($this->theRow)) ;
}
/**
* Validate a part of a trial solution.
*
* Check a row/column/square to see if there are any invalidations on this solution.
* Only items that are actually solved are compared. This is used during puzzle
* generation.
*
* @access public
* @return True if the input parameter contains a valid solution, false otherwise.
*/
function validateTrialSolution()
{
$theNewSet = array() ;
foreach($this->theRow as $theCell)
{
if ($theCell->solvedState() == 0)
{
$theNewSet[] = $theCell->getState() ;
}
}
$xxx = array_unique($theNewSet) ;
return ((count($xxx) == count($theNewSet) ? TRUE : FALSE)) ;
}
}
/**
* Row ObjectS.
*
* @package Sudoku
*/
class R extends RCS
{
/**
* @desc Constructor
* @access public
* @param string $theTag "Row", "Column", "Square", used primarily in debugging.
* @param integer $theIndex 1..9, where is this on the board. Square are numbered top
* left, ending bottom right
* @param ObjectS $a1..9 of class Cell. The cells comprising this entity. This interface is what
* limts things to 9x9 Sudoku currently.
*/
function R($theTag, $theIndex, &$a1, &$a2, &$a3, &$a4, &$a5, &$a6, &$a7, &$a8, &$a9)
{
$this->RCS($theTag, $theIndex, $a1, $a2, $a3, $a4, $a5, $a6, $a7, $a8, $a9) ;
}
/**
* @see RCS::coupling
*/
function coupling($theRow, $theColumn)
{
return $theState = $this->_coupling($theColumn) ;
}
/**
* @see RCS::coupling
* @desc Heavy lifting for row/column coupling calculations.
* @access private
* @param integer $theIndex the index of the cell within the row or column.
* @return integer the "coupling coefficient" for the cell. The sum of the
* sizes of the intersection between this and all other
* cells in the row or column.
*/
function _coupling($theIndex)
{
$theCommonState =& $this->getCell($theIndex) ;
$theCommonState =& $theCommonState->getState() ;
$theCoupling = 0 ;
for ($i = 1; $i <= count($this->theRow); $i++)
{
if ($i != $theIndex)
{
$theCell =& $this->getCell($i) ;
if ($theCell->solvedState() != 0)
{
$theCoupling += count(array_intersect($theCommonState, $theCell->getState())) ;
}
}
}
return $theCoupling ;
}
}
/**
* The column ObjectS.
*
* @package Sudoku
*/
class C extends R
{
/**
* @desc Constructor
* @access public
* @param string $theTag "Row", "Column", "Square", used primarily in debugging.
* @param integer $theIndex 1..9, where is this on the board. Square are numbered top
* left, ending bottom right
* @param ObjectS $a1..9 of class Cell. The cells comprising this entity. This interface is what
* limts things to 9x9 Sudoku currently.
*/
function C($theTag, $theIndex, &$a1, &$a2, &$a3, &$a4, &$a5, &$a6, &$a7, &$a8, &$a9)
{
$this->R($theTag, $theIndex, $a1, $a2, $a3, $a4, $a5, $a6, $a7, $a8, $a9) ;
}
/**
* @see R::coupling
*/
function coupling($theRow, $theColumn)
{
return $theState = $this->_coupling($theRow) ;
}
}
/**
* The Square ObjectS.
*
* @package Sudoku
*/
class S extends RCS
{
/**
* The cells within the 3x3 sudoku which participate in the coupling calculation for a square.
* Remember that the missing cells have already participated in the row or column coupling
* calculation.
*
* @access private
* @var array
*/
var $theCouplingOrder =
array( 1 => array(5, 6, 8, 9),
2 => array(4, 6, 7, 9),
3 => array(4, 5, 7, 8),
4 => array(2, 3, 8, 9),
5 => array(1, 3, 7, 9),
6 => array(1, 2, 7, 8),
7 => array(2, 3, 5, 6),
8 => array(1, 3, 4, 6),
9 => array(1, 2, 4, 5)) ;
/**
* @desc Constructor
* @access public
* @param string $theTag "Row", "Column", "Square", used primarily in debugging.
* @param integer $theIndex 1..9, where is this on the board. Square are numbered top
* left, ending bottom right
* @param ObjectS $a1..9 of class Cell. The cells comprising this entity. This interface is what
* limts things to 9x9 Sudoku currently.
*/
function S($theTag, $theIndex, &$a1, &$a2, &$a3, &$a4, &$a5, &$a6, &$a7, &$a8, &$a9)
{
$this->RCS($theTag, $theIndex, $a1, $a2, $a3, $a4, $a5, $a6, $a7, $a8, $a9) ;
}
/**
* @see RCS::coupling
*/
function coupling($theRow, $theColumn)
{
$theIndex = ((($theRow - 1) % 3) * 3) + (($theColumn - 1) % 3) + 1 ;
$theCommonState =& $this->getCell($theIndex) ;
$theCommonState =& $theCommonState->getState() ;
$theCoupling = 0 ;
foreach ($this->theCouplingOrder[$theIndex] as $i)
{
$theCell =& $this->getCell($i) ;
if ($theCell->solvedState() != 0)
{
$theCoupling += count(array_intersect($theCommonState, $theCell->getState())) ;
}
}
return $theCoupling ;
}
}
/**
* Solve and generate Sudoku puzzles.
*
* Solve and generate Sudoku. A simple output interface is provided for
* web pages. The primary use of this class is as infra-structure for
* Sudoku game sites.
*
* The solver side of this class (solve) relies on the usual characteristic
* of logic puzzles, i.e., at any point in time there is one (or more)
* UNIQUE solution to some part of the puzzle. This solution can be
* applied, then iterated upon to find the next part of the puzzle. A
* properly constructed Sudoku can have only one solution which guarangees
* that this is the case. (Sudoku with multiple solutions will always
* require guessing at some point which is specifically disallowed by
* the rules of Sudoku).
*
* While the solver side is algorithmic, the generator side is much more
* difficult and, in fact, the generation of Sudoku appears to be NP
* complete. That being the case, I observed that most successful
* generated initial conditions happened quickly, typically with < 40
* iterations. So the puzzle generator runs "for a while" until it
* either succeeds or doesn't generated a solveable puzzle. If we get
* to that position, I just retry and so far I've always succeeded in
* generating an initial state. Not guarateed, but in engineering terms
* "close enough".
*
* @package Sudoku
* @example ./example.php
* @example ./example1.php
* @example ./example2.php
* @example ./example3.php
*/
class Sudoku extends ObjectS
{
/**
* An array of Cell ObjectSs, organized into rows and columns.
*
* @access private
* @var array of ObjectSs of type Cell.
*/
var $theBoard = array() ;
/**
* True if debugging output is to be provided during a run.
*
* @access private
* @var boolean
*/
var $theDebug = FALSE ;
/**
* An array of RCS ObjectSs, one ObjectS for each row.
*
* @access private
* @var ObjectS of type R
*/
var $theRows = array() ;
/**
* An array of RCS ObjectSs, one ObjectS for each Column.
*
* @access private
* @var ObjectS of type C
*/
var $theColumns = array() ;
/**
* An array of RCS ObjectSs, one ObjectS for each square.
*
* @access private
* @var ObjectS of type S
*/
var $theSquares = array() ;
/**
* Used during puzzle generation for debugging output. There may
* eventually be some use of theLevel to figure out where to stop
* the backtrace when puzzle generation fails.
*
* @access private
* @var integer.
*/
var $theLevel = 0 ;
/**
* Used during puzzle generation to determine when the generation
* will fail. Failure, in this case, means to take a LONG time. The
* backtracing algorithm used in the puzzle generator will always find
* a solution, it just might take a very long time. This is a way to
* limit the damage before taking another guess.
*
* @access private
* @var integer.
*/
var $theMaxIterations = 50 ;
/**
* Used during puzzle generation to limit the number of trys at
* generation a puzzle in the event puzzle generation fails
* (@see Suduko::$theMaxIterations). I've never seen more than
* a couple of failures in a row, so this should be sufficient
* to get a puzzle generated.
*
* @access private
* @var integer.
*/
var $theTrys = 10 ;
/**
* Used during puzzle generation to count the number of iterations
* during puzzle generation. It the number gets above $theMaxIterations,
* puzzle generation has failed and another try is made.
*
* @access private
* @var integer.
*/
var $theGenerationIterations = 0 ;
function Sudoku($theDebug = FALSE)
{
$this->theDebug = $theDebug ;
for ($i = 1; $i <= 9; $i++)
{
for ($j = 1; $j <= 9; $j++)
{
$this->theBoard[$i][$j] = new Cell($i, $j) ;
}
}
$this->_buildRCS() ;
}
/**
* Apply a pending solved position to the row/square/column.
*
* At this point, the board has been populated with any pending solutions.
* This applies the "negative" inference that no row, column, or square
* containing the value within the cell.
*
* @access private
* @param integer $row The row of the board's element whose value is now fixed.
* @param integer $col The column of the board's element whose value is now fixed.
*/
function _applySolvedPosition($row, $col)
{
$theValue = $this->theBoard[$row][$col]->getState() ;
/*
** No other cell in the row, column, or square can take on the value "value" any longer.
*/
$i = (((int)(($row - 1) / 3)) * 3) ;
$i = $i + ((int)(($col - 1) / 3)) + 1 ;
$this->theRows[$row]->un_set($theValue) ;
$this->theColumns[$col]->un_set($theValue) ;
$this->theSquares[$i]->un_set($theValue) ;
}
/**
* @desc Apply all pending solved positions to the board.
* @access private
* @return boolean True if at least one solved position was applied, false
* otherwise.
*/
function _applySolvedPositions()
{
$theReturn = false ;
for ($i = 1; $i <= 9; $i++)
{
for ($j = 1; $j <= 9; $j++)
{
if (!$this->theBoard[$i][$j]->IsApplied())
{
if ($this->theBoard[$i][$j]->solvedState() == 0)
{
$this->_applySolvedPosition($i, $j) ;
/*
** Update the solved position matrix and make sure that the board actually
** has a value in place.
*/
$this->theBoard[$i][$j]->applied() ;
$theReturn = TRUE ;
}
}
}
}
return $theReturn ;
}
/**
* @desc build the row/column/square structures for the board.
* @access private
*/
function _buildRCS()
{
for ($i = 1; $i <= 9; $i++)
{
$this->theRows[$i] =
new R("Row",
$i,
$this->theBoard[$i][1],
$this->theBoard[$i][2],
$this->theBoard[$i][3],
$this->theBoard[$i][4],
$this->theBoard[$i][5],
$this->theBoard[$i][6],
$this->theBoard[$i][7],
$this->theBoard[$i][8],
$this->theBoard[$i][9]) ;
$this->theColumns[$i] =
new C("Column",
$i,
$this->theBoard[1][$i],
$this->theBoard[2][$i],
$this->theBoard[3][$i],
$this->theBoard[4][$i],
$this->theBoard[5][$i],
$this->theBoard[6][$i],
$this->theBoard[7][$i],
$this->theBoard[8][$i],
$this->theBoard[9][$i]) ;
$r = ((int)(($i - 1) / 3)) * 3 ;
$c = (($i - 1) % 3) * 3 ;
$this->theSquares[$i] =
new S("Square",
$i,
$this->theBoard[$r + 1][$c + 1],
$this->theBoard[$r + 1][$c + 2],
$this->theBoard[$r + 1][$c + 3],
$this->theBoard[$r + 2][$c + 1],
$this->theBoard[$r + 2][$c + 2],
$this->theBoard[$r + 2][$c + 3],
$this->theBoard[$r + 3][$c + 1],
$this->theBoard[$r + 3][$c + 2],
$this->theBoard[$r + 3][$c + 3]) ;
}
}
/**
* Seek alternate solutions in a solution set.
*
* Given a solution, see if there are any alternates within the solution.
* In theory this should return the "minimum" solution given any solution.
*
* @access public
* @param array $theInitialState (@see Sudoku::initializePuzzleFromArray)
* @return array A set of triples containing the minimum solution.
*/
function findAlternateSolution($theInitialState)
{
$j = count($theInitialState) ;
for ($i = 0; $i < $j; $i++)
{
$xxx = $theInitialState ;
$xxx = array_splice($xxx, $i, 1) ;
$this->Sudoku() ;
$this->initializePuzzleFromArray($xxx) ;
if ($this->solve())
{
return $this->findAlternateSolution($xxx) ;
}
}
return $theInitialState ;
}
/**
* Initialize Sudoku puzzle generation and generate a puzzle.
*
* Turns out that while the solution of Sudoku is mechanical, the creation of
* Sudoku is an NP-Complete problem. Which means that I can use the inference
* engine to help generate puzzles, but I need to test the solution to see if
* I've gone wrong and back up and change my strategy. So something in the
* recursive descent arena will be necessary. Since the generation can take
* a long time to force a solution, it's easier to probe for a solution
* if you go "too long".
*
* @access public
* @param integer $theDifficultyLevel [optional] Since virtually everybody who
* plays sudoku wants a variety of difficulties this controls that.
* 1 is the easiest, 10 the most difficult. The easier Sudoku have
* extra information.
* @param integer $theMaxInterations [optional] Controls the number of iterations
* before the puzzle generator gives up and trys a different set
* of initial parameters.
* @param integer $theTrys [optional] The number of attempts at resetting the
* initial parameters before giving up.
* @return array A set of triples suitable for initializing a new Sudoku class
* (@see Sudoku::initializePuzzleFromArray).
*/
function generatePuzzle($theDifficultyLevel = 10, $theMaxIterations = 50, $theTrys = 10)
{
$theDifficultyLevel = min($theDifficultyLevel, 10) ;
$theDifficultyLevel = max($theDifficultyLevel, 1) ;
$this->theLevel = 0 ;
$this->theTrys = $theTrys ;
$this->theMaxIterations = $theMaxIterations ;
$this->theGenerationIterations = 0 ;
for ($theTrys = 0; $theTrys < $this->theTrys ; $theTrys++)
{
$theAvailablePositions = array() ;
$theCluesPositions = array() ;
$theClues = array() ;
for ($i = 1; $i <= 9; $i++)
{
for ($j = 1; $j <= 9; $j++)
$theAvailablePositions[] = array($i, $j) ;
}
$theInitialState = $this->_generatePuzzle($theAvailablePositions, $theCluesPositions, $theClues) ;
if ($theInitialState)
{
if ($theDifficultyLevel != 10)
{
$xxx = array() ;
foreach ($theInitialState as $yyy)
$xxx[] = (($yyy[0] - 1) * 9) + ($yyy[1] - 1) ;
/*
** Get rid of the available positions already used in the initial state.
*/
sort($xxx) ;
$xxx = array_reverse($xxx) ;
foreach ($xxx as $i)
array_splice($theAvailablePositions, $i, 1) ;
/*
** Easy is defined as the number of derivable clues added to the minimum
** required information to solve the puzzle as returned by _generatePuzzle.
*/
for ($i = 0; $i < (10 - $theDifficultyLevel); $i++)
{
$xxx = mt_rand(0, count($theAvailablePositions)-1) ;
$row = $theAvailablePositions[$xxx][0] ;
$col = $theAvailablePositions[$xxx][1] ;
$theInitialState[] = array($row, $col, $this->theBoard[$row][$col]) ;
array_splice($theAvailablePositions, $xxx, 1) ;
}
}
//echo "found $theTrys<br>";
return $theInitialState ;
}
if ($this->theDebug)
printf("<br>Too many iterations (%d), %d\n", $this->theMaxIterations, $theTrys);
$this->Sudoku($this->theDebug) ;
}
/*
** No solution possible, we guess wrong too many times.
*/
//echo "try=$theTrys<br>";
return array() ;
}
/**
* Sudoku puzzle generator.
*
* This is the routine that does the heavy lifting
* for the puzzle generation. It works by taking a guess for a value of a cell, applying
* the solver, testing the solution, and if it's a valid solution, calling itself
* recursively. If during this process, a solution cannot be found, the generator backs
* up (backtrace in Computer Science parlance) and trys another value. Since the generation
* appears to be an NP complete problem (according to the literature) limits on the number
* of iterations are asserted. Once these limits are passed, the generator gives up and
* makes another try. If enough tries are made, the generator gives up entirely.
*
* @access private
* @param array $theAvailablePositions A set of pairs for all positions which have not been
* filled by the solver or the set of guesses. When we run out of available
* positions, the solution is in hand.
* @param array $theCluesPositions A set of pairs for which values have been set by the
* puzzle generator.
* @param array $theClues A set of values for each pair in $theCluesPositions.
* @return array NULL array if no solution is possible, otherwise a set of triples
* suitable for feeding to {@link Sudoku::initializePuzzleFromArray}
*/
function _generatePuzzle($theAvailablePositions, $theCluesPositions, $theClues)
{
$this->theLevel++ ;
$this->theGenerationIterations++ ;
/*
** Since the last solution sequence may have eliminated one or more positions by
** generating forced solutions for them, go through the list of available positions
** and get rid of any that have already been solved.
*/
$j = count($theAvailablePositions) ;
for ($i = 0; $i < $j; $i++)
{
if ($this->theBoard[$theAvailablePositions[$i][0]][$theAvailablePositions[$i][1]]->IsApplied())
{
array_splice($theAvailablePositions, $i, 1) ;
$i = $i - 1;
$j = $j - 1;
}
}
if (count($theAvailablePositions) == 0)
{
/*
** We're done, so we can return the clues and their positions to the caller.
** This test is being done here to accommodate the eventual implementation of
** generation from templates in which partial boards will be fed to the solver
** and then the remaining board fed in.
*/
for ($i = 0; $i < count($theCluesPositions); $i++)
array_push($theCluesPositions[$i], $theClues[$i]) ;
return $theCluesPositions ;
}
/*
** Calculate the coupling for each available position.
**
** "coupling" is a measure of the amount of state affected by any change
** to a given cell. In effect, the larger the coupling, the less constrained
** the state of the cell is and the greater the effect of any change made to
** the cell. There is some literature to this effect associated with Roku puzzles
** (4x4 grid). I'm trying this attempting to find a way to generate consistently
** more difficult Sudoku and it seems to have worked; the clue count drops to 25 or
** fewer, more in line with the numbers predicted by the literature. The remainder
** of the work is likely to be associated with finding better algorithms to solve
** Sudoku (which would have the effect of generating harder ones).
*/
$theCouplings = array() ;
foreach ($theAvailablePositions as $xxx)
{
$theRowCoupling = $this->theRows[$xxx[0]]->coupling($xxx[0], $xxx[1]) ;
$theColumnCoupling = $this->theColumns[$xxx[1]]->coupling($xxx[0], $xxx[1]) ;
$theSquareCoupling = $this->theSquares[$this->_squareIndex($xxx[0], $xxx[1])]->coupling($xxx[0], $xxx[1]) ;
$theCouplings[$theRowCoupling + $theColumnCoupling + $theSquareCoupling][] = $xxx ;
}
$theMaximumCoupling = max(array_keys($theCouplings)) ;
/*
** Pick a spot on the board and get the clues set up.
*/
$theChoice = mt_rand(0, count($theCouplings[$theMaximumCoupling])-1) ;
$theCluesPositions[] = $theCouplings[$theMaximumCoupling][$theChoice] ;
$theRow = $theCouplings[$theMaximumCoupling][$theChoice][0] ;
$theColumn = $theCouplings[$theMaximumCoupling][$theChoice][1] ;
/*
** Capture the necessary global state of the board
*/
$theCurrentBoard = $this->deepCopy($this->theBoard) ;
/*
** This is all possible states for the chosen cell. All values will be
** randomly tried to see if a solution results. If all solutions fail,
** the we'll back up in time and try again.
*/
$thePossibleClues = array_keys($this->theBoard[$theRow][$theColumn]->getState()) ;
while (count($thePossibleClues) != 0)
{
if ($this->theGenerationIterations > $this->theMaxIterations)
{
$this->theLevel = $this->theLevel - 1 ;
return array() ;
}
$theClueChoice = mt_rand(0, count($thePossibleClues)-1) ;
$theValue = $thePossibleClues[$theClueChoice] ;
array_splice($thePossibleClues, $theClueChoice, 1) ;
$theClues[] = $theValue ;
$this->theBoard[$theRow][$theColumn]->flagSolvedPosition($theValue) ;
if ($this->theDebug ) { printf("<br>(%03d, %03d) Trying (%d, %d) = %d\n", $this->theLevel, $this->theGenerationIterations, $theRow, $theColumn, $theValue) ; } ;
$theFlag = $this->solve(false) ;
if ($this->_validateTrialSolution())
{
if ($theFlag)
{
/*
** We're done, so we can return the clues and their positions to the caller.
*/
for ($i = 0; $i < count($theCluesPositions); $i++)
{
array_push($theCluesPositions[$i], $theClues[$i]) ;
}
return $theCluesPositions ;
}
else
{
$xxx = $this->_generatePuzzle($theAvailablePositions, $theCluesPositions, $theClues) ;
if ($xxx)
{
return $xxx ;
}
}
}
/*
** We failed of a solution, back out the state and try the next possible value
** for this position.
*/
$this->theBoard = $theCurrentBoard ;
$this->_buildRCS() ;
array_pop($theClues) ;
}
$this->theLevel = $this->theLevel - 1 ;
/*
** If we get here, we've tried all possible values remaining for the chosen
** position and couldn't get a solution. Back out and try something else.
*/
return array() ;
}
/**
* Return the contents of the board as a string of digits and blanks. Blanks
* are used where the corresponding board item is an array, indicating the cell
* has not yet been solved.
*
* @desc Get the current state of the board as a string.
* @access public
*/
function getBoardAsString()
{
$theString = "" ;
for ($i = 1; $i <= 9; $i++)
{
for ($j = 1; $j <= 9; $j++)
{
$theString .= $this->theBoard[$i][$j]->asString() ;
}
}
return $theString ;
}
function &getCell($r, $c)
{
return $this->theBoard[$r][$c] ;
}
/**
* Each element of the input array is a triple consisting of (row, column, value).
* Each of these values is in the range 1..9.
*
* @access public
* @param array $theArray
*/
function initializePuzzleFromArray($theArray)
{
foreach ($theArray as $xxx)
{
$c =& $this->getCell($xxx[0], $xxx[1]) ;
$c->flagSolvedPosition($xxx[2]) ;
}
}
/**
* Initialize puzzle from an input file.
*
* The input file is a text file, blank or tab delimited, with each line being a
* triple consisting of "row column value". Each of these values is in the range
* 1..9. Input lines that are blank (all whitespace) or which begin with whitespace
* followed by a "#" character are ignored.
*
* @access public
* @param mixed $theHandle [optional] defaults to STDIN. If a string is passed
* instead of a file handle, the file is opened.
*/
function initializePuzzleFromFile($theHandle = STDIN)
{
$theOpenedFileFlag = FALSE ;
/*
** If a file name is passed instead of a resource, open the
** file and process it.
*/
if (is_string($theHandle))
{
$theHandle = fopen($theHandle, "r") ;
if ($theHandle === FALSE)
{
exit() ;
}
}
$yyy = array() ;
if ($theHandle)
{
while (!feof($theHandle))
{
$theString = trim(fgets($theHandle)) ;
if (($theString != "") &&
(!preg_match('/^\s*#/', $theString)))
{
$xxx = preg_split('/\s+/', $theString) ;
if (!feof($theHandle))
{
$yyy[] = array((int)$xxx[0], (int)$xxx[1], (int)$xxx[2]) ;
}
}
}
}
$this->initializePuzzleFromArray($yyy) ;
if ($theOpenedFileFlag)
{
fclose($theHandle) ;
}
}
/**
* The input parameter consists of a string of 81 digits and blanks. If fewer characters
* are provide, the string is padded on the right.
*
* @desc Initialize puzzle from a string.
* @access public
* @param string $theString The initial state of each cell in the puzzle.
*/
function initializePuzzleFromString($theString)
{
$theString = str_pad($theString, 81, " ") ;
for ($i = 0; $i < 81; $i++)
{
if ($theString{$i} != " ")
{
$theArray[] = array((int)($i/9) + 1, ($i % 9) + 1, (int)$theString{$i}) ;
}
}
$this->initializePuzzleFromArray($theArray) ;
}
/**
* @desc predicate to determine if the current puzzle has been solved.
* @access public
* @return boolean true if the puzzle has been solved.
*/
function isSolved()
{
for ($i = 1; $i <= 9; $i++)
{
for ($j = 1; $j <=9; $j++)
{
if (!$this->theBoard[$i][$j]->IsSolved())
{
return false ;
}
}
}
return true ;
}
/**
* Convert pending to actual solutions.
*
* This step is actually unnecessary unless you want a pretty output of the
* intermediate.
*
* @access private
* @return boolean True if at least on pending solution existed, false otherwise.
*/
function _newSolvedPosition()
{
$theReturn = false ;
for ($i = 1; $i <= 9; $i++)
{
for ($j = 1; $j <= 9; $j++)
{
if ($this->theBoard[$i][$j]->solvedState() == 1)
{
$this->theBoard[$i][$j]->un_set($this->theBoard[$i][$j]->getState()) ;
$theReturn = true ;
}
}
}
return $theReturn ;
}
/**
* Print the contents of the board in HTML format.
*
* A "hook" so that extension classes can show all the steps taken by
* the solve function.
*
* @see SudokuIntermediateSolution.
*
* @access private
* @param string $theHeader [optional] The header line to be output along
* with the intermediate solution.
*/
function _printIntermediateSolution($theHeader = NULL)
{
if ($this->theDebug)
$this->printSolution($theHeader) ;
}
/**
* Print the contents of the board in HTML format.
*
* Simple output, is tailored by hand so that an initial state and
* a solution will find nicely upon a single 8.5 x 11 page of paper.
*
* @access public
* @param mixed $theHeader [optional] The header line[s] to be output along
* with the solution.
*/
function printSolution($theHeader = NULL)
{
if (($this->theDebug) && ($theHeader != NULL))
{
if (is_array($theHeader))
{
foreach ($theHeader as $aHeader)
print $aHeader ;
}
else
print $theHeader ;
}
$theColors = array("green", "blue", "red") ;
$theFontSize = array("1em", "1em", ".8em") ;
$theFontWeight = array("bold", "bold", "lighter") ;
printf("<br /><table border=\"1\" style=\"border-collapse: separate; border-spacing: 0px;\">\n") ;
$theLast = 2 ;
for ($i = 1; $i <= 9; $i++)
{
if ($theLast == 2)
printf("<tr>\n") ;
printf("<td><table border=\"1\" width=\"100%%\">\n") ;
$theLast1 = 2 ;
for ($j = 1; $j <=9; $j++)
{
if ($theLast1 == 2)
printf("<tr>\n") ;
$c = &$this->theSquares[$i] ;
$c =& $c->getCell($j) ; ;
$theSolvedState = $c->solvedState() ;
printf("<td style=\"text-align: center; padding: .6em; color: %s; font-weight: %s; font-size: %s;\">",
$theColors[$theSolvedState],
$theFontWeight[$theSolvedState],
$theFontSize[$theSolvedState]) ;
$xxx = $c->asString($this->theDebug) ;
print ($xxx == " " ? "&nbsp;" : $xxx) ;
printf("</td>\n") ;
$theLast1 = ($j - 1) % 3 ;
if ($theLast1 == 2)
printf("</tr>\n") ;
}
printf("</table></td>\n") ;
$theLast = ($i - 1) % 3 ;
if ($theLast == 2)
printf("</tr>\n") ;
}
printf("</table>\n") ;
}
/**
* Solve a Sudoku.
*
* As explained earlier, this works by iterating upon three different
* types of inference:
*
* 1. A negative one, in which a value used within a row/column/square
* may not appear elsewhere within the enclosing row/column/square.
* 2. A positive one, in which any value with is unique in a row
* or column or square must be the solution to that position.
* 3. A tuple based positive one which comes in a number of flavors:
* 3a. The "Pair" rule as stated by the author of the "other" Sudoku
* class on phpclasses.org and generalized by me, e.g., in any RCS
* two cells containing a pair of values eliminate those values from
* consideration in the rest of the RC or S.
* 3b. The n/n+1 set rule as discovered by me, e.g., in any RCS, three cells
* containing the following pattern, (i, j)/(j, k)/(i, j, k) eliminate
* the values i, j, k from consideration in the rest of the RC or S.
*
* During processing I explain which structures (row, column, square)
* are being used to infer solutions.
*
* @access public
* @param boolean $theInitialStateFlag [optional] True if the initial
* state of the board is to be printed upon entry, false
* otherwise. [Default = true]
* @return boolean true if a solution was possible, false otherwise.
*/
function solve($theInitialStateFlag = true)
{
$theHeader = "<br />Initial Position:" ;
do
{
do
{
$this->_applySolvedPositions() ;
if ($theInitialStateFlag)
{
$this->_printIntermediateSolution($theHeader) ;
$theHeader = NULL ;
}
else
{
$theInitialStateFlag = true ;
$theHeader = "<br />Apply Slice and Dice:" ;
}
} while ($this->_newSolvedPosition()) ;
$theRowIteration = FALSE ;
for ($i = 1; $i <= 9; $i++)
{
if ($this->theRows[$i]->doAnInference())
{
$theHeader = $this->theRows[$i]->getHeader() ;
$theRowIteration = TRUE ;
break ;
}
}
$theColumnIteration = FALSE ;
if (!$theRowIteration)
{
for ($i = 1; $i <= 9; $i++)
{
if ($this->theColumns[$i]->doAnInference())
{
$theHeader = $this->theColumns[$i]->getHeader() ;
$theColumnIteration = TRUE ;
break ;
}
}
}
$theSquareIteration = FALSE ;
if (!($theRowIteration || $theColumnIteration))
{
for ($i = 1; $i <= 9; $i++)
{
if ($this->theSquares[$i]->doAnInference())
{
$theHeader = $this->theSquares[$i]->getHeader() ;
$theSquareIteration = TRUE ;
break ;
}
}
}
} while ($theRowIteration || $theColumnIteration || $theSquareIteration) ;
return $this->IsSolved() ;
}
/**
* Here there be dragons. In conversations with other Sudoku folks, I find that there ARE Sudoku with
* unique solutions for which a clue set may be incomplete, i.e., does not lead to a solution. The
* solution may only be found by guessing the next move. I'm of the opinion that this violates the
* definition of Sudoku (in which it's frequently said "never guess") but if it's possible to find
* a solution, this will do it.
*
* The problem is that it can take a LONG time if there ISN'T a solution since this is basically a
* backtracing solution trier.
*
* The basic algorithm is pretty simple:
*
* 1. Find the first unsolved cell.
* 2. For every possible value, substutite value for the cell, apply inferences.
* 3. If a solution was found, we're done.
* 4. Recurse looking for the next cell to try a value for.
*
* There's a bit of bookkeeping to keep the state right when backing up, but that's pretty
* straightforward and looks a lot like that of generatePuzzle.
*
* @desc Brute force additional solutions.
* @access public
* @returns array The clues added sufficient to solve the puzzle.
*/
function solveBruteForce($i = 1, $j = 1)
{
for (; $i <= 9; $i++)
{
for (; $j <= 9; $j++)
{
if ($this->theBoard[$i][$j]->solvedState() != 0)
{
if ($this->theDebug)
{
printf("<br />Applying Brute Force to %d, %d\n", $i, $j) ;
}
$theCurrentBoard = $this->deepCopy($this->theBoard) ;
$theValues = $this->theBoard[$i][$j]->getState() ;
foreach ($theValues as $theValue)
{
$this->theBoard[$i][$j]->flagSolvedPosition($theValue) ;
$theSolutionFlag = $this->solve() ;
$theTrialSolutionFlag = $this->_validateTrialSolution() ;
if ($theTrialSolutionFlag && $theSolutionFlag)
{
return array(array($i, $j, $theValue)) ;
}
if ($theTrialSolutionFlag)
{
$theNewGuesses = $this->solveBruteForce($i, $j+1) ;
if ($theNewGuesses)
{
$theNewGuesses[] = array($i, $j, $theValue) ;
return $theNewGuesses ;
}
}
if ($this->theDebug)
{
printf("<br />Backing out\n") ;
}
$this->theBoard = $theCurrentBoard ;
$this->_buildRCS() ;
}
return array() ;
}
}
}
}
/**
* @desc Calculate the index of the square containing a specific cell.
* @param integer $theRow the row coordinate.
* @param integer $theColumn the column coordinate.
* @return integer the square index in the range 1..9
*/
function _squareIndex($theRow, $theColumn)
{
$theIndex = ((int)(($theRow - 1) / 3) * 3) + (int)(($theColumn - 1) / 3) + 1 ;
return $theIndex ;
}
/**
* Validate a complete solution.
*
* After a complete solution has been generated check the board and
* report any inconsistencies. This is primarily intended for debugging
* purposes.
*
* @access public
* @return mixed true if the solution is valid, an array containing the
* error details.
*/
function validateSolution()
{
$theReturn = array() ;
for ($i = 1; $i <= 9; $i++)
{
if (!$this->theRows[$i]->validateSolution())
{
$theReturn[0][] = $i ;
}
if (!$this->theColumns[$i]->validateSolution())
{
$theReturn[1][] = $i ;
}
if (!$this->theSquares[$i]->validateSolution())
{
$theReturn[2][] = $i ;
}
}
return (count($theReturn) == 0 ? TRUE : $theReturn) ;
}
/**
* Validate an entire trial solution.
*
* Used during puzzle generation to determine when to backtrace.
*
* @access private
* @return True when the intermediate soltuion is valid, false otherwise.
*/
function _validateTrialSolution()
{
for ($i = 1; $i <= 9; $i++)
{
if (!(($this->theRows[$i]->validateTrialSolution()) &&
($this->theColumns[$i]->validateTrialSolution()) &&
($this->theSquares[$i]->validateTrialSolution())))
{
return FALSE ;
}
}
return TRUE ;
}
}
/**
* Extend Sudoku to generate puzzles based on templates.
*
* Templates are either input files or arrays containing doubles.
*
* @package Sudoku
*/
class SudokuTemplates extends Sudoku
{
function SudokuTemplates($theDebug = FALSE)
{
$this->Sudoku($theDebug) ;
}
function generatePuzzleFromFile($theHandle = STDIN, $theDifficultyLevel = 10)
{
$yyy = array() ;
if ($theHandle)
{
while (!feof($theHandle))
{
$theString = trim(fgets($theHandle)) ;
$xxx = preg_split("/\s+/", $theString) ;
if (!feof($theHandle))
{
$yyy[] = array((int)$xxx[0], (int)$xxx[1]) ;
}
}
}
return $this->generatePuzzleFromArray($yyy, $theDifficultyLevel) ;
}
function generatePuzzleFromArray($theArray, $theDifficultyLevel = 10)
{
$this->_generatePuzzle($theArray, array(), array()) ;
/*
** Because the generation process may infer values for some of the
** template cells, we construct the clues from the board and the
** input array before continuing to generate the puzzle.
*/
foreach ($theArray as $theKey => $thePosition)
{
$theTemplateClues[] = array($thePosition[0], $thePosition[1], $this->theBoard[$thePosition[0]][$thePosition[1]]) ;
}
$theOtherClues = $this->generatePuzzle($theDifficultyLevel) ;
return array_merge($theTemplateClues, $theOtherClues) ;
}
}
/**
* Extend Sudoku to print all intermediate results.
*
* @package Sudoku
*/
class SudokuIntermediateSolution extends Sudoku
{
function SudokuIntermediateResults($theDebug = FALSE)
{
$this->Sudoku($theDebug) ;
}
function _printIntermediateSolution($theHeader = NULL)
{
$this->printSolution($theHeader) ;
}
}
function make_seed()
{
list($usec, $sec) = explode(' ', microtime());
return (float) $sec + ((float) $usec * 100000);
}
?>