unique-grid-fill-to-csv.php

<?php

/* 
 * Problem
 * -------
 * 
 * I needed a set of undefined size of card layouts on a 5x5 grid that were 
 * rotationally unique from each other. This data had to be as CSV lines in a 
 * file.
 * 
 * Solution
 * --------
 * 
 * Treat the two dimentions of an array as cartesian coordinates and transform
 * the vectors to create four rotations for each additional candidate which
 * can then be used as a string comparison against the list of accepted 
 * candidates.
 * 
 * planning
 * --------
 * 
 * 5x5 grid must have n1 to n2 filled spaces
 * If rotated in all four positions it must be unique
 * If it is add it to collection.
 * Repeat until LIMIT tries fail
 * 
 * 
00000
00000
00000
00000
00000

x2,y3

00000
00@00
0@0@0
00@00
00000

c=size+1

 x2,y3
ix=c-x=4,-> ix4,y3 
 x3,y2 (swap)
i: x3,y4 
 */

// fixed information
define('_GRID_SIZE_',5);
define('_FILE_PATH_','/path/to/grid.csv');

// stuff that I wanted to tweak
$limit = 35;    // how many fails before we give up?
$maxSize=120;   // how many to find?
$n = 4;         // size of fills (how many filled in squares)?
$low_n = 2;     // if we cannot find any more, what size may we drop down to?

mt_srand();

/**
 * Creates an array with a random grid vector
 * @return array
 */
function rand_xy(){
    return array(mt_rand(0,(_GRID_SIZE_-1)),mt_rand(0,(_GRID_SIZE_-1)));
}
/**
 * Check for rotational uniqueness.
 * @param array $test
 * @param array $collection
 * @return boolean
 */
function is_new($test,$collection){
    $stringSet = array();
    foreach($collection as $one){
        $stringSet[] = grid_as_string($one);
    }

    $testString = grid_as_string($test); # no rotation
    $r1 = array();
    $r2 = array();
    $r3 = array();
    foreach($test as $x=>$row){
        foreach($row as $y=>$bool){
            if($bool){
                $r1[_GRID_SIZE_-$x][$y]=TRUE;   # 2nd rotation  :: $invX = _GRID_SIZE_-$x; // we're already plus one!!
                $r2[$y][$x]=TRUE;               # 1st rotation  :: swap X,Y
                $r3[$y][_GRID_SIZE_-$x]=TRUE;   # 3rd and final :: swap invX,Y
            }
        }
    }
    $testStringR1 = grid_as_string($r1);
    $testStringR2 = grid_as_string($r2);
    $testStringR3 = grid_as_string($r2);
    
    if(     in_array($testString, $stringSet)   ||
            in_array($testStringR1, $stringSet) ||
            in_array($testStringR2, $stringSet) ||
            in_array($testStringR3, $stringSet) 
        ){ return FALSE; }
        
    # it must be good
    return TRUE;
}

function size_of_collection($collection){
    return count($collection); // this was probably a bit pointless
}

function grid_as_string($ar,$join='',$FF='0',$TT='1'){
    $str='';
    $first=TRUE;
    for ($i = 0; $i < (_GRID_SIZE_*_GRID_SIZE_); $i++) {
        if(!$first){
            $str .= $join;
        }
        $str .= $FF;
        $first=FALSE;
    }
    #print_r($ar);
    foreach($ar as $x=>$row){
        foreach($row as $y=>$bool){
            #if($bool){
                $pos = ($x+(_GRID_SIZE_*$y))*strlen($FF);
                $pos = $pos*(strlen($join))+$pos;
                $str[$pos]=$TT;
            #}
        } 
    }
    return $str;
}
/**
 * Hard and slow
 * @param array $ar
 */
function fill_count($ar){
    $c=0;
    foreach($ar as $x=>$row){
        foreach($row as $y=>$bool){
            $c++;
        } 
    }
    return $c;
}

function fill_with(&$ar,$n){
    $i=0;
    while( (fill_count($ar)<$n) && $i<12 ){
        $get = rand_xy();
        $ar[$get[0]][$get[1]]=TRUE;
    }
}

$collection = array();
$i=0;

while($i<$limit){
    $test = array();
    fill_with($test, $n);
    if(is_new($test, $collection)){
        $collection[]=$test;// add to collection
        $i=0;
    }else{
        ++$i;
    }
    if(size_of_collection($collection)>=$maxSize){
        $i=$limit;
        break;
    }
    if($i>($limit-3)){
        if($n>$low_n){
            --$n;
            $i=0;
        }
    }
}

$stringSet = array();
foreach($collection as $one){
    $stringSet[] = grid_as_string($one,',','N','Y');
}
$str = implode("\n", $stringSet);
file_put_contents(_FILE_PATH_, $str);

#echo "<pre>";
#print_r($collection);