สอบถามปัญหาการสลับเลข มีแนวทางการแก้ไขปัญหายังไงบ้างครับ

/**
 * Multiply step down by one until number is 1.
 * 
 * Example: number is 3 will be 3*2*1 = 6<br>
 * number is 4 will be 4*3*2*1 = 24
 *
 * @param number $number
 * @return number
 */
function factorial($number)
{
    if ($number == 1) {
        return $number;
    } else {
        return $number * factorial($number - 1);
    }
}

include_once 'factorial.php';


$testNumber = 113;
$numbersArray = str_split($testNumber);
if (is_array($numbersArray)) {
    $totalNumbers = count($numbersArray);
    // 2 numbers possibility arrange is 2*1 = 2, 
    // 3 numbers possibility is 3*2*1 = 6, 
    // 4 numbers possibility is 4*3*2*1 = 24,
    // 5 numbers possibility is 5*4*3*2*1 = 120
    $maxPossibilityArrange = factorial($totalNumbers);

    $output = [];
    $outputKeys = [];
    $numberArrayKeys = array_keys($numbersArray);

    while (count($outputKeys) < $maxPossibilityArrange) {
        shuffle($numberArrayKeys);
        if (!in_array($numberArrayKeys, $outputKeys)) {
            $outputKeys[] = $numberArrayKeys;
        }
    }

    unset($maxPossibilityArrange, $numberArrayKeys, $totalNumbers);

    foreach ($outputKeys as $eachArray) {
        $number = '';
        foreach ($eachArray as $eachKey) {
            if (isset($numbersArray[$eachKey])) {
                $number .= $numbersArray[$eachKey];
            }
        }
        $output[] = $number;
    }
    unset($number, $outputKeys);

    sort($output);
    echo '<pre>'.print_r($output, true).'</pre>'.PHP_EOL;
} else {
    echo 'unable to continue, cannot split numbers into array.';
    exit();
}

<?php
function Modi(&$f,&$s, &$ar){
	$l=strlen($s);
	for($i=0; $i<$l; $i++){			
		$x=$f.substr($s,$i,1);
		//------------------------------------
		if($i==0){$y=substr($s,1);}
		elseif($i==($l-1)){ $y=substr($s,0,$i);} 
		else{$y=substr($s,0,$i).substr($s,$i+1);}
		if ($f.$s!=$x.$y) $ar[]=$x.$y;
		Modi($x, $y, $ar);
	}
}
function map($s, &$ar){
	foreach($ar as $x){
		$z='';
		for($i=0; $i<strlen($x); $i++){
			$z.=$s[$x[$i]];
		}
		echo '<br>',$z;
	}
}
$st = time();
$digit = isset($_GET['digit'])? $_GET['digit']: 5; // default สำหรับ 5 หลัก
$number = str_repeat('0123456789',$digit);
echo $src = substr(str_shuffle($number),0,$digit),'<br>';
$z=''; $tmp=substr('0123456789',0,$digit);
$ar=[$tmp];
Modi($z, $tmp, $ar);
$en = time();
echo '<br>TimeUse = ', $en - $st, '<br>Loop = ',count($ar);
map($src,$ar);