问PHP从答案生成数学方程

EN

<?php

$n = 6688650;

//generates a list of all factors
function primefactor($num) {
    $sqrt = sqrt($num);
    for ($i = 2; $i <= $sqrt; $i++) {
        if ($num % $i == 0) {
            return array_merge(primefactor($num/$i), array($i));
        }
    }
    return array($num);
}

//generates multiplication equation
//  Let's scramble those numbers

$factors = primefactor($n);

//let's randomly combine some of our prime factors
for ($i = 0, $len = count($factors); $i < $len; $i++) {
  if (mt_rand(0,1)) {
    $keys = array_rand($factors,2);
    $to = $factors[$keys[0]]*$factors[$keys[1]];
    array_push($factors, $to);
    unset($factors[$keys[0]]);
    unset($factors[$keys[1]]);
  }
}

//now, let's insert some random addition
foreach ($factors as $key => $value) {
  if (mt_rand(0,1)) {
    $delta = mt_rand(1,$factors[$key]-1);
    $factors[$key] = '(' . ($value-$delta) . '+' . $delta . ')';
  }
}

//output the information
$myValues = array_values($factors);
shuffle($myValues);
echo join('*',$myValues);

?>

5185*(145+1145)
3*(59+27)*(23+62)*(269+36)
1462*(26+35)*5*5*(2+1)