两个数组的所有组合PHP

Question

I am reposting this, reworded, as the initial question didn't make much sense written down.

I am trying to write a little piece of code that will add maths questions to a database. These ones are ratio questions.

For instance I want to add lots of questions like 'Simplify 10: 6' and store the answer as '5 : 3'.

I was thinking the best thing to do would be store the digits as an array, and the early primes as an array (I only want prime multiples for now).

I could then loop though this array. This I can do. However, I want every single possible combination of my digits, not just to loop through the array once.

For instance I want the questions 2 : 4 , 3: 6, 5 : 10, 7: 14 etc etc

So I want to pair digits[0...8] with every other digit, and then loop though the primes multiplying these combinations with every prime. I get that this would probably be some kind of nested for loop, but i've not really got much of an idea where to start.

This is what I have so far. It does exactly nothing. I realise it would have been quicker to manually input all there but I want to learn a bit of coding, too.

   $digits = array(9,8,7,6,5,4,3,2,1);
   $primes = array(2,3,5,7,11);

   for ($first = 0; $first < count($digits)-1; $first++) {
         $num1 = $digits[$first];
      for ($second = 1; $second < count($digits)-2; $second++) {
         $num2 = $digits[$second];
            for ($third = 0; $third < count($primes)-1; $third++) {
         $num3 = $num1 * $primes[$third];
         $num4 = $num2 * $primes[$third];

         $questionlead = "Simplify <br>" .$num3. " : " . $num4 ;
         $ans = $num1. " : " . $num2 ;

   $dbhost = 'nope';
   $dbuser = 'notfor';
   $dbpass = 'you';

   $conn = mysql_connect($dbhost, $dbuser, $dbpass);

   if(! $conn ) {
      die('Could not connect: ' . mysql_error());
   }

   $sql = "INSERT INTO QuestionDB(TopicID, TopicName, SubtopicID, SubtopicName, Question, Answer, Difficulty, Author, Projectable) VALUES (6,'Ratio',1,'Simplifying ratio','".$questionlead. "','".$ans. "',1,'Richard Tock','Yes')";
   mysql_select_db('db_name');
   $retval = mysql_query( $sql, $conn );

   if(! $retval ) {
      die('Could not get data: ' . mysql_error());
   }

      }
}
}
   mysql_close($conn);
?>

I'm lost at sea here

Answer 1

This first function is the "smart" part because it does all the arithmetic. It does not do simplifying after the fact, so if you end up finding an answer in the loop, it may be worth checking out if 1 is divided by 1, then you could just return 1. But I wanted to keep it this way depending on how you wanted to use it!

function simplify(Int $num, Int $denom, Array $primes){
    //going from high primes to low primes
    foreach(array_reverse($primes) as $prime) {
        if (($num % $prime == 0) && ($denom % $prime == 0)) {
            if ($num % $denom == 0) {
                return [intdiv($num,$denom)];
            } elseif ($denom % $num == 0) {
                return [1,intdiv($denom,$num)];
            }
            return [$num / $prime,$denom / $prime];
        }
    }
    return [$num,$denom];
}

This next function does the looping through 2 arrays of numbers. It is fairly ugly, I don't usually like nested for loops.

function simplifyArrays(Array $arr1, Array $arr2, Array $primes) {
    for($i=0; $i<count($arr1); $i++){
        $num1 = $arr1[$i];
        for($j=0; $j<count($arr2); $j++){
            $num2 = $arr2[$j];
            echo "simplify: $num1 / $num2 = " . implode("/",simplify($num1,$num2,$primes)) . "\n";
        }
    }
}

And to see it in action: https://3v4l.org/qmgJX