Finding cartesian product with PHP associative arrays

Question

Say that I have an array like the following:

Array
(
    [arm] => Array
        (
            [0] => A
            [1] => B
            [2] => C
         


        

Answer 1

Another solution:

function getAllVariations($input) {
    $result = array();
    $cnt = array_product(array_map('count', $input));
    $step = 1;
    foreach ($input as $key=>$array) {
        for ($i=0; $i<$cnt; $i++) {
            foreach ($array as $value) {
                for ($k=0; $k<$step; $k++) {
                    $result[$i+$k][$key] = $value;
                }
                $i += $step;
            }
            $i--;
        }
        $step = $step * count($array);
    }
    return $result;
}

Usage:

$input = array(
    'arm' => array('A', 'B', 'C'),
    'gender' => array('Female', 'Male'),
    'location' => array('Vancouver', 'Calgary'),
    'name' => array('Rio', 'Mark')
);

echo "<pre>";
var_dump(getAllVariations($input));

Answer 2

If memory consumption is important or you don't need all the combinations in the end you could use an iterator to generate one combination at a time. If you need all the combinations you can use iterator_to_array.

function cartezianIterator($inputArray)
{
    $maximumPosition = array_map('count', $inputArray);
    $position = array_pad([], count($inputArray), 0);

    while (false !== ($item = buildItemAtPosition($inputArray, $position))) {

        yield $item;

        $position = incrementPosition($position, $maximumPosition);
    }
}

function buildItemAtPosition($inputArray, $positions)
{
    if ($positions[0] >= count($inputArray[0])) {
        return false;
    }

    $item = [];
    foreach ($inputArray as $rowIndex => $row) {
        $position = $positions[$rowIndex];

        $item[] = $row[$position];
    }

    return $item;
}

function incrementPosition($position, $maximumPosition)
{
    $digitToIncrement = count($position) - 1;

    do {
        $position[$digitToIncrement]++;

        if ($position[$digitToIncrement] < $maximumPosition[$digitToIncrement] || 0 === $digitToIncrement) {
            //no overflow
            break;
        }

        //overflow, reset to zero and increment parent digit
        $position[$digitToIncrement] = 0;

        $digitToIncrement--;
    } while ($digitToIncrement >= 0);

    return $position;
}

Then, to get one solution at a time you could use a foreach or next, like this:

$iterator = cartezianIterator($inputArray);

//of course, you need to do something with the result...
$combination = next($iterator);
$combination = next($iterator);
$combination = next($iterator);
$combination = next($iterator);
$combination = next($iterator);
$combination = next($iterator);

This solution is very very fast if you need only a few combinations. Also, the memory consumption is very low (it uses a flat array to store some integers).

Note: recursive functions are not used.

Answer 3

Here is optimized version of @Jon's cartesian function:

function cartesian($input) {
    $result = array(array());

    foreach ($input as $key => $values) {
        $append = array();

        foreach($result as $product) {
            foreach($values as $item) {
                $product[$key] = $item;
                $append[] = $product;
            }
        }

        $result = $append;
    }

    return $result;
}

Read more about the math behind this algorithm: http://en.wikipedia.org/wiki/Cartesian_product

See more examples of this algorithm in different languages: https://rosettacode.org/wiki/Cartesian_product_of_two_or_more_lists

Answer 4

In PHP 7 @Serg's answer can be shortened to:

function cartesian(array $input)
{
    $result = [[]];
    foreach ($input as $key => $values) {
        $append = [];
        foreach ($values as $value) {
            foreach ($result as $data) {
                $append[] = $data + [$key => $value];
            }
        }
        $result = $append;
    }

    return $result;
}

Answer 5

Why not use a database to do this?

It's easy in MySQL..

table arm
   id integer primary key
   label char

table gender
   id integer primary key
   gender enum('male','female')

table location
   id integer primary key
   city varchar(255)

Then do a query

$query = mysql_query(" 
  SELECT a.label, g.gender, l.city
  FROM arm a
  CROSS JOIN gender g
  CROSS JOIN location l
  ORDER BY a.id
") or die("Could not execute query");

while($row = mysql_fetch_array($query) )
{
   ....
}

And read that out:

Answer 6

I quickly adjusted your code a bit , my attempt is crude i think but see if this works as you want:

$result = array();
$nm = '';
foreach ($map as $name => $a) {
    if (empty($result)) {
        $result = $a;
        $nm = $name;
        continue;
    }

    $res = array();
    foreach ($result as $r) {
        foreach ($a as $v) {
            $myr = $r;
            $myv = $v;
            if(!is_array($r)) $myr = array($nm => $r);
            if(!is_array($v)) $myv = array($name => $v);

            $res[] = array_merge($myr, $myv);
        }
    }
    $result = $res;
}
echo "<pre>";
print_r($result);