How to Compute the Cartesian Product of PHP Associative Arrays While Preserving Key-Value Pairs?

Finding Cartesian Product with PHP Associative Arrays, Preserving Key-Value Pairs

Given an associative array with multiple sub-arrays representing different attributes, the task is to compute the Cartesian product while preserving the keys and their corresponding values.

Rationale

For an array $input with N sub-arrays, where each sub-array has Cn elements, we can proceed with induction:

• For N = 1, the Cartesian product is simply the input array itself.

• Assuming we have the Cartesian product of the first N-1 sub-arrays, we can compute the product of the Nth sub-array by:

  • In each item (array) within the product, add the pair KN => VN,1.
  • For each value VN,2 to VN,CN, add a copy of each item to the product, changing the value of KN to VN,m (for all 2 ≤ m ≤ CN).

Code

function cartesian($input) {
    $result = [];

    while (list($key, $values) = each($input)) {
        if (empty($values)) {
            continue;
        }

        if (empty($result)) {
            foreach ($values as $value) {
                $result[] = [$key => $value];
            }
        } else {
            $append = [];

            foreach ($result as &$product) {
                $product[$key] = array_shift($values);
                $copy = $product;

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

                array_unshift($values, $product[$key]);
            }

            $result = array_merge($result, $append);
        }
    }

    return $result;
}

Usage

$input = [
    'arm' => ['A', 'B', 'C'],
    'gender' => ['Female', 'Male'],
    'location' => ['Vancouver', 'Calgary'],
];

print_r(cartesian($input));

Will output the desired Cartesian product, preserving the keys and values:

Array
(
    [0] => Array
        (
            [arm] => A
            [gender] => Female
            [location] => Vancouver
        )

    [1] => Array
        (
            [arm] => A
            [gender] => Female
            [location] => Calgary
        )

    [2] => Array
        (
            [arm] => A
            [gender] => Male
            [location] => Vancouver
        )

...etc.

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