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

Here's what I could come up with:

function inject($elem, $array) {
    return array_map(function ($n) use ($elem) { return array_merge((array)$elem, (array)$n); }, $array);
}

function zip($array1, $array2) {
    return array_reduce($array1, function ($v, $n) use ($array2) { return array_merge($v, inject($n, $array2));  }, array());
}

function cartesian_product($array) {
    $keys = array_keys($array);
    $prod = array_shift($array);
    $prod = array_reduce($array, 'zip', $prod);
    return array_map(function ($n) use ($keys) { return array_combine($keys, $n); }, $prod);
}

---

(Using pseudo array/list/dictionary notation below since PHP is simply too verbose for such things.)

The inject function transforms a, [b] into [(a,b)], i.e. it injects a single value into each value of an array, returning an array of arrays. It doesn't matter whether a or b already is an array, it'll always return a two dimensional array.

inject('a', ['foo', 'bar'])
    =>  [('a', 'foo'), ('b', 'bar')]

The zip function applies the inject function to each element in an array.

zip(['a', 'b'], ['foo', 'bar'])
    =>  [('a', 'foo'), ('a', 'bar'), ('b', 'foo'), ('b', 'bar')]

Note that this actually produces a cartesian product, so zip is a slight misnomer. Simply applying this function to all elements in a data set in succession gives you the cartesian product for an array of any length.

zip(zip(['a', 'b'], ['foo', 'bar']), ['42', '76'])
    =>  [('a', 'foo', '42'), ('a', 'foo', '76'), ('a', 'bar', '42'), …]

This does not contain the keys, but since the elements are all in order within the result set, you can simply re-inject the keys into the result.

array_combine(['key1', 'key2', 'key3'], ['a', 'foo', '42'])
    =>  [ key1 : 'a', key2 : 'foo', key3 : '42' ]

Applying this to all elements in the product gives the desired result.

You can collapse the above three functions into a single long statement if you wish (which would also clear up the misnomers).

---

An "unrolled" version without anonymous functions for PHP <= 5.2 would look like this:

function inject($elem, $array) {
    $elem = (array)$elem;
    foreach ($array as &$a) {
        $a = array_merge($elem, (array)$a);
    }
    return $array;
}

function zip($array1, $array2) {
    $prod = array();
    foreach ($array1 as $a) {
        $prod = array_merge($prod, inject($a, $array2));
    }
    return $prod;
}

function cartesian_product($array) {
    $keys = array_keys($array);
    $prod = array_shift($array);
    $prod = array_reduce($array, 'zip', $prod);

    foreach ($prod as &$a) {
        $a = array_combine($keys, $a);
    }
    return $prod;
}