all combinations of boolean values in PHP

Question

Related to Generating all the combinations of a set of boolean variables in Haskell and various other questions of the type.

I have a bunch of toggle switches in a database and want to get a list of all possible settings. The number of switches can change, specifically, users can add or remove.

I can get them into an array like

$switches = array('aaa', 'bbb', 'ccc');

and I would like to generate all possibilities, i.e. something like:

$states = array(
array('aaa' => false, 'bbb' => false, 'ccc' => false),
array('aaa' => false, 'bbb' => false, 'ccc' => true),
array('aaa' => false, 'bbb' => true, 'ccc' => false),
array('aaa' => false, 'bbb' => true, 'ccc' => true),
...
);

I don't particularily care in which order the result set is.

What's an elegant way to generate that?

recursion would be the right approach here. You should be able to work something out based on the answers here: https://stackoverflow.com/questions/21556945/all-possible-combinations-in-array-recursion — Jarek.D, Mar 05 '19 at 15:11
did you *try* anything so far? personally, i'd count the switches, iterate from 0 to ^2n-1 and map the bits of the integer to the switches. — Franz Gleichmann, Mar 05 '19 at 16:48
@FranzGleichmann That exactly what I offered in my answer :) — dWinder, Mar 05 '19 at 16:50
@FranzGleichmann yes, I tried a naive recursive approach that didn't quite work out. — Tom, Mar 05 '19 at 17:09
neither of the two answers given so far work if the keys are integers, btw. — Tom, Mar 06 '19 at 09:42
@dWinder I might've made a mistake in the data output behind your code. — Tom, Mar 06 '19 at 13:14
@dWinder gave it a quick check and it seems to work, but I went with the other answer in the end. — Tom, Mar 10 '19 at 18:08

score 1 · Accepted Answer · answered Mar 05 '19 at 15:14

Dunno if it's elegant, but for example use array_reduce with a callback:

$a = ['a', 'b', 'c'];
$states = array_reduce($a, function ($t, $v) {
    $newt = [];
    if (empty($t)) {
        $newt = [
            [$v => false],
            [$v => true],
        ];
    } else {
        foreach ($t as $item) {
            $newt[] = array_merge($item, [$v => false]);
            $newt[] = array_merge($item, [$v => true]);
        }
    }

    return $newt;
}, []);
var_dump($states);

replace the array_merge with the + operator and it works for numerical keys, too. — Tom, Mar 06 '19 at 09:47

dWinder · Answer 2 · 2019-03-05T15:51:45.280

I would have going or the idea of using the binary representation of integers (using decbin):

$keys = ["aaa", "bbb", "ccc"];
$n = count($keys);
for($i = 0; $i < pow(2,$n); $i++) {
    $num = array_reverse(str_split(decbin($i)));
    $res[] = array_pad($num, $n, 0);   
}

foreach($res as &$e) // adding the keys to the result
    $e = array_combine($keys, $e);

Notice the decbin can return string less then 2^$n so I reverse the string and pad with 0 using array-pad

Notice this will generate array with 0 and 1 instead of true and false but in PHP they very much alike - anyway, swapping them for true and false is easy enough so I leave it to you...

all combinations of boolean values in PHP

2 Answers2