Combinations, Dispositions and Permutations in PHP

Question

What is the most efficient way to generate all the combinations, dispositions and permutations of an array in PHP?

Answer 1

Here is code to get all permutations:

http://php.net/manual/en/function.shuffle.php#90615

With the code to get the power set, permutations are those of maximal length, the power set should be all combinations. I have no idea what dispositions are, so if you can explain them, that would help.

Answer 2

You can use this class: http://pear.php.net/package/Math_Combinatorics

and use it like:

$combinatorics = new Math_Combinatorics;

$words_arr = array(
    'one'   => 'a',
    'two'   => 'b',
    'three' => 'c',
    'four'  => 'd',
    );

for ($i=count($words_arr)-1;$i>=1;$i--) {
    echo '<br><br>' . $i . ':<br>';
    $combinations_arr = $combinatorics->combinations($words_arr, $i);
    foreach ($combinations_arr as $combinations_arr_item) {
        echo implode(', ', $combinations_arr_item) . '<br>';
    }
}

Answer 3

I'd like to suggest my solution of a CombinationsGenerator, which generates combinations of array items.

It's limited to all combinations are of the full length, and not repeats any item. But I believe implementation would not be too hard.

class CombinationsGenerator
{
    public function generate(array $list): \Generator
    {
        if (count($list) > 2) {
            for ($i = 0; $i < count($list); $i++) {
                $listCopy = $list;

                $entry = array_splice($listCopy, $i, 1);
                foreach ($this->generate($listCopy) as $combination) {
                    yield array_merge($entry, $combination);
                }
            }
        } elseif (count($list) > 0) {
            yield $list;

            if (count($list) > 1) {
                yield array_reverse($list);
            }
        }
    }
}

$generator = new \CombinationsGenerator();

foreach ($generator->generate(['A', 'B', 'C', 'D']) as $combination) {
    var_dump($combination);
}

It's in PHP7 style, it uses a \Generator 'cause I believe there are good reasons for doing it.

Answer 4

/* Combinations */
function nCr($n, $r)
{
  if ($r > $n)
  {
    return NaN;
  }
  if (($n - $r) < $r)
  {
    return nCr($n, ($n - $r));
  }
  $return = 1;
  for ($i = 0; $i < $r; $i++)
  {
    $return *= ($n - $i) / ($i +1);
  }
  return $return;
}

/* Permutations */
function nPr($n, $r)
{
  if ($r > $n)
  {
    return NaN;
  }
  if ($r)
  {
    return $n * (nPr($n -1, $r -1));
  }
  else
  {
    return 1;
  }
}

Answer 5

I had to modify @hejdav's answer so that it includes partial combinations, so that it fully delivers all of the results.

I scoured the Internet for this solution and as of June 2019, I believe this is the only publicly accessible answer (anywhere) that truly lists all possible, non-duplicating possibilities.

class CombinationsGenerator
{
    /**
     * Taken from https://stackoverflow.com/a/39447347/430062.
     * 
     * @param array $list
     * @return \Generator
     */
    public function generate(array $list): \Generator
    {
        // Generate even partial combinations.
        $list = array_values($list);
        $listCount = count($list);
        for ($a = 0; $a < $listCount; ++$a) {
            yield [$list[$a]];
        }

        if ($listCount > 2) {
            for ($i = 0; $i < count($list); $i++) {
                $listCopy = $list;

                $entry = array_splice($listCopy, $i, 1);
                foreach ($this->generate($listCopy) as $combination) {
                    yield array_merge($entry, $combination);
                }
            }
        } elseif (count($list) > 0) {
            yield $list;

            if (count($list) > 1) {
                yield array_reverse($list);
            }
        }
    }
}