Finding the subsets of an array in PHP

You wish for the power set of $attributes? That is what your question implies.

An example can be found here (quoted for completeness)

<?php 
/** 
* Returns the power set of a one dimensional array, a 2-D array. 
* [a,b,c] -> [ [a], [b], [c], [a, b], [a, c], [b, c], [a, b, c] ]
*/ 
function powerSet($in,$minLength = 1) { 
   $count = count($in); 
   $members = pow(2,$count); 
   $return = array(); 
   for ($i = 0; $i < $members; $i++) { 
      $b = sprintf("%0".$count."b",$i); 
      $out = array(); 
      for ($j = 0; $j < $count; $j++) { 
         if ($b{$j} == '1') $out[] = $in[$j]; 
      } 
      if (count($out) >= $minLength) { 
         $return[] = $out; 
      } 
   } 
   return $return; 
} 

Using php array_merge we can have a nice short powerSet function

function powerSet($array) {
    // add the empty set
    $results = [[]];

    foreach ($array as $element) {
        foreach ($results as $combination) {
            $results[] = array_merge(array($element), $combination);
        }
    }

    return $results;
}

Here a backtracking solution.

given a function that returns all the L-lenght subsets of the input set, find all the L-lenght subsets from L = 2 to dataset input length

<?php

function subsets($S,$L) {
    $a = $b = 0;
    $subset = [];
    $result = [];
    while ($a < count($S)) {
        $current = $S[$a++];
        $subset[] = $current;
        if (count($subset) == $L) {
            $result[] = json_encode($subset);
            array_pop($subset);
        }
        if ($a == count($S)) {
            $a = ++$b;
            $subset = [];
        }
    }
    return $result;
}



$S = [ 'A', 'B', 'C', 'D'];
$L = 2;


// L = 1 -> no need to do anything
print_r($S);

for ($i = 2; $i <= count($S); $i++)
    print_r(subsets($S,$i));

Based on @Yada's answer, this will generate the power set of an array, but preserve the original array's keys in each subset (the return value is still numerically & sequentially indexed). This very useful if you need subsets of an associative array.

The subsets also retain the element order of the original array. I added a stable sort to $results because I needed it, but you can omit it.

function power_set($array) {
    $results = [[]];
    foreach ($array as $key => $value) {
        foreach ($results as $combination) {
            $results[] = $combination + [$key => $value];
        }
    }

    # array_shift($results); # uncomment if you don't want the empty set in your results
    $order = array_map('count', $results);
    uksort($results, function($key_a, $key_b) use ($order) {
        $comp = $order[$key_a] - $order[$key_b]; # change only this to $order[$key_b] - $order[$key_a] for descending size
        if ($comp == 0) {
            $comp = $key_a - $key_b;
        }
        return $comp;
    });
    return array_values($results);
}

Given OP's input, var_dump(power_set(['A', 'B', 'C', 'D'])); provides:

array(16) {
  [0] =>
  array(0) {
  }
  [1] =>
  array(1) {
    [0] =>
    string(1) "A"
  }
  [2] =>
  array(1) {
    [1] =>
    string(1) "B"
  }
  [3] =>
  array(1) {
    [2] =>
    string(1) "C"
  }
  [4] =>
  array(1) {
    [3] =>
    string(1) "D"
  }
  [5] =>
  array(2) {
    [0] =>
    string(1) "A"
    [1] =>
    string(1) "B"
  }
  [6] =>
  array(2) {
    [0] =>
    string(1) "A"
    [2] =>
    string(1) "C"
  }
  [7] =>
  array(2) {
    [1] =>
    string(1) "B"
    [2] =>
    string(1) "C"
  }
  [8] =>
  array(2) {
    [0] =>
    string(1) "A"
    [3] =>
    string(1) "D"
  }
  [9] =>
  array(2) {
    [1] =>
    string(1) "B"
    [3] =>
    string(1) "D"
  }
  [10] =>
  array(2) {
    [2] =>
    string(1) "C"
    [3] =>
    string(1) "D"
  }
  [11] =>
  array(3) {
    [0] =>
    string(1) "A"
    [1] =>
    string(1) "B"
    [2] =>
    string(1) "C"
  }
  [12] =>
  array(3) {
    [0] =>
    string(1) "A"
    [1] =>
    string(1) "B"
    [3] =>
    string(1) "D"
  }
  [13] =>
  array(3) {
    [0] =>
    string(1) "A"
    [2] =>
    string(1) "C"
    [3] =>
    string(1) "D"
  }
  [14] =>
  array(3) {
    [1] =>
    string(1) "B"
    [2] =>
    string(1) "C"
    [3] =>
    string(1) "D"
  }
  [15] =>
  array(4) {
    [0] =>
    string(1) "A"
    [1] =>
    string(1) "B"
    [2] =>
    string(1) "C"
    [3] =>
    string(1) "D"
  }
}