Finding the subsets of an array in PHP - php

Question

I have a Relational Schema with attributes (A B C D).
I have a set of Functional Dependencies with me too.
Now I need to determine the closure for all the possible subsets of R's attributes. That's where I am stuck. I need to learn how to find subsets (non-repeating) in PHP.
My Array is stored like this.
$ATTRIBUTES = ('A', 'B', 'C', 'D').
so my subsets should be
$SUBSET = ('A', 'B', 'C', 'D', 'AB', 'AC', AD', 'BC', 'BD', 'CD', 'ABC', 'ABD', 'BCD', 'ABCD')
The code shouldn't be something big but for some reason I can't get my head around it.

Answer 1

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;
}

Answer 2

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;
}

Answer 3

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));

Answer 4

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"
}
}

Answer 5

Following #fbstj answer, I update the function:
Use bitwize operators instead of sprintf (#Titus comments)
Handle empty set (#James Stott & #fbstj comments)
Update syntax to PHP 7+
function powerSet(array $in, int $minLength = 0): array
{
$return = [];
if ($minLength === 0) {
$return[] = [];
}
for ($i = 1 << count($in); --$i;) {
$out = [];
foreach ($in as $j => $u) {
if ($i >> $j & 1) {
$out[] = $u;
}
}
if (count($out) >= $minLength) {
$return[] = $out;
}
}
return $return;
}
Since power set functions can increase by a lot the memory load (2count($in) iterations), consider using Generator:
function powerSet(array $in, int $minLength = 0): \Generator
{
if ($minLength === 0) {
yield [];
}
for ($i = 1 << count($in); --$i;) {
$out = [];
foreach ($in as $j => $u) {
if ($i >> $j & 1) {
$out[] = $u;
}
}
if (count($out) >= $minLength) {
yield $out;
}
}
}
Usage:
foreach (powerSet(range(1, 10)) as $value) {
echo implode(', ', $value) . "\n";
}