Write an algorithm for enumerating options with weight?

Question

PHP

Tell me even stupid I don’t know how to do it, there is such an array.

<?php
$a = [
    0 => 'a',
    1 => 'b',
    2 => 'c'
];

I need to iterate over all possible options, but with the weight saved, as the weight is the array index.
Now I will explain in more detail: that is, the element with index 0 cannot go after index 1 and index 1 cannot be before zero.
For the current array, you get the following options:

a
b
c
ab
ac
bc
abc

Please note that variants of the acb type cannot be obtained because the index b is less than the index c.
I hope I explained it clearly, the algorithm for enumerating all possible options is not suitable here. And it doesn't even occur to me how to write it adequately.

Answer 1

If permutations are not needed, then everything is simple. Each element is either included in the next option or not. Accordingly, you loop 1 to pow(2, count($arr)). You convert each loop number to binary with the decbin built-in function, reverse the result, and use it to make a new version - if 1 is in the corresponding place in the returned decbin string, then include the element, if 0, then exclude it.

$arr = [0 => 'a', 1 => 'b', 2 => 'c'];
$res = [];

for ($i = 1; $i < pow(2, count($arr)); $i++ ) {
    $bin = decbin($i);
    $case = "";
    foreach(str_split(strrev($bin)) as $ind => $symb) if ($symb == "1") $case .= $arr[$ind];
    $res[] = $case;
}

echo implode(", ", $res); // a, b, ab, c, ac, bc, abc