PHP algorithm to generate all combinations of a specific size from a single set
A possible algorithm would be:
$array_elems_to_combine = array('A', 'B', 'C');
$size = 4;
$current_set = array('');
for ($i = 0; $i < $size; $i++) {
$tmp_set = array();
foreach ($current_set as $curr_elem) {
foreach ($array_elems_to_combine as $new_elem) {
$tmp_set[] = $curr_elem . $new_elem;
}
}
$current_set = $tmp_set;
}
return $current_set;
Basically, what you will do is take each element of the current set and append all the elements of the element array.
In the first step: you will have as result ('a', 'b', 'c')
, after the seconds step: ('aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc')
and so on.
You can do this recursively. Note that as per your definition, the "combinations" of length n+1
can be generated from the combinations of length n
by taking each combination of length n
and appending one of the letters from your set. If you care you can prove this by mathematical induction.
So for example with a set of {A,B,C}
the combinations of length 1 are:
A, B, C
The combinations of length 2 are therefore
(A, B, C) + A = AA, BA, CA
(A, B, C) + B = AB, BB, BC
(A, B, C) + C = AC, CB, CC
This would be the code and here on ideone
function comb ($n, $elems) {
if ($n > 0) {
$tmp_set = array();
$res = comb($n-1, $elems);
foreach ($res as $ce) {
foreach ($elems as $e) {
array_push($tmp_set, $ce . $e);
}
}
return $tmp_set;
}
else {
return array('');
}
}
$elems = array('A','B','C');
$v = comb(4, $elems);
I would use a recursive function. Here's a (working) example with comments. Hope this works for you!
function sampling($chars, $size, $combinations = array()) {
# if it's the first iteration, the first set
# of combinations is the same as the set of characters
if (empty($combinations)) {
$combinations = $chars;
}
# we're done if we're at size 1
if ($size == 1) {
return $combinations;
}
# initialise array to put new values in
$new_combinations = array();
# loop through existing combinations and character set to create strings
foreach ($combinations as $combination) {
foreach ($chars as $char) {
$new_combinations[] = $combination . $char;
}
}
# call same function again for the next iteration
return sampling($chars, $size - 1, $new_combinations);
}
// example
$chars = array('a', 'b', 'c');
$output = sampling($chars, 2);
var_dump($output);
/*
array(9) {
[0]=>
string(2) "aa"
[1]=>
string(2) "ab"
[2]=>
string(2) "ac"
[3]=>
string(2) "ba"
[4]=>
string(2) "bb"
[5]=>
string(2) "bc"
[6]=>
string(2) "ca"
[7]=>
string(2) "cb"
[8]=>
string(2) "cc"
}
*/