How to compute the cartesian power of a range of characters? - php

Question

I would like to make a function that is able to generate a list of letters and optional numbers using a-z,0-9.
$output = array();
foreach(range('a','z') as $i) {
foreach(range('a','z') as $j) {
foreach(range('a','z') as $k) {
$output[] =$i.$j.$k;
}
}
}
Thanks
example:
myfunction($include, $length)
usage something like this:
myfunction('a..z,0..9', 3);
output:
000
001
...
aaa
aab
...
zzz
The output would have every possible combination of the letters, and numbers.

Answer 1

Setting the stage
First, a function that expands strings like "0..9" to "0123456789" using range:
function expand_pattern($pattern) {
$bias = 0;
$flags = PREG_SET_ORDER | PREG_OFFSET_CAPTURE;
preg_match_all('/(.)\.\.(.)/', $pattern, $matches, $flags);
foreach ($matches as $match) {
$range = implode('', range($match[1][0], $match[2][0]));
$pattern = substr_replace(
$pattern,
$range,
$bias + $match[1][1],
$match[2][1] - $match[1][1] + 1);
$bias += strlen($range) - 4; // 4 == length of "X..Y"
}
return $pattern;
}
It handles any number of expandable patterns and takes care to preserve their position inside your source string, so for example
expand_pattern('abc0..4def5..9')
will return "abc01234def56789".
Calculating the result all at once
Now that we can do this expansion easily, here's a function that calculates cartesian products given a string of allowed characters and a length:
function cartesian($pattern, $length) {
$choices = strlen($pattern);
$indexes = array_fill(0, $length, 0);
$results = array();
$resets = 0;
while ($resets != $length) {
$result = '';
for ($i = 0; $i < $length; ++$i) {
$result .= $pattern[$indexes[$i]];
}
$results[] = $result;
$resets = 0;
for ($i = $length - 1; $i >= 0 && ++$indexes[$i] == $choices; --$i) {
$indexes[$i] = 0;
++$resets;
}
}
return $results;
}
So for example, to get the output described in the question you would do
$options = cartesian(expand_pattern('a..z0..9'), 3);
See it in action (I limited the expansion length to 2 so that the output doesn't explode).
Generating the result on the fly
Since the result set can be extremely large (it grows exponentially with $length), producing it all at once can turn out to be prohibitive. In that case it is possible to rewrite the code so that it returns each value in turn (iterator-style), which has become super easy with PHP 5.5 because of generators:
function cartesian($pattern, $length) {
$choices = strlen($pattern);
$indexes = array_fill(0, $length, 0);
$resets = 0;
while ($resets != $length) {
$result = '';
for ($i = 0; $i < $length; ++$i) {
$result .= $pattern[$indexes[$i]];
}
yield $result;
$resets = 0;
for ($i = $length - 1; $i >= 0 && ++$indexes[$i] == $choices; --$i) {
$indexes[$i] = 0;
++$resets;
}
}
}
See it in action.

Answer 2

See this answer for a code that produces all possible combinations:
https://stackoverflow.com/a/8567199/1800369
You just need to add the $length parameter to limit the combinations size.

Answer 3

You can use a recursive function
assuming you mean it can be any number of levels deep, you can use a recursive function to generate an array of the permutations e.g.:
/**
* take the range of characters, and generate an array of all permutations
*
* #param array $range range of characters to itterate over
* #param array $array input array - operated on by reference
* #param int $depth how many chars to put in the resultant array should be
* #param int $currentDepth internal variable to track how nested the current call is
* #param string $prefix internal variable to know what to prefix the current string with
* #return array permutations
*/
function foo($range, &$array, $depth = 1, $currentDepth = 0, $prefix = "") {
$start = !$currentDepth;
$currentDepth++;
if ($currentDepth > $depth) {
return;
}
foreach($range as $char) {
if ($currentDepth === $depth) {
$array[] = $prefix . $char;
continue;
}
foo($range, $array, $depth, $currentDepth, $prefix . $char);
}
if ($start) {
return $array;
}
With the above function, initialize the return variable and call it:
$return = array();
echo implode(foo(range('a', 'z'), $return, 3), "\n");
And you're output will be all three char combinations from aaa, to zzz:
aaa
aab
...
zzy
zzz
The numeric parameter determins how recursive the function is:
$return = array();
echo implode(foo(range('a', 'z'), $return, 1), "\n");
a
b
c
...
Here's a live example.

Answer 4

$number= range(0, 9);
$letters = range('a', 'z');
$array= array_merge($number, $letters);
//print_r($array);
for($a=0;$a<count($array);$a++){
for($b=0;$b<count($array);$b++){
for($c=0;$c<count($array);$c++){
echo $array[$a].$array[$b].$array[$c]."<br>";
}
}
}
tested and working :)