PHP - All permutations in a 2D array - Unique and ordered values

Question

I have a 2d array. Assuming each position i have a number os candidates to fill it.

Ex:

Position 0 -> Candidates: 1,2,3
Position 1 -> Candidates: 3,4,5
Position 2 -> Candidates: 4,5

Translating:

Array_Position(
  array('1', '2', '3'),
  array('3', '4','5'),
  array('4', '5')   
);

I want all the combinations, with 2 restrictions:

1. No repetitions (if a candidate is already in one position, it can´t appear again in another position).
   This can´t happen:
   1-4-4
   3-3-4

2. A candidate can´t be "smaller" than his previous.
   This can´t happen:
   1-5-4
   3-5-4

In this particular case, the all possible combinations would be:
1-3-4
1-3-5
1-4-5
2-3-4
2-3-5
2-4-5
3-4-5

I saw some answers like this:

<?php       
    function array_cartesian() {
        $_ = func_get_args();
        if(count($_) == 0)
            return array(array());
        $a = array_shift($_);
        $c = call_user_func_array(__FUNCTION__, $_);
        $r = array();
        foreach($a as $v)
            foreach($c as $p)
                $r[] = array_merge(array($v), $p);
        return $r;
    }

    $cross = array_cartesian(
        array('1', '2', '3'),
        array('3', '4','5'),
        array('4', '5') 
    );

    print_r($cross);

?>

but none of them resolve the 2 restrictions.

Any help?

Tks!

Answer 1

Since any candidate can't be smaller than his previous, then any position can't be repeated in the chain. The following code does the trick, check if it works for you.

<?php

function permute()
{
    $result = array();

    if (func_num_args() == 0)
        return $result; // empty array

    foreach (func_get_arg(0) as $value)
        nextPermute($result, $value, $value, 1, func_get_args());

    return $result;
}

function nextPermute(&$result_array, $permute_value,
                    $last_value, $next_arg, $all_args)
{
    if ($next_arg < count($all_args))
    {
        foreach ($all_args[$next_arg] as $value)
            if ($value > $last_value)
                nextPermute($result_array, $permute_value . '-' . $value, $value, $next_arg + 1, $all_args);
    }
    else
        array_push($result_array, $permute_value);
}

$cross = permute(
    array('1', '2', '3'),
    array('3', '4', '5'),
    array('4', '5')
);

print_r($cross);

?>