# Generate a combination of numbers

I have a PHP page with two variables: $nbRank and $nbNumeric. Depending of these two variables, I want to generate an array containing all combinations existing. For example:

If $nbRank = 3 and $nbNumeric = 2 I would have:

0 0 0 0 0 1 0 0 2 0 1 0 0 1 1 0 1 2 0 2 0 0 2 1 0 2 2 1 0 0 1 0 1 1 0 2 1 1 0 1 1 1 1 1 2 1 2 0 1 2 1 1 2 2 2 0 0 2 0 1 2 0 2 2 1 0 2 1 1 2 1 2 2 2 0 2 2 1 2 2 2

So, I create different loop and formulas to get the final result, but it doesn't works. This is what I did :

$result = array(); $nbIntRank = 0; $nbIntNumeric = 0; $nbRank = array(); $nbNumeric = array(); $nb_rangs = 3; $nb_chiffres = 2; for ($i = 1; $i <= $nb_rangs; $i++){ $nbRank[$i] = 0; } $nbIntRank = count($nbRank); for ($i = 0; $i <= $nb_chiffres; $i++){ $nbNumeric[$i] = $i; } $nbIntNumeric = count($nbNumeric); $algo = ($nb_rangs * ($nb_chiffres + 1)) * ($nb_rangs * ($nb_chiffres + 1)); $nbLine = $algo / ($nb_rangs); $occ = 0; for ($i = 0; $i < $nbLine; $i++){ foreach ($nbRank as $nbrItem => $nbrValue){ $result[$i][] = $nbrValue; $occ++; } } echo '#############<br />'; echo '### DATAS ###<br />'; echo '#############<br /><br />'; echo '- Nb Elements : '.$algo.'<br />'; echo '- Nb Lines : '.$nbLine.'<br />'; echo '- Nb Valuable Occurency : '.$occ.'<br />'; echo '<br /><hr /><br />'; echo '##############<br />'; echo '### PARSER ###<br />'; echo '##############<br /><br />'; echo '<pre>'; var_dump($result); echo '</pre>';

I managed to create my final array with empty values (81 values, in 27 lines of 3 elements) but it only contains 0.

## Answers

Here's a recursive solution:

$nbRank = 3; $nbNumeric = 2; function getCombinations ($length, $min, $max, $aStartingCombinations) { if ($length == 1) { return range ($min, $max); } $final = array (); foreach (getCombinations ($length - 1, $min, $max, $aStartingCombinations) as $combination) { for ($i = $min; $i <= $max; $i++) { $final [] = $combination . $i; } } return $final; } print_r (getCombinations ($nbRank, 0, $nbNumeric, array ()));

You indicated you'll be fine with pseudo-code.. Sorry I cannot offer specific correction for your php code [if these answers appear - they might be more educating], but I'd chose a recursive solution for this problem.

In each level of the recursion, **try all possibilities, and call the same function to find all combinations of one smaller size**.

**Pseudo-Code:**

findCombinations(range,size,sol,resultList): if (size ==0): #base clause resultList.append(copy(sol)) #making a copy of sol and appending it as a solution return for each i in (0,range): sol.append(i) findCombinations(range,size-1,sol,resultList) #recursive invokation, with smaller size sol.deleteLast() #clean up environment before next calls

Invoke with findCombinations(3,3,[],resultList) where [] is just empty list, and resultList will hold the list of combination when the algorithm is done. this invokation will get all combinations of size 3 with elemenets 0,1,2.

**Complexity note:**
The number of possibilities is growing exponentially [O(rangesize)], so if you try to invoke it with 20,20 for instance - it might take some [very long] time, for any solution.

$nbRank = 3; $nbNumeric = 2; foreach (range(0, base_convert(str_pad('', $nbRank, $nbNumeric), $nbNumeric+1, 10)) as $i) { echo str_pad(base_convert($i, 10, $nbNumeric+1), 3, 0, STR_PAD_LEFT) . PHP_EOL; }

Simple idea: What you want is every number from 0 to X with base $nbNumeric, thus we just convert the maximum number to base 10, iterate over it with the common 10-based operators, and convert it back to base $nbNumeric again.

Probably more readable, but in fact exactly the same

$nbRank = 3; $nbNumeric = 2; // Top is "base_convert(222, 3, 10);" and therefore the upper limit $top = base_convert(str_pad('', $nbRank, $nbNumeric), $nbNumeric+1, 10); for ($i = 0; $i <= $top; $i++) { echo str_pad(base_convert($i, 10, $nbNumeric+1), 3, 0, STR_PAD_LEFT) . PHP_EOL; }