Distribute options uniquely algorithm - php

Question

I have a 2 dimensional array. Each subarray consists out of a number of options. I am trying to write a script which picks one of these options for each row. The chosen options have to be unique. An example:
$array = array(
1 => array(3,1),
2 => array(3),
3 => array(1,5,3),
);
With a solution:
$array = array(
1 => 1,
2 => 3,
3 => 5,
);
I have finished the script, but i am not sure if it is correct. This is my script. The description of what i am doing is in the comments.
function pickUnique($array){
//Count how many times each option appears
$counts = array();
foreach($array AS $options){
if(is_array($options)){
foreach($options AS $value){
//Add count
$counts[$value] = (isset($counts[$value]) ? $counts[$value]+1 : 1);
}
}
}
asort($counts);
$didChange = false;
foreach($counts AS $value => $count){
//Check one possible value, starting with the ones that appear the least amount of times
$key = null;
$scoreMin = null;
//Search each row with the value in it. Pick the row which has the lowest amount of other options
foreach($array AS $array_key => $array_options){
if(is_array($array_options)){
if(in_array($value,$array_options)){
//Get score
$score = 0;
$score = count($array_options)-1;
if($scoreMin === null OR ($score < $scoreMin)){
//Store row with lowest amount of other options
$scoreMin = $score;
$key = $array_key;
}
}
}
}
if($key !== null){
//Store that we changed something while running this function
$didChange = true;
//Change to count array. This holds how many times each value appears.
foreach($array[$key] AS $delValue){
$counts[$delValue]--;
}
//Remove chosen value from other arrays
foreach($array AS $rowKey => $options){
if(is_array($options)){
if(in_array($value,$options)){
unset($array[$rowKey][array_search($value,$options)]);
}
}
}
//Set value
$array[$key] = $value;
}
}
//validate, check if every row is an integer
$success = true;
foreach($array AS $row){
if(is_array($row)){
$success = false;
break;
}
}
if(!$success AND $didChange){
//Not done, but we made changes this run so lets try again
$array = pickUnique($array);
}elseif(!$success){
//Not done and nothing happened this function run, give up.
return null;
}else{
//Done
return $array;
}
}
My main problem is is that i have no way to verify if this is correct. Next to that i also am quite sure this problem has been solved a lot of times, but i cannot seem to find it. The only way i can verificate this (as far as i know) is by running the code a lot of times for random arrays and stopping when it encounters an insolvable array. Then i check that manually. So far the results are good, but this way of verication is ofcourse not correct.
I hope somebody can help me, either with the solution, the name of the problem or the verification method.