Finding all possible combinations of numbers to reach a given sum

Question

How would you go about testing all possible combinations of additions from a given set N of numbers so they add up to a given final number?

A brief exam

Answer 1

Thank you.. ephemient

i have converted above logic from python to php..

0;$i--)
  {
    if($res[$i]!=0)
    {
        return $res[$i];
        break;
    }
  }
return array();
}
?>