Permutations of an array of arrays of strings

Question

I simply cannot wrap my head around how to solve this problem and after a thorough search on Google with no results, I turn to you with hopes of a solution.

Given the sa

Answer 1

Supposing you have only one nesting level, what you want is:

$my_ar[group1][0].(rest_of_the_group_perms[0])
$my_ar[group1][0].(rest_of_the_group_perms[1])
...
$my_ar[group1][N].(rest_of_the_group_perms[K])

that is, you can see the problem as having to join two lists/arrays. The first being the first subarray of your array and the second being the (recursively already made) rest.

So you need a function like this:

perms($my_arr) {
   foreach($elem in $group1) {
      $return_list[] = $elem.$rest;
   }
}

where $group1 is the first subarray of your array and $group_rest is what is left. So:

perms($my_arr) {
   $group1 = head($my_arr);
   $group_rest = tail($my_arr);

   $rest = perms($group_rest);
   $return_list = array();
   foreach($elem in $group1) {
      $return_list[] = "$elem, $rest";
   }
   return $return_list;
}

but $rest is also an array so you have to loop over that too:

perms($my_arr) {
   $group1 = head($my_arr);
   $group_rest = tail($my_arr);

   $rest = perms($group_rest);
   $return_list = array();
   foreach($elem in $group1) {
      foreach($relem in $rest) {
          $return_list[] = $elem.$relem;
      }
   }
   return $return_list;
}

add the ending condition (null $group_rest) and you are set:

perms($my_arr) {
   $group1 = head($my_arr);
   $group_rest = tail($my_arr);

  if (length($group_rest) == 0) 
       $rest = array();
  else
       $rest = perms($group_rest);
   $return_list = array();
   foreach($elem in $group1) {
      foreach($relem in $rest) {
          $return_list[] = $elem.$relem;
      }
   }
   return $return_list;
}