get all items of category and its child

I'm about to give 100 bounty points for answer to this question

So I have very difficult question about recursions - how to get all items count of category and all childs that contains that parent and more deeper until the end?

I have table:

+----+---------------+-----------------+
| id | category name | category_parent |
+----+---------------+-----------------+
| 1  | cars          |        0        |
+----+---------------+-----------------+
| 2  | real estate   |        0        |
+----+---------------+-----------------+
| 3  | clothes       |        0        |
+----+---------------+-----------------+
| 4  | bmw           |        1        |
+----+---------------+-----------------+
| 5  | audi          |        1        |
+----+---------------+-----------------+
| 6  | 100           |        5        |
+----+---------------+-----------------+
| 7  | 80            |        5        |
+----+---------------+-----------------+
| 8  | A4            |        5        |
+----+---------------+-----------------+
| 9  | QUATRO        |        8        |
+----+---------------+-----------------+
| 10 | TDI           |        8        |
+----+---------------+-----------------+
| 11 | Black         |        9        |
+----+---------------+-----------------+
| 12 | White         |        9        |
+----+---------------+-----------------+
| 13 | 2 doors       |        11       |
+----+---------------+-----------------+
| 14 | 5 doors       |        11       |
+----+---------------+-----------------+

and my products table look like this:

+----+---------------+-----------------+
| id | category_id   | name            |
+----+---------------+-----------------+

and for example I want to count all items that are in cars category. So basically I should pass this category id (1) and somehow make a recursion to count all items. But I have no idea how to deal with it, becouse childs of that category could be unlimited.

So when I want to know all items of that parent count, I should make something like this:

1++:
  4++
  5++:
    6++
    7++
    8++:
      9++:
        11++:
           13++
           14++
        12++
      10++

I hope you will understand what I need and give me any suggestion that could help me.

also, this is the begining I have made so far - I could implement it but in the future I will stuck in recursion... so its worth nothing.

public function get_category_tree_id_list($cat_id, $list_array = FALSE)
{
    if ( !$list_array ){
        $items = $this->system->_getCustomTableData('categories', array(array('category_parent' => $cat_id)), 'id DESC');
        $this->__tmp['id_list'] = [];
        foreach ( $items as $key => $value ) {
            $this->__tmp['id_list'][] = $value['id'];
        }
    }        
}