I have a table whose 'path' column has values and I would like to update the table's 'child_count' column so that I get the following output.

 path   | child_count 
--------+-------------
        |           5
 /a     |           3
 /a/a   |           0
 /a/b   |           1
 /a/b/c |           0
 /b     |           0

My present solution - which is way too inefficient - uses a stored procedure as follows:

CREATE FUNCTION child_count() RETURNS VOID AS $$
DECLARE
  parent VARCHAR; 
BEGIN   
  FOR parent IN
    SELECT path FROM my_table
  LOOP
    DECLARE
      tokens VARCHAR[] := REGEXP_SPLIT_TO_ARRAY(parent, '/');
      str VARCHAR := '';
    BEGIN
      FOR i IN 2..ARRAY_LENGTH(tokens, 1)
      LOOP
        UPDATE my_table
          SET child_count = child_count + 1
        WHERE path = str;
        str := str || '/' || tokens[i];     
      END LOOP;
    END;    
  END LOOP;
END;
$$ LANGUAGE plpgsql;

Anyone knows of a single UPDATE statement that does the same thing?