Cacher is the code snippet organizer for pro developers

ALTER TABLE many_to_many ADD order_column INT;

CREATE TEMPORARY TABLE tmp_many_to_many AS (
	SELECT  many_to_many.id, 
	        many_to_many.type_id,
      		(
      			CASE many_to_many.type_id
      				WHEN @type_id THEN @cur_row := @cur_row + 1
      				ELSE @cur_row := 1 AND @type_id := many_to_many.type_id 
      			END
      		) AS `order_column`
	FROM	many_to_many, 
		(SELECT @cur_row := 0, @type_id := 0) var_table
	ORDER BY many_to_many.type_id, many_to_many.id
);

UPDATE	many_to_many, tmp_many_to_many
SET		many_to_many.order_column = tmp_many_to_many.order_column
WHERE	many_to_many.id = tmp_many_to_many.id;