Is postorder tree traversal possible with recursive CTE's?

Hi all,

I'm struggling with a hierarchical query where I'm tasked to calculate weights of items in an (exploded) Bill of Materials, based on the weights of their components. Not all components are measured with a weight, sometimes there are pieces, meters, areas, etc, and the hierarchy is of varying levels of depth.

It would help if I could track a sum() throughout the explosion that would write back onto parent rows when the recursion returns: postorder traversal.

I created a simplified example about making pizza:

CREATE TABLE ingredient (
name text NOT NULL
);

CREATE TABLE recipe (
name text NOT NULL,
ingredient text NOT NULL,
quantity numeric(6,2) NOT NULL,
unit text NOT NULL,
step integer NOT NULL
);

COPY ingredient (name) FROM stdin;
tomato
basil
salt
tomato sauce
flour
water
yeast
dough
pizza bottom
pizza
\.

COPY recipe (name, ingredient, quantity, unit, step) FROM stdin;
tomato sauce tomato 100.00 g 1
dough flour 150.00 g 1
tomato sauce basil 10.00 g 2
pizza pizza bottom 1.00 pcs 2
tomato sauce salt 3.00 g 3
dough salt 1.00 pinch 3
pizza tomato sauce 1.00 pcs 1
pizza bottom dough 1.00 pcs 2
dough water 50.00 g 2
\.

ALTER TABLE ONLY ingredient
ADD CONSTRAINT ingredient_pkey PRIMARY KEY (name);

ALTER TABLE ONLY recipe
ADD CONSTRAINT recipe_pkey PRIMARY KEY (name, ingredient);

ALTER TABLE ONLY recipe
ADD CONSTRAINT recipe_ingredient_fkey FOREIGN KEY (ingredient) REFERENCES ingredient(name);

ALTER TABLE ONLY recipe
ADD CONSTRAINT recipe_name_fkey FOREIGN KEY (name) REFERENCES ingredient(name);

A query listing the recipe for 'pizza' would be as follows:
development=> with recursive pizza (name, step, ingredient, quantity, unit, rel_qty, path, weight)
as (
select
name, step, ingredient, quantity, unit
, quantity::numeric(10,2)
, step::text
, case when unit = 'g' then quantity::numeric(10,2) else null end
from recipe
where name = 'pizza'
union all
select
recipe.name, recipe.step, recipe.ingredient, recipe.quantity, recipe.unit
, (pizza.rel_qty * recipe.quantity)::numeric(10,2)
, pizza.path || '.' || recipe.step
, case when recipe.unit = 'g' then (pizza.rel_qty * recipe.quantity)::numeric(10,2) else null end
from pizza
join recipe on (recipe.name = pizza.ingredient)
)
select path, ingredient, quantity, rel_qty, unit, weight
from pizza
order by path;

path | ingredient | quantity | rel_qty | unit | weight
-------+--------------+----------+---------+-------+--------
1 | tomato sauce | 1.00 | 1.00 | pcs |
1.1 | tomato | 100.00 | 100.00 | g | 100.00
1.2 | basil | 10.00 | 10.00 | g | 10.00
1.3 | salt | 3.00 | 3.00 | g | 3.00
2 | pizza bottom | 1.00 | 1.00 | pcs |
2.2 | dough | 1.00 | 1.00 | pcs |
2.2.1 | flour | 150.00 | 150.00 | g | 150.00
2.2.2 | water | 50.00 | 50.00 | g | 50.00
2.2.3 | salt | 1.00 | 1.00 | pinch |
(9 rows)

With these results, I somehow need to calculate that the weights of 'tomato sauce', 'dough' and 'pizza bottom' are 113 g, 200 g and 200 g respectively, bringing the total weight of 'pizza' to 313 g.

My first thought was to traverse the result of this recursive CTE using another one, but in the opposite direction. But since this tends to be kept as a temporary materialized result set with no indices, that's not performing great and it adds a fair amount of complexity to the query too.

Then I realised that if we somehow could track the sum() of 'weight' throughout exploding these recipe items, by using a postorder tree traversal, the desired result would be readily available to pick up when the recursive CTE travels up through the hierarchy.

In above example; When the CTE would reach '1.3 salt', it would write the summed 'weight' value 113 back on the result for '1 tomato sauce' and when it reached '2.2.2 salt' it would write back 200 to '2.2 dough' and then 200 to '2 pizza bottom'.

Is that possible?

I've seen a couple of "solutions" on the internet that just summed up the results of the CTE, but that won't do as it would not put the correct weights onto intermediate levels of the tree as far as I can see (in above, the weight of 'dough').

Regards,

Alban Hertroys

PS. Don't try to make pizza using this recipe, it probably won't succeed. I forgot the yeast, for one thing, and quantities are probably way off. Not to mention that there are probably more ingredients missing…

PS2. In my real case the ingredients have a base quantity and unit, which makes adjusting to relative quantities actually viable. Those aren't necessary to describe the problem though.
--
If you can't see the forest for the trees,
cut the trees and you'll find there is no forest.