How can I query a table for transitive matches? - sql

Question

Giving the following tables
Units:
| id | singular | plural |
|----|----------|--------|
| 3 | onion | onions |
| 4 | bag | bags |
| 5 | gram | grams |
| 6 | ml | ml |
| 7 | mm | mm |
and
Conversions:
| id | convert_from | convert_to | factor |
|----|--------------|------------|--------|
| 3 | 4 | 3 | 5 |
| 4 | 3 | 5 | 125 |
How could I obtain all possible conversion factors from (for example) bag (unit 4)?
I would expect the answers to resemble the form
| convert_from | convert_to | factor |
|--------------|------------|--------|
| 4 | 3 | 5 |
| 4 | 5 | 625 |
Caveats:
There is no guarantee about which column of the conversions table (convert_from, convert_to) a unit might appear in.
Conversions that transit through units 5, 6, or 7 should be ignored.
That is to say,
1->2->4->5 is valid, 1->2->4->5->7 is not.
A SQL solution (or re-architecting of the database to facilitate a SQL solution) would be ideal, but a code solution that makes multiple SQL queries would also be appreciated.
There will be other units in the units table that should be ignored if they do not form part of the conversion graph (or if they form part of the branch through an invalid transition (5, 6, or 7)). This is a simplified view.
Illustrative example
Ignoring SQL and retrieving the data for a moment, here's what I'm trying to achieve:
I want to build a system where users can store household products. A product has a unit associated with it. The unit might be an SI unit, such as mm, ml, g.. or it might be a discrete unit such as onion, or can.
Units can have relationships amongst themselves, so for example 1 can -> 330 ml.
The complexity of my question comes from the fact that the conversions for a single unit might be spread across many products.
Considering the can example again, we can have a product called pepsi (crate of 24) with the unit being crate, and another product called pepsi (can) with the unit of can.
When the user creates the pepsi (can) product, they provide the following conversion:
1 can -> 330 ml
Later, the user creates the pepsi (crate of 24) product, and provides the following conversion:
1 crate -> 24 can
Finally, the user asks the question "how much pepsi do I have?"
I'd like to be able to answer:
25 cans
1.0417 crates
8250 ml.
However, I don't know how to convert crates to ml.
Here's another example in illustrated form:
Edit:
Changed mms and mls to mm and ml. Not sure what I was thinking...
Added diagram to help clarify what i'm looking for rather than the solution.

Answer 1

You can use a recursive CTE, assuming there are no cycles in the data.
I added an extra is_terminal column to identify the terminal units where you don't want to convert from anymore (5, 6, and 7). The query is:
with recursive
e (convert_from, convert_to, factor, is_terminal) as (
select id, id, 1, is_terminal from units where id = 4 -- bag
union all
select e.convert_from, c.convert_to, e.factor * c.factor, u.is_terminal
from e
join conversions c on c.convert_from = e.convert_to
join units u on u.id = c.convert_to
where not e.is_terminal
)
select * from e where convert_from <> convert_to
Result:
convert_from convert_to factor is_terminal
------------ ---------- ------ -----------
4 3 5 false
4 5 625 true
See running example at DB Fiddle . Here's the data script I used to test:
create table units (
id int,
is_terminal boolean
);
insert into units (id, is_terminal) values
(3, false), (4, false),
(5, true), (6, true), (7, true);
create table conversions (
id int,
convert_from int,
convert_to int,
factor int
);
insert into conversions (id, convert_from, convert_to, factor) values
(3, 4, 3, 5),
(4, 3, 5, 125);