Find a Max in relational algebra - relational-database

Im having trouble on a homework question, im finding it difficult to understand the logic behind what to do.
Q: Write a query which will list the customer name and book title for the customer who has purchased the most expensive book.
Relational Schema
Customer(CID, Name, Address)
Orders(Ordernum, CID, Order_date, Cardnum)
Orderlist(Ordernum, ISBN, Qty, Ship_date)
Book(ISBN, Title, Author, Qty_in_stock, Price)
this is my attempt:
rename(expensive,projection cid (orders) join Orderlist join (selection price < d.price ((book) cross-product Pd Book))
exp - projection price (Book)
projection name Customer join exp

Your attempt with the cross-product and price comparison shows you're thinking in the right direction, but not quite there yet. After you get all the books for which cheaper books exist, how do you get the books for which NO cheaper books exist? Working from the inside out, you need to do that before you join to Orderlist, Orders and Customer to find the buyer.
Take care with your syntax and order of operations. As it is, your answer is difficult to make sense of. For example, what are Pd, d, and exp? Why rename something to expensive and then never use that term? How does projection cid (orders) join with Orderlist if the two expressions have no attributes in common? It should help to write out the header of the result of every sub-expression (working from the inside out) to visualize the sequence of operations.
When you want to break a complex RA expression into multiple steps, you can assign the result of one expression to a variable to use in the next expression. Remember, this is algebra just like in grade school, only with more complex values and operators.

T1(price)<--Ƴmax(price)(Book)
T2<--Πisbn,title,price(Book natural join T1)
T3<--(T2 natural join orderlist) natural join orders
T4<--πname,title(T3 natural join Customer)

Related

MySQL - When shouldn't I Join tables? Combinatorial Explosion of values

I am working on a database called classicmodels, which I found at: https://www.mysqltutorial.org/mysql-sample-database.aspx/
I realized that when I executed an Inner Join between 'payments' and 'orders' tables, a 'cartesian explosion' occurred. I understand that these two tables are not meant to be joined. However, I would like to know if it is possible to identify this just by looking at the relational schema or if I should check the tables one by one.
For instance, the customer number '141' appears 26 times in the 'orders table', which I found by using the following code:
SELECT
customerNumber,
COUNT(customerNumber)
FROM
orders
WHERE customerNumber=141
GROUP BY customerNumber;
And the same customer number (141) appears 13 times in the payments table:
SELECT
customerNumber,
COUNT(customerNumber)
FROM
payments
WHERE customerNumber=141
GROUP BY customerNumber;
Finally, I executed an Inner Join between 'payments' and 'orders' tables, and selected only the rows with customer number '141'. MySQL returned 338 rows, which is the result of 26*13. So, my query is multiplying the number of times this 'customer n°' appears in 'orders' table by the number of times it appears in 'payments'.
SELECT
o.customernumber,
py.amount
FROM
customers c
JOIN
orders o ON c.customerNumber=o.customerNumber
JOIN
payments py ON c.customerNumber=py.customerNumber
WHERE o.customernumber=141;
My questions is the following:
1 ) Is there a way to look at the relational schema and identify if a Join can be executed (without generating a combinatorial explosion)? Or should I check table by table to understand how the relationship between them is?
Important Note: I realized that there are two asterisks in the payments table's representation in the relational schema below. Maybe this means that this table has a composite primary key (customerNumber+checkNumber). The problem is that 'checkNumber' does not appear in any other table.
This is the database's relational schema provided by the 'MySQL Tutorial' website:
Thank you for your attention!
This is called "combinatorial explosion" and it happens when rows in one table each join to multiple rows in other tables.
(It's not "overestimation" or any sort of estimation. It's counting data items multiple times when it should only count them once.)
It's a notorious pitfall of summarizing data in one-to-many relationships. In your example each customer may have no orders, one order, or more than one. Independently, they may have no payments, one, or many.
The trick is this: Use subqueries so your toplevel query with GROUP BY avoids joining one-to-many relationships serially. In the query you showed us, that's happening.
You can this subquery to get a resultset with just one row per customer. (try it.)
SELECT customernumber,
SUM(amount) amount
FROM payments
GROUP BY customernumber
Likewise you can get the value of all orders for each customer with this
SELECT c.customernumber,
SUM(od.qytOrdered * od.priceEach) amount
FROM orders o
JOIN orderdetails od ON o.orderNumber = od.orderNumber
GROUP BY c.customernumber
This JOIN won't explode in your face because customer can have multiple orders, and each order can have multiple details. So it's a strict hierarchical rollup.
Now, we can use these subqueries in the main query.
SELECT c.customernumber, p.payments, o.orders
FROM customers c
LEFT JOIN (
SELECT c.customernumber,
SUM(od.qytOrdered * od.priceEach) orders
FROM orders o
JOIN orderdetails od ON o.orderNumber = od.orderNumber
GROUP BY c.customernumber
) o ON c.customernumber = o.customernumber
LEFT JOIN (
SELECT customernumber,
SUM() payment
FROM payments
GROUP BY customernumber
) p on c.customernumber = p.customernumber
Takehome tricks:
A subquery IS a table (a virtual table) that can be used whereever you might mention a table or a view.
The GROUP BY stuff in this query happens separately in two subqueries, so no combinatorial explosions.
All three participants in the toplevel JOIN have either one or zero rows per customernumber.
The LEFT JOINs are there so we can still see customers with (importantly for a business) no orders or no payments. With the ordinary inner JOIN, rows have to match both sides of the ON conditions or they're omitted from the resultset.
Pro tip Format your SQL queries fanatically carefully: They are really verbose. Adm. Grace Hopper would be proud. That means they get quite long and nested, putting the Structured in Structured Query Language. If you, or anybody, is going to reason about them in future, we must be able to grasp the structure easily.
Pro tip 2 The data engineer who designed this database did a really good job thinking it through and documenting it. Aspire to this level of quality. (Rarely reached in the real world.)
In this particular case, your behavior should depend on the accounting style being supported by the database, and this does not appear to be "open item" style accounting ie when an order is raised for 1000 there does not need to be a payment against it for 1000.. This is perhaps unusual in most consumer experience because you will be quite familiar with open item style ordering from Amazon - you buy a 500 dollar tv and a 500 dollar games console, the order is a thousand dollars and you pay for it, the payment going against the order. However, you're also familiar with "balance forward" accounting if you paid for that order using your credit card because you make similar purchases every day for a month and hen you get a statement from your bank saying you owe 31000 and you pay a lump of money, doesn't even have to be 31k. You aren't expected to make 31 payments of 1000 to your bank at the end of the month. Your bank allocate it to the oldest items on the account (if they're nice, or the newest items if they're not) and may eventually charge you interest on unpaid transactions
1 ) Is there a way to look at the relational schema and identify if a Join can be executed
Yes, you can tell looking at the schema- customer has many orders, customer makes many payments, but there is no relation between the order and payment tables at all so we can see there is no attempt to directly attach a payment to an order. You can see that customer is a parent table of payment and order, and therefore enjoys a relationship with each of them but they do not relate to each other. If you had Person, Car and Address tables, a person has many addresses during their life, and many cars but it doesn't mean there is a relationship between cars and addresses
In such a case it simply doesn't make sense to join payments to customers to orders because they do not relate that way. If you want to make such a join and not suffer a Cartesian explosion then you absolutely have to sum one side or the other (or both) to ensure that your joins are 1:1 and 1:M (or 1:1 and 1:1). You cannot arrange a join that is a pair of 1:M.
Going back to the car/person/address example to make any meaningful joins, you have to build more information into the question and arrange the join to create the answer. Perhaps the question is "what cars did they own while they lived at" - this flattens the Person:Address relationship to 1:1 but leaves Person:Car as 1:M so they might have owned many cars during their time in that house. "What was the newest car they owned while living at..." might be 1:1 on both sides if there is a clear winner for "newest" (though if they bought two cars manufactured at identical times...)
Which side you sum in your orders case will depend on what you want to know, but in this case I'd say you usually want to know "which orders haven't been paid for" and that's summing all payments and rolling summing all orders then looking at what point the rolling sum exceeds the sum of payments.. those are the unpaid orders
Take a look again at your database graph (the one that was present in the first iteration of your question). See the lines between tables have 3 angled legs on one end - that's the many end. You can start at any table in the graph and join to other tables by walking along the relationship. If you're going from the many end to the one end, and assuming you've picked out a single row in the start table (a single order) you can always walk to any other table in the many->one direction and not increase your row count. If you walk the other way you potentially increase your row count. If you split and walk two ways that both increase row count you get a Cartesian explosion. Of course, also you don't have to only join on relation lines, but that's out of scope for the question
ps: this is easier to see on the db diagram than the ERD in the question because the database purely concerns itself with the columns that are foreign keyed. The ERD is saying a customer has zero or one payments with a particular check number but the database will only be concerned with "the customer ID appears once in the customer table and multiple times in the payment table" because only part of the compound primary key of payment is keyed to the customer table. In other words, the ERD is concerned with business logic relations too, but the db diagram is purely how tables relate and they aren't necessarily aligned. For this reason the db diagrams are probably easier to read when walking round for join strategies
After seeing the answers of Caius Jard and O.Jones (please, check their replies), which kindly helped me to clarify this doubt, I decided to create a table to identify which customers paid for all orders they made and which ones did not. This creates a pertinent reason to join 'orders', 'orderdetails', 'payments' and 'customers' tables, because some orders may have been cancelled or still may be 'On Hold', as we can see in their corresponding 'status' in the 'orders' table. Also, this enables us to execute this join without generating a 'combinatorial explosion'.
I did this by using the CASE statement, which registers when py.amount and amount_in_orders match, don't match or when they are NULL (customers which did not make orders or payments):
SELECT
c.customerNumber,
py.amount,
amount_in_orders,
CASE
WHEN py.amount=amount_in_orders THEN 'Match'
WHEN py.amount IS NULL AND amount_in_orders IS NULL THEN 'NULL'
ELSE 'Don''t Match'
END AS Match
FROM
customers c
LEFT JOIN(
SELECT
o.customerNumber, SUM(od.quantityOrdered*od.priceEach) AS amount_in_orders
FROM
orders o
JOIN orderdetails od ON o.orderNumber=od.orderNumber
GROUP BY o.customerNumber
) o ON c.customerNumber=o.customerNumber
LEFT JOIN(
SELECT customernumber, SUM(amount) AS amount
FROM payments
GROUP BY customerNumber
) py ON c.customerNumber=py.customerNumber
ORDER BY py.amount DESC;
The query returned 122 rows. The images below are fractions of the generated output, so you can visualize what happened:
For instance, we can see that the customers identified by the numbers '141', '124', '119' and '496' did not pay for all the orders they made. Maybe some of them where cancelled or maybe they simply did not pay for them yet.
And this image shows some of the columns (not all of them) that are NULL:

Have to enter mySQL criteria twice?

Say I have two tables:
Table: customers
Fields: customer_id, first_name, last_name
Table: customer_cars
Fields: car_id, customer_id, car_brand, car_active
Say I am trying to write a query that shows all customers with a first name of "Karl," and the brands of the ** active ** cars they have. Not all customers will have an active car. Some cars are active, some are inactive.
Please keep in mind that this is a representative example that I just made up, for sake of clarity and simplicity. Please don't reply with questions about why we would do it this way, that I could use table aliases, how it's possible to have an inactive car, or that my field names could be better written. It's a fake example that is intended be very simple in order to illustrate the point. It has a structure and issue that I encounter all the time.
It seems like this would be best done with a LEFT JOIN and subquery.
SELECT
customer_id,
first_name,
last_name,
car_brand
FROM
customers
LEFT JOIN
(SELECT
customer_id,
car_brand
FROM
customer_cars
INNER JOIN customers ON customer_cars.customer_id = customers.customer_id
WHERE
first_name = 'Karl' AND
customer_cars.car_active = '1') car_query ON customers.customer_id = car_query.customer_id
WHERE
first_name = 'Karl'
The results might look like this:
first_name last_name car_brand
Karl Johnson Dodge
Karl Johnson Jeep
Karl Smith NULL
Karl Davis Chrysler
Notice the duplication of 'Karl' in both WHERE clauses, and the INNER JOIN in the subquery that is the same table in the outer query. My understanding of mySQL is that this duplication is necessary because it processes the subquery first before processing the outer query. Therefore, the subquery must be properly limited so it doesn't scan all records, then it tries to match on the resulting records.
I am aware that removing the car_active = '1' condition would change things, but this is a requirement.
I am wondering if a query like this can be done in a different way that only causes the criteria and joins to be entered once. Is there a recommended way to prioritize the outer query first, then match to the inner one?
I am aware that two different queries could be written (find all records with Karl, then do another that finds matching cars). However, this would cause multiple connections to the database (one for every record returned) and would be very taxing and inefficient.
I am also aware of correlating subqueries, but from my understanding and experience, this is for returning one field per customer (e.g., an aggregate field such as how much money Karl spent) within the fieldset. I am looking for a similar approach as this, but where one customer could be matched to multiple other records like in the sample output above.
In your response, if you have a recommended query structure that solves this problem, it would be really helpful if you could write a clear example instead of just describing it. I really appreciate your time!
First, is a simple and straight query not enough?
Say I am trying to write a query that shows all customers with a first
name of "Karl," and the brands of the ** active ** cars they have. Not
all customers will have an active car. Some cars are active, some are
inactive.
Following this requirement, I can just do something like:
SELECT C.first_name
, C.last_name
, CC.car_brand
FROM customers C
LEFT JOIN cutomer_cars CC ON CC.customer_id = C.customer_id
AND car_active = 1
WHERE C.first_name = 'Karl'
Take a look at the SQL Fiddle sample.

SQL Natural Join Dilemma re Order, Customer & Salesman tables

I was given the following question:
Write a SQL statement to make a join on the tables salesman, customer and orders in such a form that the same column of each table will appear once and only the relational rows will come.
I executed the following query:
SELECT * FROM orders NATURAL JOIN customer NATURAL JOIN salesman;
However, I was not expecting the following result:
My doubt lies in step 2.
Why didn't I get the rows with salesman_id 5002, 5003 & 5007?
I know that natural join uses the common columns to finalize the rows.
Here all the Salesman_ids are present in the result from step 1.
Why isn't the final result equal to the table resulting from step 1 with non duplicate columns from salesman added to it?
... the same column of each table will appear once
Yes Natural Join does that.
... and only the relational rows will come.
I don't know what that means.
I disagree with those who are saying: do not use Natural Join. But it is certainly true that if you plan to use Natural Join for your queries, you must design the schema so that (loosely speaking) 'same column name means same thing'.
Then this exercise is teaching you the dangers of having same-named columns that do not mean the same thing. The danger is sometimes called the 'connection trap' or 'join trap'. (Not really a trap: you just need to learn ways to write queries over poorly-designed schemas.)
A more precise way to put that: if you have columns named the same in two different tables, the column must be a key of at least one of them. So:
city is not a key in any of those tables,
so should not get 'captured' in a Natural Join.
salesman_id is not a key in table customer,
so should not get 'captured' in the join from table orders.
The main way to fix up this query is by renaming some columns to avoid 'capture' (see below). It's also worth mentioning that some dialects of SQL allow:
SELECT *
FROM orders
NATURAL JOIN customer ON customer_id
...
The ON column(s) phrase means: validate that the only columns in common between the two tables are those named. Otherwise reject the query. So your query would be rejected.
Renaming means that you shouldn't use SELECT *. (Anyway, that's dangerous for 'production code' because your query might produce different columns each time there's a schema change.) The easiest way to tackle this might be to create three Views for your three base tables, with the 'accidental' same-named columns given some other name. For this one query:
SELECT ord_no, purch_amt, ord_date, customer_id,
salesman_id AS order_salesman_id
FROM orders
NATURAL JOIN (SELECT customer_id, cust_name,
city AS cust_city, grade,
salesman_id AS cust_salesman_id
FROM customer) AS customer_grr
NATURAL JOIN (SELECT salesman_id, name,
city AS salesman_city,
commission
FROM salesman) AS salesman_grr
I'm using explicit AS to show renaming. Most dialects of SQL allow you to omit that keyword; just put city cust_city, ....
Why isn't the final result equal to the table resulting from step 1 with [...]?
Because natural join doesn't work how you expect--whatever that is, since you don't say.
In terms of relational algebra: Natural join returns the rows
• whose column set is the union of the input column sets and
• that have a subrow in both inputs.
In business terms: Every table & query result holds the rows that make some statement template--its (characteristic) predicate--its "meaning"--into a true statement. The designer gives the predicates for the base tables. Here, something like:
Orders = rows where
order [ord_no] ... and was sold by salesman [salesman_id] to customer [customer_id]
Customer = rows where
customer [customer_id] has name [cust_name] and lives in city [city]
and ... and is served by salesman [salesman_id]
Salesman = rows where
salesman [salesman_id] has name [name] and works in city [city] ...
Natural join is defined so that if each input holds the rows that make its predicate into a true statement then their natural join holds the rows that make the AND/conjunction of those predicates into a true statement. So (your query):
Orders natural join Customer natural join Salesman = rows where
order [ord_no] ... and was sold by salesman [salesman_id] to customer [customer_id]
and customer [customer_id] has name [cust_name] and lives in city [city]
and ... and is served by salesman [salesman_id]
and salesman [salesman_id] has name [name] and works in city [city] ...
So that natural join is asking for rows where, among other things, the customer lives in the city that the salesman works in. If that's not what you want, then you shouldn't use that expression.
Note how the meaning of a natural join of tables is a (simple) function of the meanings of its input tables. That's so for all the relational operators. So every query expression has a meaning, built from its base table meanings & relational operators.
Is there any rule of thumb to construct SQL query from a human-readable description?
Why didn't I get the rows with salesman_id 5002, 5003 & 5007?
Because those salesmen don't work a city in which one of their customers lives.

Whats the best way to implement a database with multivalued attributes?

i am trying to implement a database which has multi valued attributes and create a filter based search. For example i want my people_table to contain id, name, address, hobbies, interests (hobbies and interests are multi-valued). The user will be able to check many attributes and sql will return only those who have all of them.
I made my study and i found some ways to implement this but i can't decide which one is the best.
The first one is to have one table with the basic info of people (id, name, address), two more for the multi-valued attributes and one more which contains only the keys of the other tables (i understand how to create this tables, i don't know yet how to implement the search).
The second one is to have one table with the basic info and then one for each attribute. So i will have 20 or more tables (football, paint, golf, music, hiking etc.) which they only contain the ids of the people. Then when the user checks the hobbies and the activities i am going to get the desired results with the use of the JOIN feature (i am not sure about the complexity, so i don't know how fast is going to be if the user do many checks).
The last one is an implementation that i didn't find on internet (and i know there is a reason :) ) but in my mind is the easiest to implement and the fastest in terms of complexity. Use only one table which will have the basic infos as normal and also all the attributes as boolean variables. So if i have 1000 people in my table there are going to be only 1000 loops and which i imagine with the use of AND condition are going to be fast enough.
So my question is: can i use the the third implementation or there is a big disadvantage that i don't get? And also which one of the first two ways do you suggest me to use?
That is a typical n to m relation. It works like this
persons table
------------
id
name
address
interests table
---------------
id
name
person_interests table
----------------------
person_id
interest_id
person_interests contains a record for each interest of a person. To get the interests of a person do:
select i.name
from interests i
join person_interests pi on pi.interest_id = i.id
join persons p on pi.person_id = p.id
where p.name = 'peter'
You could create also tables for hobbies. To get the hobbies do the same in a separate query. To get both in one query you can do something like this
select p.id, p.name,
i.name as interest,
h.name as hobby
from persons p
left join person_interests pi on pi.person_id = p.id
left join interests i on pi.interest_id = i.id
left join person_hobbies ph on ph.person_id = p.id
left join hobbies h on ph.hobby_id = h.id
where p.name = 'peter'
The basic way to deal with this is with a many-to-many join table. Each user can have many hobbies. Each hobby can have many users. That's basic stuff you can find information about anywhere, and #juergend already covered that.
The harder part is tracking different information about various hobbies and interests. Like if their hobby is "baseball" you might want to track what position they play, but if their hobby is "travel" you might want to track their favorite countries. Doing this with typical SQL relationships will lead to a rapid proliferation of tables and columns.
A hybrid approach is to use the new JSON data type to store some unstructured data. To expand on #juergend's example, you might add a field to Person_Interests which can store some of those details about that person's interest.
create table Person_Interests (
InterestID integer references Interests(ID),
PersonID integer references Persons(ID),
Details JSON
);
And now you could add that Person 45 has Interest 12 (travel), their favorite country is Djibouti, and they've been to 45 countries.
insert into person_interests
(InterestID, PersonID, Details)
(12, 45, '{"favorite_country": "Djibouti", "countries_visited": 45}');
And you can use JSON search functions to find, for example, everyone whose favorite country is Djibouti.
select p.id, p.name
from person_interests pi
join persons p on p.id = pi.personid
where pi.details->"$.favorite_country" = "Djibouti"
The advantage here is flexibility: interests and their attributes aren't limited by your database schema.
The disadvantages is performance. The JSON data type isn't the most efficient, and indexing a JSON column in MySQL is complicated. Good indexing is critical to good SQL performance. So as you figure out common patterns you might want to turn commonly used attributes into real columns in real tables.
The other option would be to use table inheritance. This is a feature of Postgres, not MySQL, and I'd recommend considering switching. Postgres also has better and more mature JSON support and JSON columns are easier to index.
With table inheritance, rather than having to write a completely new table for every different interest, you can make specific tables which inherit from a more generic one.
create table person_interests_travel (
FavoriteCountry text,
CountriesVisited text[]
) inherits(person_interests);
This still has InterestID, PersonID, and Details, but it's added some specific columns for tracking their favorite country and countries they've visited.
Note that text[]. Postgresql also supports arrays so you can store real lists without having to create another join table. You can also do this in MySQL with a JSON field, but arrays offer type constraints that JSON does not.

Why would a SQL query need to be so complicated like this feature allows?

I am studying for SQL exam, and I came across this fact, regarding subqueries:
2. Main query and subquery can get data from different tables
When is a case when this feature would be useful? I find it difficult to imagine such a case.
Millions of situations call for finding information in different tables, it's the basis of relational data. Here's an example:
Find the emergency contact information for all students who are in a chemistry class:
SELECT Emergency_Name, Emergency_Phone
FROM tbl_StudentInfo
WHERE StudentID IN (SELECT b.StudentID
FROM tbl_ClassEnroll b
WHERE Subject = 'Chemistry')
SELECT * FROM tableA
WHERE id IN (SELECT id FROM tableB)
There is plenty of reasons why you have to get data from different tables, such as select sth from main query, which is based on subquery/subqueries from another tables. The usage is really huge.
choose customers from main query which is based on regions and their values
SELECT * FROM customers
WHERE country IN(SELECT name FROM country WHERE name LIKE '%land%')
choose products from main query which is greater or lower than average incoming salary of customers and so on...
You could do something like,
SELECT SUM(trans) as 'Transactions', branch.city as 'city'
FROM account
INNER JOIN branch
ON branch.bID = account.bID
GROUP BY branch.city
HAVING SUM(account.trans) < 0;
This would for a company to identify which branch makes the most profit and which branch is making a loss, it would help identify if the company had to make changes to their marketing approach in certain regions, in theory allowing for the company to become more dynamic and reactive to changes in the economy at any give time.