SZU data design and Analysis Chapter 3 relational algebra

Posted by harman on Sat, 08 Jan 2022 09:15:10 +0100


Relational algebra

1. Union (U)

1.1 definition:

Union (\ (\ cup \)
The result of this operation, R  S, is a relationship that contains all tuples in R or S or both. Duplicate tuples do not appear in the output.
Formally: \ (R\) \(\cup\) \(S\) \(=\) \(\{\) \(t | t\) \(\in\) R or t \(\in\) S \ (\} \)
Joint compatibility: let R and S be two relationships with attributes \ ((A1, A2,..., an) \) and \ ((B1, B2,..., BN) \) respectively. If you want to merge R and S, you should meet the following two rules:

Rule 1: relationships \ (R \) and \ (S \) must have the same degree (attribute).
Rule 2: the domain of attribute \ (i \) of \ (R \) and attribute \ (i \) of S must be the same.
\(dom(A_i) = dom(B_i) \), where 1 \(\leq\) i \(\leq\) n.

1.2 example diagram

2. Difference operation

2.1 definitions

Like unions, relational difference operators require their operands to be of the same type.
Format: R - S
Formally: R - S = {t | t \ (\ in \) r and t \(\notin\) S}
Semantics: given two relationships R and s of the same type, the difference between the two relationships R-S is a relationship that contains all tuples in r that do not appear in S.

2.2 example diagram

3. Intersection

3.1 definitions

The expression r ∩ S returns all tuples that appear in relationships R and S.
Like Union and difference sets, relational intersection operators require their operands to be of the same type.
Formally: R \ (\ cap \) s = {t | t \ (\ in \) r and t \(\in\) S}
Derive from existing operator:
R \(\cap\) S = R - (R - S) = S - (S - R)

3.2 example diagram

4. Cartesian product (X)

4.1 definitions

Cartesian product or cross product is a binary operation used to combine two relationships. Suppose R and s are related to n and m attributes, Cartesian product, R × S can be written as,
R (A1, A2, ..., An) × S (B1, B2, ..., Bm)
The result of the above setting operation is,
Q (A1, A2, ..., An, B1, B2, ..., Bm)
Degree (Q) = n + m
Count (q) = number of tuples in R * number of tuples in S.

4.2 example diagram

5. Select \ (\ partial \)

Multiple choice

6. Projection \ (\ pi \)

The projection operation is used to select only a few columns from the relationship.

7.join \(\infty\)

7.1 Theta Join(\(\Theta\)) || NoEqui Join

7.2 Equi join

7.3 natural connection

When we omit conditions when connecting two relationships, it is called natural connection (*):

Let the relationship R1 have attributes (x1,x2,x3,M) respectively,
R2 has attributes (y1,y2,y3,y4,y5,M) respectively.
That is, the M attribute is common to the two relationships.
Then, the natural connection between R1 and R2 is a relationship with Heading(x1,x2,x3,M, y1,y2,y3,y4,y5) and body. The body is composed of all tuples, and the duplicate attribute M is deleted.


8. Division

If B contains all the attributes of A and B \ (common \) at the same time, it can be ignored directly

9. SQL statement

9.1 create database + database name

9.2 drop database + database name

9.3 ALTER TABLE Persons (ADD DateOfBirth date / MODIFY DateOfBirth year / DROP COLUMN DateOfBirth)

9.4 create table (primary key + foreign key)

    Date_Rented DATE NOT NULL,
    Date_Returned DATE NOT NULL,
    Optional_Insurance TINYINT DEFAULT 0,
    Customer_ID VARCHAR(10),
    Bag_ID int,
    reverted TINYINT DEFAULT 0,
    CONSTRAINT + (Constraint name) + FOREIGN key(Customer_ID) REFERENCES customers(Customer_ID),

9.5 view

create view table_name as + sentence

mysql> ALTER VIEW view_students_info
    -> AS SELECT id,name,age
    -> FROM tb_students_info;

mysql> DESC view_students_info;
| Field | Type        | Null | Key | Default | Extra |
| id    | int(11)     | NO   |     | 0       |       |
| name  | varchar(45) | YES  |     | NULL    |       |
| age   | int(11)     | YES  |     | NULL    |       |

drop view view_name

9.6 Oracle view

9.7 adding constraints

1.Primary key constraint
 add to:alter table  table_name add primary key (field)
delete:alter table table_name drop primary key
2.Non NULL constraint
 add to:alter  table table_name modify Column name data type  not null 
delete:alter table table_name modify Column name data type null
3.Unique constraint
 add to:alter table table_name add unique Constraint name (field)
delete:alter table table_name drop key Constraint name
4.Automatic growth
 add to:alter table table_name  modify Listing int  auto_increment
 delete:alter table table_name modify Listing int  
5.Foreign key constraint
 add to:alter table table_name add constraint Constraint name foreign key(Foreign key column) 
references Primary key table (primary key column)
First step:Delete foreign key
alter table table_name drop foreign key Constraint name
 Step 2:Delete index
alter  table table_name drop  index Index name
The constraint name is the same as the index name
6.Default value
 add to:alter table table_name alter Listing  set default 'value'
delete:alter table table_name alter Listing  drop default


After where and having, there are filter criteria, but there are differences:

1.where before group by, having after group by

2. Aggregate functions (avg, sum, max, min, count) cannot be placed after where as a condition, but can be placed after having

SELECT, SUM(access_log.count) AS nums FROM Websites
INNER JOIN access_log
WHERE Websites.alexa < 200 
HAVING SUM(access_log.count) > 200;


mysql> select DISTINCT(name) from info;
| name |
| addd |
| adsd |
| dcj  |
3 rows in set (0.00 sec)


When using join, the differences between on and where conditions are as follows:

1. The on condition is used when generating temporary tables. It returns the records in the left table regardless of whether the condition in on is true or not.
2. The where condition is the condition for filtering the temporary table after the temporary table is generated. At this time, there is no meaning of left join (the records in the left table must be returned). If the condition is not true, all items will be filtered out.


The left table lists them all

9.13 JOIN summary


9.15 UNOIN / intersect / minus

The UNION operator is used to combine the result sets of two or more SELECT statements.

Note that each SELECT statement inside a UNION must have the same number of columns. Columns must also have similar data types. At the same time, the order of columns in each SELECT statement must be the same.

SELECT column_name(s) FROM table1
UNION ALL(No, ALL) Default de duplication/ instersect/ minus
SELECT column_name(s) FROM table2;

9.16 sub query

Hyperdetailed links

9.17 Exist And No Exist

It's good to analyze layer by layer. After adding not exists, consider what information to display



 delete from info where age < 0;

Topics: Database