Chapter II relational database

2.1 Relationship

Relation is a data structure of relation model .
The logical structure is reflected in a table ：

• Each column of the relationship is called attribute , For example, in the table user_id Is the user identification number , Attribute can describe the meaning of the value of this column .
• Relationships are sometimes called surface .

Basic concepts

Domain

Write it down as D（domain）

The cartesian product

Cartesian product is an operation on a field , Write it down as ：
$$D_1\times D_2\times ...\times D_n=\{(d_1,d_2,...,d_n)|d_i\in D_i,i=1,2,...,n\}$$

There are currently three domains （ Teachers' 、 Course 、 Student ）

Use one that may not be accurate , But an easy way to describe Cartesian product ： Cartesian product is a combination of elements in different fields

For example, here is 【 Li Yi 】 and 【 mathematics 、 English 】、【 Student 】 The combination of .

• Cartesian product has no semantics , It's like you can't make sure 【 Li Yi 】 teach 3 Subjects , The student of the subject happens to be that 3 A student .

• Every combination in Cartesian product （ Every line ） Is called a n Tuples , It depends on how many columns there are in each row （ In the above example is 3 Tuples ）, Write it down as ：
  $$(d_1,d_2,...,d_n)$$

• A value in a tuple is called component （[ Li Yi | English | Wang Chieh ] Chinese and English are one component ）.

• The different values allowed in a domain are called the values of this domain base （ The base number of teachers =2, The cardinality of the subject =2, The cardinality of the student field =3）.
  Cardinality in Cartesian product = The product of the cardinality of each field

Relationship

• Relationship Is a subset of the Cartesian product , Expressed as ：
  $$R(D_1,D_2,...,D_n)$$
  R Express Relation;n It's a relationship Objective or degree , Is how many attributes a relationship has .
  Special ,n=1 It's called Unit relationship ,n=2 It's called Binary relationship .
• Candidate code ： A set of attributes can determine a unique tuple .
  ① This group can't do without one attribute
  ② You can have only one attribute
• If a relationship has multiple candidates , Then select one of them as Main code .
  For example, in the student information table , There are two candidate codes ：
  1.{ Student number }
  2.{ ID number }
  At this point, if you select { Student number } As the unique identification of students , that { Student number } It is called the main code （ choice { ID number } Of course, it can be ）.
• Main attribute ： Attributes in candidate code .
• Non primary property ： Attributes that do not belong to the candidate code .
• In extreme cases , All attributes in a relationship are candidates for that relationship , Then call this candidate code Full size .

Three types of relational tables

• Basic table （ Also known as Basic relationship or Base watch ）
  The actual table ：
  
• Query table
  The table obtained according to the query results .
  Query age is greater than 20 Year old user ：
  
• View table
  It's a virtual table , Does not exist in disk space .
  It is actually a collection of query statements , Is encapsulated , Like a function .
  There will be Check age 20 Users older than This requirement , The package becomes a View .
  
  So the view table ：
  

The nature of the basic relationship

Every component of the basic relationship , Must be inseparable .
That is, every data item must be a basic data type （ integer 、 character string 、…）, It cannot be a table .

2.1.2 Relationship model

The relational pattern is represented in Chapter 2 as R(U, D, DOM)
U： The set of attribute names that make up the relationship
D：U The domain from which the attribute in the
DOM： Property to a collection of domain images

Roast about the textbook , this DOM Is the description of a person's words ？

for instance , A relationship is as follows ：

that ：
U：{ Faculty number 、 Student number 、 Course no. }
D：{ Teachers' 、 Student 、 Course }
DOM：{DOM( Faculty number ) = Teachers' 、DOM( Student number )= Student 、DOM( Course no. )= Course }

Mapping is like a function , Give it an input , Get an output .
DOM It's input. attribute Get the Domain .

2.2 Relationship operation

Additions and deletions , Understand everything .

Insert 、 Delete 、 modify 、 Inquire about .

• Query operations include ：
  choice 、 Projection 、 Connect 、 except 、 and 、 Bad 、 hand over 、 The cartesian product etc. .
• The objects and results of the operation are collections .

2.3 The integrity of the relationship

• Entity integrity ：
  If the property ( Group )A It's the relationship R The main attribute of , that A Not empty .

In fact, the primary attribute is to distinguish a tuple in the relationship （ A line ） Of Conditions , If the condition is empty , That is, unconditional , Then it is impossible to distinguish any tuple in the relationship .

• Referential integrity ：

Student （ Student number , full name , major ）
Course （ Course no. , Course name , credits ）
Elective （ Course no. , Student number , Class hours ）
Student number Is the student's main code , Course no. Is the main code of the course , Course no. and Student number It is the main code of elective course .
Reference refers to ： An attribute of a basic relationship quote The properties of other relationships .

hypothesis F It's the relationship R Properties of （ One or a group of ）, but F No Relationship R The main code of ,K_s yes Relationship S The main code of . If F And K_s Corresponding （ identical ）, said F yes R Of Outer code ,R by Reference relationship ,S by The referential relationship or Target relationship .

R Each tuple in F The value on the property is either empty , Or for the relationship S The main code value of a tuple on .

Student （ Major number , Student number , full name ）
major （ Major number , Major name ）
In student relations , The major number is either empty （ No major assigned ）, Or it is a major code value in the specialty （ A major ）

• User defined integrity
  There are many user-defined integrity , such as ：
  A property must be non empty
  The value of a property must be in 0~100 Between （ achievement ）
  wait .

2.4 Relational algebra

2.4.1 Traditional set operations

hand over 、 and , Everyone knows .

• Bad ：
  Relationship R And relationships S The difference is recorded as R-S, Is to remove R Of S Part of .
  
• The cartesian product
  Relationship R And relationship S The Cartesian product of is written as ：
  $$R\times S=\{\overgroup{t_r{t}_s}|tr\in R\wedge ts\in S\}$$

2.4.2 Special relational operations

1. choice

$${\sigma }_F(R)=\{t\in R\wedge F(t)=true\}$$
among F On condition that , The effect of the selection operation is ： Filter out the conditions in the relationship F tuples .



Choose the conditions ： Older than 20：

2. Projection

Select a column from the relationships as the new relationship .
$$\prod _A=\{t[A]|t\in R\}$$

3. Connect

Connections are also known as θ Connect , It is to select the part satisfying the condition from the Cartesian product of two relations , Write it down as ：
$$R\underset{A\theta B}{\bowtie }S=\{\overgroup{t_r{t}_s}|t_r\in R\wedge t_s\in S\wedge t_r[A]\theta t_s[B]\}$$
θ Is the equivalent connection , From the relationship R and S Select an attribute from the list A and B Equal tuples , Spliced into the same tuple .
Natural join The attributes in the connected tuple will be removed A Or attributes B（ Because they are both equal ）.

3.1 External connection

Equivalent connection is actually to filter out the parts with the same attributes in two relationships .
There are two tables. ：

Both tables have a common attribute ： Professional code , So through this property , We can find out the corresponding major of each student .

Full outer join ：

Professional code It's redundant .

Left outer connection and right outer connection

Relationship R And S Do according to attribute F Equivalent connection ,R Some tuples in may not exist S in F Property has the same value .（S Some tuples in may also be in R No correspondence found in ）
Then it will be discarded in the all outer connection , These discarded tuples are called Floating tuples .

According to the example, it means ：
A student's major number is wrong for some reason , Cannot find in the specialty table .
A major is too popular , None of the students chose .

Remember R And S The connection is marked as ：
$$R\underset{A\theta B}{\bowtie }S$$
The left outer join Just keep it R Medium Floating tuples , Right connection Just keep it S Medium Floating tuples .

take R Write it down as a student form ,S Record it as a professional table

• The left outer join （ Retain Student list Medium Floating tuples ）
  

• Right connection （ Retain Professional watch Medium Floating tuples ）