First Normal Form, Second Normal Form, Third Normal Form

Excerpted from https://www.zhihu.com/question/24696366

1. Functional dependency: If in a table, when the value of attribute (or attribute group) X is determined, the value of attribute Y must be determined, thenIt can be said that the Y function depends on X, written X → Y (one X does not correspond to two Y, Y = f(X))
2. Complete functional dependency: attribute set X → Y, for any proper subset X' of X, there is X' ! → Y, then Y is said to be completely functionally dependent on X
3. Partial functional dependency: attribute set X → Y, there is a proper subset X' of X, and X' → Y, then Y is said to be partially functionally dependent on X
4. The transfer function depends on: X → Y, Y → Z (premise: Y is not included in X, and Y ! → X), then we say that the transfer function of Z depends on X

1. Student ID → Name, Department Name → Department Chair
2. Score fully functionally dependent on name+course; grade entirely dependent on student number+course
3. Department nameSome functions depend on student number + name; because the student number can be used to determine the department name (the function of the department name depends on the student number); the name can also be determined by the name
4. Department Chair The transfer function depends on the student number; the student number determines the department name, and the department name determines the department chair

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Note: if the second normal form is satisfied, the first normal form must be satisfied; if the third normal form is satisfied, the second normal form must be satisfied

5. First Normal Form: Columns are inseparable
   First Normal Form is the most basic normal form. All fields in the data table are inseparable atomic values, which means that the data table satisfies the First Normal Form
   Subscripts are notFirst normal form:
   

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6. Second normal form: there is no partial dependence of non-primary attributes on candidate codes

1. Find all candidate codes (minimum set of attributes that can identify the uniqueness of a set of data)
2. The attributes included in all candidate codes are called primary attributes
3. Attributes other than primary attributes are called non-primary attributes
4. Determine whether there is a partial functional dependence of non-primary attributes on the candidate code

Analyze the above image:

1. Candidate code: student number + course ((minimum attribute set that can identify the uniqueness of a set of data))
   Check all individual attributes, when its value is determined, whether all the remaining attribute values ​​arecan be determined.
   View all attribute groups that contain two attributes, when its value is determined, whether all remaining attribute values ​​can be determined.
   ……
   View all attribute groups that contain six attributes, that is, all attributes. When its value is determined, whether all the remaining attribute values ​​can be determined.
   
2. Main attributes: student ID, course
3. Non-Primary Attributes: Name, Department Name, Department Chair, Score
4. Judgment: name, department name, department chair are all part of the function depends on the candidate code
5. Conclusion: Not in Second Normal Form

Split the table, both tables are in second normal form

1. The first table:
   Candidate code: student number + course
   Main attribute: student number, course
   Non-main attribute: score
   Judgment: the score is completely functionally dependent on (student number +course)
2. The second table:
   Candidate code: student number (considering the same name, name will not be listed as a candidate key)
   Primary attribute: student number
   Non-primary attribute: name, department name, departmentDirector
   Judgment: The non-primary attribute is completely functionally dependent on the candidate code

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7. Third normal form: there is no transfer function dependence of non-attribute codes on candidate keys
   

Observe the table above,

1. Candidate code: student number
2. Main attribute: student ID
3. Non-primary attributes: name, department name, department chair
4. Judgment: student number → department name, department name → department chair
5. Not in third normal form

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8. BCNF is an improvement on third normal form

A condition that satisfies the relational schema of BCNF:

1. All non-primary properties are fully functionally dependent on each code.
2. All main properties are also fully functionally dependent on every code that does not contain it.
3. No attribute is fully functionally dependent on any set of attributes that are not code.

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