揭秘数据库系统中的关系代数运算，助你玩转数据世界

2023-01-14 05:52:12

关系代数：数据库系统的魔法公式

前言

关系代数是一种强有力的工具，可以帮助你轻松驾驭数据，操纵关系，并从数据海洋中挖掘出有价值的信息。就像数学中的公式一样，关系代数可以作为数据库系统的魔法公式，让你在数据世界中挥洒自如。

集合运算符：数据海洋中的拼图游戏

集合运算符将关系视为元组的集合，让你能够从行的角度操作数据。就像玩拼图游戏一样，这些运算符可以让你组合和比较关系，将不同的数据块拼接成有意义的信息。

**并集 (UNION)** 
关系 A: {1, 2, 3}
关系 B: {3, 4, 5}
A UNION B = {1, 2, 3, 4, 5}

**交集 (INTERSECT)** 
关系 A: {1, 2, 3}
关系 B: {3, 4, 5}
A INTERSECT B = {3}

**差集 (MINUS)** 
关系 A: {1, 2, 3}
关系 B: {3, 4, 5}
A MINUS B = {1, 2}

**笛卡尔积 (CARTESIAN PRODUCT)** 
关系 A: {(1, "John"), (2, "Mary")}
关系 B: {(3, "New York"), (4, "London")}
A CARTESIAN PRODUCT B = {(1, "John"), (2, "Mary"), (3, "John"), (4, "Mary"), (1, "New York"), (2, "New York"), (3, "Mary"), (4, "Mary")}

关系运算符：数据的解剖手术

关系运算符不仅涉及行，还涉及列，让你能够对关系进行更深入的分析和处理。就像数据库系统中的手术刀一样，这些运算符可以让你精细地切割和重组数据，从不同的角度审视和理解信息。

**选择 (SELECT)** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
SELECT * FROM students WHERE major = "Computer Science"
结果：{{"John", 18, "Computer Science"}}

**投影 (PROJECT)** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
PROJECT students {name}
结果：{{"John"}, {"Mary"}, {"Bob"}}

**自然连接 (NATURAL JOIN)** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
关系 courses: {{"CS101", "Introduction to Computer Science"}, {"MATH101", "Introduction to Mathematics"}, {"HIST101", "Introduction to History"}}
STUDENTS NATURAL JOIN COURSES
结果：{{"John", 18, "Computer Science", "CS101", "Introduction to Computer Science"}, {"Mary", 19, "Mathematics", "MATH101", "Introduction to Mathematics"}, {"Bob", 20, "History", "HIST101", "Introduction to History"}}

**外连接 (OUTER JOIN)** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
关系 courses: {{"CS101", "Introduction to Computer Science"}, {"MATH101", "Introduction to Mathematics"}}
STUDENTS LEFT OUTER JOIN COURSES
结果：{{"John", 18, "Computer Science", "CS101", "Introduction to Computer Science"}, {"Mary", 19, "Mathematics", "MATH101", "Introduction to Mathematics"}, {"Bob", 20, "History", NULL, NULL}}

算术比较符：数据的真假裁判

算术比较符可以辅助专门的关系运算符进行操作，就像数学中的比较符号一样，让你能够对关系中的数值进行比较和判断。就像裁判手中的哨子一样，这些运算符可以对数据中的真假和大小进行裁决。

**等于 (=)** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
SELECT * FROM students WHERE age = 18
结果：{{"John", 18, "Computer Science"}}

**不等于 (<>)** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
SELECT * FROM students WHERE age <> 18
结果：{{"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}

**大于 (>)** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
SELECT * FROM students WHERE age > 18
结果：{{"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}

逻辑运算符：数据的逻辑推理

逻辑运算符可以辅助专门的关系运算符进行操作，就像逻辑学中的连接词一样，让你能够对关系中的条件进行组合和判断。就像逻辑学中的推理工具一样，这些运算符可以让你对数据中的关系和规律进行严谨的分析和推断。

**AND** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
SELECT * FROM students WHERE age > 18 AND major = "Mathematics"
结果：{{"Mary", 19, "Mathematics"}}

**OR** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
SELECT * FROM students WHERE age > 18 OR major = "Mathematics"
结果：{{"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}

**NOT** 
关系 students: {{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}, {"Bob", 20, "History"}}
SELECT * FROM students WHERE NOT major = "History"
结果：{{"John", 18, "Computer Science"}, {"Mary", 19, "Mathematics"}}