SQL进阶系列之7用SQL进行集合运算

Posted 2022-11-30 evian-jeff

写在前面

集合论是SQL语言的根基，因为这种特性，SQL也被称为面向集合语言

导入篇：集合运算的几个注意事项

• 注意事项1：SQL能操作具有重复行的集合(multiset、bag)，可以通过可选项ALL来支持

  SQL的集合运算符提供了允许重复和不允许重复两种用法，UNION和INTERSECT结果里不会出现重复的行，UNION ALL则会保留重复行；ALL的作用和SELECT子句中的DISTINCT相反。ALL有助于优化查询性能，这是因为使用ALL后不再进行排序

• 注意事项2：集合运算符存在优先级

  标准SQL规定：INTERSECT比UNION和EXCEPT优先级高

• 注意事项3：各个DBMS提供商在集合运算上的实现程度不同

  mysql不支持，Oracle使用MINUS替代EXCEPT

• 注意事项4：除法运算没有标准定义

  四则运算的和(UNION)、差(EXCEPT)、积(CROSS JOIN)都被引入了标准SQL，商却迟迟没有进入SQL标准

比较表和表：检查集合相等性之基础篇

/* 比较表和表：检查集合相等性 */
CREATE TABLE Tbl_A
 (keycol  CHAR(1) PRIMARY KEY,
  col_1   INTEGER, 
  col_2   INTEGER, 
  col_3   INTEGER);

CREATE TABLE Tbl_B
 (keycol  CHAR(1) PRIMARY KEY,
  col_1   INTEGER, 
  col_2   INTEGER, 
  col_3   INTEGER);

/* 表相等的情况 */
DELETE FROM Tbl_A;
INSERT INTO Tbl_A VALUES('A', 2, 3, 4);
INSERT INTO Tbl_A VALUES('B', 0, 7, 9);
INSERT INTO Tbl_A VALUES('C', 5, 1, 6);

DELETE FROM Tbl_B;
INSERT INTO Tbl_B VALUES('A', 2, 3, 4);
INSERT INTO Tbl_B VALUES('B', 0, 7, 9);
INSERT INTO Tbl_B VALUES('C', 5, 1, 6);

/* B行不同的情况 */
DELETE FROM Tbl_A;
INSERT INTO Tbl_A VALUES('A', 2, 3, 4);
INSERT INTO Tbl_A VALUES('B', 0, 7, 9);
INSERT INTO Tbl_A VALUES('C', 5, 1, 6);

DELETE FROM Tbl_B;
INSERT INTO Tbl_B VALUES('A', 2, 3, 4);
INSERT INTO Tbl_B VALUES('B', 0, 7, 8);
INSERT INTO Tbl_B VALUES('C', 5, 1, 6);

/* 包含NULL的情况（相等） */
DELETE FROM Tbl_A;
INSERT INTO Tbl_A VALUES('A', NULL, 3, 4);
INSERT INTO Tbl_A VALUES('B', 0, 7, 9);
INSERT INTO Tbl_A VALUES('C', NULL, NULL, NULL);

DELETE FROM Tbl_B;
INSERT INTO Tbl_B VALUES('A', NULL, 3, 4);
INSERT INTO Tbl_B VALUES('B', 0, 7, 9);
INSERT INTO Tbl_B VALUES('C', NULL, NULL, NULL);

/* 包含NULL的情况（C行不同） */
DELETE FROM Tbl_A;
INSERT INTO Tbl_A VALUES('A', NULL, 3, 4);
INSERT INTO Tbl_A VALUES('B', 0, 7, 9);
INSERT INTO Tbl_A VALUES('C', NULL, NULL, NULL);

DELETE FROM Tbl_B;
INSERT INTO Tbl_B VALUES('A', NULL, 3, 4);
INSERT INTO Tbl_B VALUES('B', 0, 7, 9);
INSERT INTO Tbl_B VALUES('C', 0, NULL, NULL);

如果两表相同，有如下逻辑：A UNION B = A = B ；还有 A \(\cup\) B = A \(\cap\) B

-- 判断两表是否完全相等(判断之前可以看看行数相不相同)
SELECT COUNT(*) AS row_cnt FROM 
((SELECT * FROM Tbl_A ) 
UNION 
(SELECT * FROM Tbl_B)) AS Total;

对上面的表，我们发现对任意的表S都有如下的公式成立：S UNION S = S 这称之为幂等性，同一个集合加多少次结果都相同。

比较表和表：检查集合相等性之进阶篇

集合论里判断两个集合相等一般使用下面两个方法：

• A \(\subset\) B 且 A \(\supset\) B \(\Leftrightarrow\) A = B
• A \(\cup\) B = A \(\cap\) B \(\Leftrightarrow\) A = B

-- A union B = A intersect B means A = B,不难发现intersect也是一个幂等运算符
-- 两张表相等时返回"相等",否则返回"不相等"
SELECT CASE WHEN COUNT(*) = 0 
            THEN '相等' ELSE '不相等' END AS result
FROM ((SELECT * FROM tbl_A) UNION (SELECT * FROM tbl_B) 
      EXCEPT 
      (SELECT * FROM tbl_A) INTERSECT (SELECT * FROM tbl_B)) AS TMP;

-- 查看量表不一样的记录
(SELECT * FROM Tbl_A EXCEPT SELECT * FROM Tbl_B)
UNION ALL
(SELECT * FROM Tbl_B EXCEPT SELECT * FROM Tbl_A);

用差集实现关系除法运算

• 嵌套使用NOT EXISTS
• 使用HAVING子句转换成一对一关系
• 把重复变成减法

-- 建表语句
/* 用差集实现关系除法运算 */
CREATE TABLE Skills 
(skill VARCHAR(32),
 PRIMARY KEY(skill));

CREATE TABLE EmpSkills 
(emp   VARCHAR(32), 
 skill VARCHAR(32),
 PRIMARY KEY(emp, skill));

INSERT INTO Skills VALUES('Oracle');
INSERT INTO Skills VALUES('UNIX');
INSERT INTO Skills VALUES('Java');

INSERT INTO EmpSkills VALUES('相田', 'Oracle');
INSERT INTO EmpSkills VALUES('相田', 'UNIX');
INSERT INTO EmpSkills VALUES('相田', 'Java');
INSERT INTO EmpSkills VALUES('相田', 'C#');
INSERT INTO EmpSkills VALUES('神崎', 'Oracle');
INSERT INTO EmpSkills VALUES('神崎', 'UNIX');
INSERT INTO EmpSkills VALUES('神崎', 'Java');
INSERT INTO EmpSkills VALUES('平井', 'UNIX');
INSERT INTO EmpSkills VALUES('平井', 'Oracle');
INSERT INTO EmpSkills VALUES('平井', 'php');
INSERT INTO EmpSkills VALUES('平井', 'Perl');
INSERT INTO EmpSkills VALUES('平井', 'C++');
INSERT INTO EmpSkills VALUES('若田部', 'Perl');
INSERT INTO EmpSkills VALUES('渡来', 'Oracle');

-- 用求差集的方法进行关系除法运算(有余数)
SELECT DISTINCT emp 
FROM EmpSkills ES1
WHERE NOT EXISTS 
(SELECT skill FROM Skills EXCEPT SELECT skill FROM EmpSkills ES2 WHERE ES1.emp = ES2.emp);

寻找相等的子集

/* 4.寻找相等的子集 */
CREATE TABLE SupParts
(sup  CHAR(32) NOT NULL,
 part CHAR(32) NOT NULL,
 PRIMARY KEY(sup, part));

INSERT INTO SupParts VALUES('A',  '螺丝');
INSERT INTO SupParts VALUES('A',  '螺母');
INSERT INTO SupParts VALUES('A',  '管子');
INSERT INTO SupParts VALUES('B',  '螺丝');
INSERT INTO SupParts VALUES('B',  '管子');
INSERT INTO SupParts VALUES('C',  '螺丝');
INSERT INTO SupParts VALUES('C',  '螺母');
INSERT INTO SupParts VALUES('C',  '管子');
INSERT INTO SupParts VALUES('D',  '螺丝');
INSERT INTO SupParts VALUES('D',  '管子');
INSERT INTO SupParts VALUES('E',  '保险丝');
INSERT INTO SupParts VALUES('E',  '螺母');
INSERT INTO SupParts VALUES('E',  '管子');
INSERT INTO SupParts VALUES('F',  '保险丝');

-- 生成供应商的全部组合
SELECT SP1.sup AS s1,SP2.sup AS s2
FROM SupParts SP1,SupParts SP2
WHERE SP1.sup < SP2.sup
GROUP BY SP1.sup,SP2.sup;

SELECT SP1.sup AS s1,SP2.sup AS s2
FROM SupParts SP1,SupParts SP2
WHERE SP1.sup < SP2.sup
AND SP1.part = SP2.part
GROUP BY SP1.sup,SP2.sup
HAVING COUNT(*) = (SELECT COUNT(*) FROM SupParts SP3 WHERE SP3.sup = SP1.sup)
AND COUNT(*) = (SELECT COUNT(*) FROM SupParts SP4 WHERE SP4.sup = SP2.sup);

用于删除重复行的高效SQL

/* 5.用于删除重复行的高效SQL */
/* 在PostgreSQL中，需要把“with oids”添加到CREATE TABLE语句的最后 */
CREATE TABLE Products
(name  CHAR(16),
 price INTEGER);

INSERT INTO Products VALUES('苹果',  50);
INSERT INTO Products VALUES('橘子', 100);
INSERT INTO Products VALUES('橘子', 100);
INSERT INTO Products VALUES('橘子', 100);
INSERT INTO Products VALUES('香蕉',  80);

-- 删除重复行：使用关联子查询
DELETE FROM Products
WHERE rowid < (SELECT MAX(P2.rowid) FROM Products P2 WHERE Products.name = P2.name AND Product.price = P2.price);

-- 用于删除重复行的高效SQL语句(1):通过EXCEPT求补集
DELETE FROM Products
WHERE rowid IN (SELECT rowid FROM Products EXCEPT SELECT MAX(rowid) FROM Products GROUP BY name,price)

-- 用于删除重复行的高效SQL语句(2):通过NOT IN求补集
DELETE FROM Products
WHERE rowid  NOT IN (SELECT MAX(rowid) FROM Products GROUP BY name,price)

小结

• 集合运算方面，SQL的标准化进行的非常缓慢，使用时需要注意
• 如果集合运算符不指定ALL选项，重复行会被排除掉，而且这种情况下还会发生排序，所以性能方面不够好
• UNION和INTERSECT都具有幂等性，而EXCEPT不具有幂等性
• 标准SQL没有关系除法的运算符，需要自己实现
• 判断两个集合是否相等，可以通过幂等性或一一映射两种方式
• 使用EXCEPT可以很简单地求得补集

练习题

/* 练习题1-7-1：改进“只使用UNION的比较” */
SELECT CASE WHEN COUNT(*) = (SELECT COUNT(*) FROM tbl_A )
             AND COUNT(*) = (SELECT COUNT(*) FROM tbl_B )
            THEN '相等'
            ELSE '不相等' END AS result
  FROM ( SELECT * FROM tbl_A
         UNION
         SELECT * FROM tbl_B ) TMP;

/* 练习题1-7-2：精确关系除法运算 */
SELECT DISTINCT emp
  FROM EmpSkills ES1
 WHERE NOT EXISTS
        (SELECT skill
           FROM Skills
         EXCEPT
         SELECT skill
           FROM EmpSkills ES2
          WHERE ES1.emp = ES2.emp)
  AND NOT EXISTS
        (SELECT skill
           FROM EmpSkills ES3
          WHERE ES1.emp = ES3.emp
         EXCEPT
         SELECT skill
           FROM Skills );

/* 练习题1-7-2：精确关系除法运算 */
SELECT emp
  FROM EmpSkills ES1
 WHERE NOT EXISTS
        (SELECT skill
           FROM Skills
         EXCEPT
         SELECT skill
           FROM EmpSkills ES2
          WHERE ES1.emp = ES2.emp)
 GROUP BY emp
HAVING COUNT(*) = (SELECT COUNT(*) FROM Skills);