MySQL的子查询及相关优化学习教程_MySQL
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互联网集市收集整理的这篇技术教程文章主要介绍了MySQL的子查询及相关优化学习教程_MySQL，小编现在分享给大家，供广大互联网技能从业者学习和参考。文章包含19512字，纯文字阅读大概需要28分钟。
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一、子查询1、where型子查询
（把内层查询结果当作外层查询的比较条件）
#不用order by 来查询最新的商品 select goods_id,goods_name from goods where goods_id = (select max(goods_id) from goods);
#取出每个栏目下最新的产品(goods_id唯一) select cat_id,goods_id,goods_name from goods where goods_id in(select max(goods_id) from goods group by cat_id);
2、from型子查询
(把内层的查询结果供外层再次查询)
#用子查询查出挂科两门及以上的同学的平均成绩
思路：
#先查出哪些同学挂科两门以上 select name,count(*) as gk from stu where score < 60 having gk >=2; #以上查询结果，我们只要名字就可以了，所以再取一次名字 select name from (select name,count(*) as gk from stu having gk >=2) as t; #找出这些同学了，那么再计算他们的平均分 select name,avg(score) from stu where name in (select name from (select name,count(*) as gk from stu having gk >=2) as t) group by name;
3、exists型子查询
（把外层查询结果拿到内层，看内层的查询是否成立）
#查询哪些栏目下有商品，栏目表category,商品表goods select cat_id,cat_name from category where exists(select * from goods where goods.cat_id = category.cat_id);
二、优化
从句式的形式看，子查询分为特殊格式子查询和非特殊格式子查询，特殊格式的子查询中又包括IN、ALL、ANY、SOME、EXISTS等类型的子查询，对于有的类型的子查询，MySQL有的支持优化，有的不支持，具体情况如下。
示例一，MySQL不支持对EXISTS类型的子查询的优化：
EXISTS类型的相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE EXISTS (SELECT 1 FROM t2 WHERE t1.a1= t2.a2 AND t2.a2>10);
+----+--------------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+--------------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | DEPENDENT SUBQUERY | t2 | ALL | NULL | Using where | +----+--------------------+-------+------+------+-------------+ 2 rows in set, 2 warnings (0.00 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where exists(/* select#2 */ select 1 from `test`.`t2` where ((`test`.`t1`.`a1` = `test`.`t2`.`a2`) and (`test`.`t2`.`a2` > 10)) )
从查询执行计划看，子查询存在，MySQL没有进一步做子查询的优化工作。
另外的一个EXISTS类型的相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE EXISTS (SELECT 1 FROM t2 WHERE t1.b1= t2.b2 AND t1.a1=10);
+----+--------------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+--------------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | DEPENDENT SUBQUERY | t2 | ALL | NULL | Using where | +----+--------------------+-------+------+------+-------------+ 2 rows in set, 3 warnings (0.02 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where exists(/* select#2 */ select 1 from `test`.`t2` where ((`test`.`t1`.`b1` = `test`.`t2`.`b2`) and (`test`.`t1`.`a1` = 10)) )
从查询执行计划看，子查询存在，MySQL没有进一步做子查询的优化工作。
示例二，MySQL不支持对NOT EXISTS类型的子查询的优化：
NOT EXISTS类型的相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE NOT EXISTS (SELECT 1 FROM t2 WHERE t1.a1= t2.a2 AND t2.a2>10);
+----+--------------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+--------------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | DEPENDENT SUBQUERY | t2 | ALL | NULL | Using where | +----+--------------------+-------+------+------+-------------+ 2 rows in set, 2 warnings (0.00 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where (not(exists( /* select#2 */ select 1 from `test`.`t2` where ((`test`.`t1`.`a1` = `test`.`t2`.`a2`) and (`test`.`t2`.`a2` > 10)))) )
从查询执行计划看，子查询存在，MySQL没有进一步做子查询的优化工作。
另外的一个NOT EXISTS类型的相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE NOT EXISTS (SELECT 1 FROM t2 WHERE t1.b1= t2.b2 AND t1.a1=10);
+----+--------------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+--------------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | DEPENDENT SUBQUERY | t2 | ALL | NULL | Using where | +----+--------------------+-------+------+------+-------------+ 2 rows in set, 3 warnings (0.00 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where (not(exists( /* select#2 */ select 1 from `test`.`t2` where ((`test`.`t1`.`b1` = `test`.`t2`.`b2`) and (`test`.`t1`.`a1` = 10)))) )
从查询执行计划看，子查询存在，MySQL没有进一步做子查询的优化工作。
示例三，MySQL支持对IN类型的子查询的优化，按也有不支持的情况存在：
IN非相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 IN (SELECT a2 FROM t2 WHERE t2.a2>10);
+----+--------------+-------------+------+------+----------------------------------------------------+ | id | select_type | table | type | key | Extra | +----+--------------+-------------+------+------+----------------------------------------------------+ | 1 | SIMPLE || ALL | NULL | NULL | | 1 | SIMPLE | t1 | ALL | NULL | Using where; Using join buffer (Block Nested Loop) | | 2 | MATERIALIZED | t2 | ALL | NULL | Using where | +----+--------------+-------------+------+------+----------------------------------------------------+ 3 rows in set, 1 warning (0.00 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` semi join (`test`.`t2`) where ((`test`.`t1`.`a1` = ``.`a2`) and (`test`.`t2`.`a2` > 10))
从查询执行计划看，表t2被物化后，与表t1执行了半连接（semi join）。尽管有“subquery2”这样的内容看起来是子查询，但是表t2已经被上拉到表t1层执行了半连接，所以MySQL支持IN子查询优化为半连接操作。
另外一个IN非相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 IN (SELECT a2 FROM t2 WHERE t2.a2=10);
+----+--------------+-------------+------+------+----------------------------------------------------+ | id | select_type | table | type | key | Extra | +----+--------------+-------------+------+------+----------------------------------------------------+ | 1 | SIMPLE || ALL | NULL | Using where | | 1 | SIMPLE | t1 | ALL | NULL | Using where; Using join buffer (Block Nested Loop) | | 2 | MATERIALIZED | t2 | ALL | NULL | Using where | +----+--------------+-------------+------+------+----------------------------------------------------+ 3 rows in set, 1 warning (0.02 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` semi join (`test`.`t2`) where ((``.`a2` = 10) and (`test`.`t1`.`a1` = 10) and (`test`.`t2`.`a2` = 10))
从查询执行计划看，子查询不存在，表t1和t2直接做了块嵌套循环半连接（Block Nested Loop），把子查询上拉到父查询中用嵌套循环半连接完成IN操作。另外，由于子查询上拉，使得增加连接条件“a1=a2”，而原先的条件“a2=10”可以利用常量传递优化技术，使得“a1=a2=10”，所以查询执行计划中，两个索引扫描的条件分别为：a1 = 10、a2 = 10。
另外一个IN非相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 IN (SELECT a2 FROM t2 WHERE t1.a1=10);
+----+-------------+-------+------+------------------------------------------------------------------+ | id | select_type | table | type | Extra | +----+-------------+-------+------+------------------------------------------------------------------+ | 1 | SIMPLE | t2 | ALL | Using where; Start temporary | | 1 | SIMPLE | t1 | ALL | Using where; End temporary; Using join buffer (Block Nested Loop)| +----+-------------+-------+------+------------------------------------------------------------------+ 2 rows in set, 2 warnings (0.00 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` semi join (`test`.`t2`) where ((`test`.`t2`.`a2` = 10) and (`test`.`t1`.`a1` = 10))
从查询执行计划看，子子查询不存在，表t1和t2直接做了块嵌套循环连接（Block Nested Loop），但属于半连接操作（semi join），把子查询上拉到父查询中用嵌套循环半连接完成IN操作。
示例四，MySQL支持对NOT IN类型的子查询的优化
NOT IN非相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 NOT IN (SELECT a2 FROM t2 WHERE t2.a2>10);
+----+-------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+-------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | SUBQUERY | t2 | ALL | NULL | Using where | +----+-------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.02 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where (not(( `test`.`t1`.`a1`,`test`.`t1`.`a1` in ( (/* select#2 */ select `test`.`t2`.`a2` from `test`.`t2` where (`test`.`t2`.`a2` > 10) having 1 ), ( `test`.`t1`.`a1` in on where ((`test`.`t1`.`a1` = `materialized-subquery`.`a2`)) ) ) )) )
从查询执行计划看，表t2做了子查询（SUBQUERY）。而子查询被物化（materialize）。所以，MySQL对于NOT IN子查询采用了物化的优化方式，但不支持子查询的消除。
另外一个NOT IN非相关子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 NOT IN (SELECT a2 FROM t2 WHERE t2.a2=10);
+----+-------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+-------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | SUBQUERY | t2 | ALL | NULL | Using where | +----+-------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.00 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`,`test`.`t1`.`b1` AS `b1` from `test`.`t1` where (not(( `test`.`t1`.`a1`,`test`.`t1`.`a1` in ( (/* select#2 */ select `test`.`t2`.`a2` from `test`.`t2` where (`test`.`t2`.`a2` = 10) having 1 ), ( `test`.`t1`.`a1` in on where ((`test`.`t1`.`a1` = `materialized-subquery`.`a2`)) ) ) )) )
从查询执行计划看，表t2做了子查询（SUBQUERY）。而子查询被物化（materialize）。所以，MySQL对于NOT IN子查询采用了物化的优化方式，但不支持子查询的消除。
示例五，MySQL支持对ALL类型的子查询的优化：
不相关的ALL子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 >ALL (SELECT a2 FROM t2 WHERE t2.a2>10);
+----+-------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+-------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | SUBQUERY | t2 | ALL | NULL | Using where | +----+-------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.00 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`,`test`.`t1`.`b1` AS `b1` from `test`.`t1` where((`test`.`t1`.`a1` <= ( /* select#2 */ select `test`.`t2`.`a2` from `test`.`t2` where (`test`.`t2`.`a2` > 10) ) ))
从查询执行计划看，出现了子查询（SUBQUERY），但是，子查询被“<=
不相关的ALL子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 =ALL (SELECT a2 FROM t2 WHERE t2.a2=10);
+----+--------------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+--------------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | DEPENDENT SUBQUERY | t2 | ALL | NULL | Using where | +----+--------------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.00 sec)
被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`,`test`.`t1`.`b1` AS `b1` from `test`.`t1` where( ( `test`.`t1`.`a1`, ( /* select#2 */ select 1 from `test`.`t2` where ((`test`.`t2`.`a2` = 10) and (outer_field_is_not_null, (( (`test`.`t1`.`a1`) <> 10) or (isnull(10))), true ) ) having (outer_field_is_not_null, (`test`.`t2`.`a2`), true) ) ))
从查询执行计划看，出现了子查询（SUBQUERY），但是被查询优化器处理后的语句中包含“exists”，这表明MySQL对于“=ALL”式的子查询优化用“EXISTS strategy”方式优化，所以MySQL支持“=ALL”式的子查询优化。
不相关的ALL子查询，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1
+----+-------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+-------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | SUBQUERY | t2 | ALL | NULL | Using where | +----+-------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.00 sec)被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`,`test`.`t1`.`b1` AS `b1` from `test`.`t1` where((`test`.`t1`.`a1` >= (/* select#2 */ select `test`.`t2`.`a2` from `test`.`t2` where (`test`.`t2`.`a2` = 10) ) )) 从查询执行计划看，出现了子查询（SUBQUERY），但是，子查询被“>=
”操作符限制，而子查询中的被查询列a2上存在唯一索引，所以可以利用索引求最值，所以MySQL支持“
示例六，MySQL支持对SOME类型的子查询的优化：
使用了“>SOME”式子的子查询被优化，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 >SOME (SELECT a2 FROM t2 WHERE t2.a2>10);
+----+-------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+-------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | SUBQUERY | t2 | ALL | NULL | Using where | +----+-------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.05 sec)被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where((`test`.`t1`.`a1` > ( /* select#2 */ select min(`test`.`t2`.`a2`) from `test`.`t2` where (`test`.`t2`.`a2` > 10) ))) 从查询执行计划看，出现了子查询（SUBQUERY），但是，子查询被“min”函数限制，而子查询中的被查询列a2上存在唯一索引，所以可以利用索引求最值，所以MySQL支持“>SOME”式的子查询优化，子查询只被执行一次即可求得最大值。
使用了“=SOME”式子的子查询被优化，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 =SOME (SELECT a2 FROM t2 WHERE t2.a2=10);
+----+--------------+-------------+------+------+----------------------------------------------------+ | id | select_type | table | type | key | Extra | +----+--------------+-------------+------+------+----------------------------------------------------+ | 1 | SIMPLE || ALL | NULL | Using where | | 1 | SIMPLE | t1 | ALL | NULL | Using where; Using join buffer (Block Nested Loop) | | 2 | MATERIALIZED | t2 | ALL | NULL | Using where | +----+--------------+-------------+------+------+----------------------------------------------------+ 3 rows in set, 1 warning (0.01 sec) 被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` semi join (`test`.`t2`) where ((``.`a2` = 10) and (`test`.`t1`.`a1` = 10) and (`test`.`t2`.`a2` = 10)) 从查询执行计划看，没有出现了子查询，表t2被物化，与表t1进行了半连接。
使用了“<SOME”式子的子查询被优化，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 <SOME (SELECT a2 FROM t2 WHERE t2.a2=10);
+----+-------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+-------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | SUBQUERY | t2 | ALL | NULL | Using where | +----+-------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.00 sec)被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where( ( `test`.`t1`.`a1` < (/* select#2 */ select max(`test`.`t2`.`a2`) from `test`.`t2` where (`test`.`t2`.`a2` = 10) ) ) ) 从查询执行计划看，出现了子查询（SUBQUERY），但是，子查询被“max”函数限制，而子查询中的被查询列a2上存在唯一索引，所以可以利用索引求最值，所以MySQL支持“<SOME”式的子查询优化，子查询只被执行一次即可求得最大值。
示例七，MySQL支持对ANY类型的子查询的优化：
使用了“>ANY”式子的子查询被优化，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 >ANY (SELECT a2 FROM t2 WHERE t2.a2>10);
+----+-------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+-------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | SUBQUERY | t2 | ALL | NULL | Using where | +----+-------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.00 sec)被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where( ( `test`.`t1`.`a1` > (/* select#2 */ select min(`test`.`t2`.`a2`) from `test`.`t2` where (`test`.`t2`.`a2` > 10) ) ) ) 从查询执行计划看，出现了子查询（SUBQUERY），但是，子查询被“min”函数限制，而子查询中的被查询列a2上存在唯一索引，所以可以利用索引求最值，所以MySQL支持“>ANY”式的子查询优化，子查询只被执行一次即可求得最小值。
使用了“=ANY”式子的子查询被优化，查询执行计划如下：
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 =ANY (SELECT a2 FROM t2 WHERE t2.a2>10);
+----+--------------+-------------+------+------+----------------------------------------------------+ | id | select_type | table | type | key | Extra | +----+--------------+-------------+------+------+----------------------------------------------------+ | 1 | SIMPLE || ALL | NULL | NULL | | 1 | SIMPLE | t1 | ALL | NULL | Using where; Using join buffer (Block Nested Loop) | | 2 | MATERIALIZED | t2 | ALL | NULL | Using where | +----+--------------+-------------+------+------+----------------------------------------------------+ 3 rows in set, 1 warning (0.02 sec) 被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` semi join (`test`.`t2`) where ((`test`.`t1`.`a1` = ``.`a2`) and (`test`.`t2`.`a2` > 10)) 从查询执行计划看，没有出现了子查询，表t2被物化，与表t1进行了半连接。
使用了“
mysql> EXPLAIN EXTENDED SELECT * FROM t1 WHERE t1.a1 10);
+----+-------------+-------+------+------+-------------+ | id | select_type | table | type | key | Extra | +----+-------------+-------+------+------+-------------+ | 1 | PRIMARY | t1 | ALL | NULL | Using where | | 2 | SUBQUERY | t2 | ALL | NULL | Using where | +----+-------------+-------+------+------+-------------+ 2 rows in set, 1 warning (0.00 sec)被查询优化器处理后的语句为：
/* select#1 */ select `test`.`t1`.`id1` AS `id1`,`test`.`t1`.`a1` AS `a1`, `test`.`t1`.`b1` AS `b1` from `test`.`t1` where( ( `test`.`t1`.`a1` < (/* select#2 */ select max(`test`.`t2`.`a2`) from `test`.`t2` where (`test`.`t2`.`a2` > 10) ) ) ) 从查询执行计划看，出现了子查询（SUBQUERY），但是，子查询被“max”函数限制，而子查询中的被查询列a2上存在唯一索引，所以可以利用索引求最值，所以MySQL支持“<ANY”式的子查询优化，子查询只被执行一次即可求得最大值。
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