MySQL explain详解

Explain简介

本文主要讲述如何通过 explain 命令获取 select 语句的执行计划,通过 explain 我们可以知道以下信息:表的读取顺序,数据读取操作的类型,哪些索引可以使用,哪些索引实际使用了,表之间的引用,每张表有多少行被优化器查询等信息。

下面是使用 explain 的例子: 

在 select 语句之前增加 explain 关键字,MySQL 会在查询上设置一个标记,执行查询时,会返回执行计划的信息,而不是执行这条SQL(如果 from 中包含子查询,仍会执行该子查询,将结果放入临时表中)。

mysql> explain select * from actor;
+----+-------------+-------+------+---------------+------+---------+------+------+-------+
| id | select_type | table | type | possible_keys | key  | key_len | ref  | rows | Extra |
+----+-------------+-------+------+---------------+------+---------+------+------+-------+
|  1 | SIMPLE      | actor | ALL  | NULL          | NULL | NULL    | NULL |    2 | NULL  |
+----+-------------+-------+------+---------------+------+---------+------+------+-------+

在查询中的每个表会输出一行,如果有两个表通过 join 连接查询,那么会输出两行。表的意义相当广泛:可以是子查询、一个 union 结果等。

explain 有两个变种:

1)explain extended:会在 explain  的基础上额外提供一些查询优化的信息。紧随其后通过 show warnings 命令可以得到优化后的查询语句,从而看出优化器优化了什么。额外还有 filtered 列,是一个半分比的值,rows * filtered/100 可以估算出将要和 explain 中前一个表进行连接的行数(前一个表指 explain 中的id值比当前表id值小的表)。

mysql> explain extended select * from film where id = 1;
+----+-------------+-------+-------+---------------+---------+---------+-------+------+----------+-------+
| id | select_type | table | type  | possible_keys | key     | key_len | ref   | rows | filtered | Extra |
+----+-------------+-------+-------+---------------+---------+---------+-------+------+----------+-------+
|  1 | SIMPLE      | film  | const | PRIMARY       | PRIMARY | 4       | const |    1 |   100.00 | NULL  |
+----+-------------+-------+-------+---------------+---------+---------+-------+------+----------+-------+

mysql> show warnings;
+-------+------+--------------------------------------------------------------------------------+
| Level | Code | Message                                                                        |
+-------+------+--------------------------------------------------------------------------------+
| Note  | 1003 | /* select#1 */ select '1' AS `id`,'film1' AS `name` from `test`.`film` where 1 |
+-------+------+--------------------------------------------------------------------------------+

2)explain partitions:相比 explain 多了个 partitions 字段,如果查询是基于分区表的话,会显示查询将访问的分区。

explain 中的列

接下来我们将展示 explain 中每个列的信息。

1. id列

   id列的编号是 select 的序列号,有几个 select 就有几个id,并且id的顺序是按 select 出现的顺序增长的。MySQL将 select 查询分为简单查询和复杂查询。复杂查询分为三类:简单子查询、派生表(from语句中的子查询)、union 查询。

   1)简单子查询

mysql> explain select (select 1 from actor limit 1) from film;
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+
| id | select_type | table | type  | possible_keys | key      | key_len | ref  | rows | Extra       |
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+
|  1 | PRIMARY     | film  | index | NULL          | idx_name | 32      | NULL |    1 | Using index |
|  2 | SUBQUERY    | actor | index | NULL          | PRIMARY  | 4       | NULL |    2 | Using index |
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+

   2)from子句中的子查询

mysql> explain select id from (select id from film) as der;
+----+-------------+------------+-------+---------------+----------+---------+------+------+-------------+
| id | select_type | table      | type  | possible_keys | key      | key_len | ref  | rows | Extra       |
+----+-------------+------------+-------+---------------+----------+---------+------+------+-------------+
|  1 | PRIMARY     | <derived2> | ALL   | NULL          | NULL     | NULL    | NULL |    2 | NULL        |
|  2 | DERIVED     | film       | index | NULL          | idx_name | 32      | NULL |    1 | Using index |
+----+-------------+------------+-------+---------------+----------+---------+------+------+-------------+

    这个查询执行时有个临时表别名为der,外部 select 查询引用了这个临时表

   3)union查询

mysql> explain select 1 union all select 1;
+----+--------------+------------+------+---------------+------+---------+------+------+-----------------+
| id | select_type  | table      | type | possible_keys | key  | key_len | ref  | rows | Extra           |
+----+--------------+------------+------+---------------+------+---------+------+------+-----------------+
|  1 | PRIMARY      | NULL       | NULL | NULL          | NULL | NULL    | NULL | NULL | No tables used  |
|  2 | UNION        | NULL       | NULL | NULL          | NULL | NULL    | NULL | NULL | No tables used  |
| NULL | UNION RESULT | <union1,2> | ALL  | NULL          | NULL | NULL    | NULL | NULL | Using temporary |
+----+--------------+------------+------+---------------+------+---------+------+------+-----------------+

    union结果总是放在一个匿名临时表中,临时表不在SQL总出现,因此它的id是NULL。

2. select_type列

    select_type 表示对应行是是简单还是复杂的查询,如果是复杂的查询,又是上述三种复杂查询中的哪一种。

    1)simple:简单查询。查询不包含子查询和union

mysql> explain select * from film where id = 2;
+----+-------------+-------+-------+---------------+---------+---------+-------+------+-------+
| id | select_type | table | type  | possible_keys | key     | key_len | ref   | rows | Extra |
+----+-------------+-------+-------+---------------+---------+---------+-------+------+-------+
|  1 | SIMPLE      | film  | const | PRIMARY       | PRIMARY | 4       | const |    1 | NULL  |
+----+-------------+-------+-------+---------------+---------+---------+-------+------+-------+

    2)primary:复杂查询中最外层的 select

    3)subquery:包含在 select 中的子查询(不在 from 子句中)

    4)derived:包含在 from 子句中的子查询。MySQL会将结果存放在一个临时表中,也称为派生表(derived的英文含义)

    用这个例子来了解 primary、subquery 和 derived 类型

mysql> explain select (select 1 from actor where id = 1) from (select * from film where id = 1) der;
+----+-------------+------------+--------+---------------+---------+---------+-------+------+-------------+
| id | select_type | table      | type   | possible_keys | key     | key_len | ref   | rows | Extra       |
+----+-------------+------------+--------+---------------+---------+---------+-------+------+-------------+
|  1 | PRIMARY     | <derived3> | system | NULL          | NULL    | NULL    | NULL  |    1 | NULL        |
|  3 | DERIVED     | film       | const  | PRIMARY       | PRIMARY | 4       | const |    1 | NULL        |
|  2 | SUBQUERY    | actor      | const  | PRIMARY       | PRIMARY | 4       | const |    1 | Using index |
+----+-------------+------------+--------+---------------+---------+---------+-------+------+-------------+

   5)union:在 union 中的第二个和随后的 select

   6)union result:从 union 临时表检索结果的 select

   用这个例子来了解 union 和 union result 类型:

mysql> explain select 1 union all select 1;
+----+--------------+------------+------+---------------+------+---------+------+------+-----------------+
| id | select_type  | table      | type | possible_keys | key  | key_len | ref  | rows | Extra           |
+----+--------------+------------+------+---------------+------+---------+------+------+-----------------+
|  1 | PRIMARY      | NULL       | NULL | NULL          | NULL | NULL    | NULL | NULL | No tables used  |
|  2 | UNION        | NULL       | NULL | NULL          | NULL | NULL    | NULL | NULL | No tables used  |
| NULL | UNION RESULT | <union1,2> | ALL  | NULL          | NULL | NULL    | NULL | NULL | Using temporary |
+----+--------------+------------+------+---------------+------+---------+------+------+-----------------+

3. table列

   这一列表示 explain 的一行正在访问哪个表。

   当 from 子句中有子查询时,table列是 <derivenN> 格式,表示当前查询依赖 id=N 的查询,于是先执行 id=N 的查询。

   当有 union 时,UNION RESULT 的 table 列的值为 <union1,2>,1和2表示参与 union 的 select 行id。

4. type列

   这一列表示关联类型或访问类型,即MySQL决定如何查找表中的行。

   依次从最优到最差分别为:system > const > eq_ref > ref > fulltext > ref_or_null > index_merge > unique_subquery > index_subquery > range > index > ALL

   NULL:mysql能够在优化阶段分解查询语句,在执行阶段用不着再访问表或索引。

   例如:在索引列中选取最小值,可以单独查找索引来完成,不需要在执行时访问表

mysql> explain select min(id) from film;
+----+-------------+-------+------+---------------+------+---------+------+------+------------------------------+
| id | select_type | table | type | possible_keys | key  | key_len | ref  | rows | Extra                        |
+----+-------------+-------+------+---------------+------+---------+------+------+------------------------------+
|  1 | SIMPLE      | NULL  | NULL | NULL          | NULL | NULL    | NULL | NULL | Select tables optimized away |
+----+-------------+-------+------+---------------+------+---------+------+------+------------------------------+

  const, system:mysql能对查询的某部分进行优化并将其转化成一个常量(可以看show warnings 的结果)。用于 primary key 或 unique key 的所有列与常数比较时,所以表最多有一个匹配行,读取1次,速度比较快。

mysql> explain extended select * from (select * from film where id = 1) tmp;
+----+-------------+------------+--------+---------------+---------+---------+-------+------+----------+-------+
| id | select_type | table      | type   | possible_keys | key     | key_len | ref   | rows | filtered | Extra |
+----+-------------+------------+--------+---------------+---------+---------+-------+------+----------+-------+
|  1 | PRIMARY     | <derived2> | system | NULL          | NULL    | NULL    | NULL  |    1 |   100.00 | NULL  |
|  2 | DERIVED     | film       | const  | PRIMARY       | PRIMARY | 4       | const |    1 |   100.00 | NULL  |
+----+-------------+------------+--------+---------------+---------+---------+-------+------+----------+-------+

mysql> show warnings;
+-------+------+---------------------------------------------------------------+
| Level | Code | Message                                                       |
+-------+------+---------------------------------------------------------------+
| Note  | 1003 | /* select#1 */ select '1' AS `id`,'film1' AS `name` from dual |
+-------+------+---------------------------------------------------------------+

   eq_ref:primary key 或 unique key 索引的所有部分被连接使用 ,最多只会返回一条符合条件的记录。这可能是在 const 之外最好的联接类型了,简单的 select 查询不会出现这种 type。

mysql> explain select * from film_actor left join film on film_actor.film_id = film.id;
+----+-------------+------------+--------+---------------+-------------------+---------+-------------------------+------+-------------+
| id | select_type | table      | type   | possible_keys | key               | key_len | ref                     | rows | Extra       |
+----+-------------+------------+--------+---------------+-------------------+---------+-------------------------+------+-------------+
|  1 | SIMPLE      | film_actor | index  | NULL          | idx_film_actor_id | 8       | NULL                    |    3 | Using index |
|  1 | SIMPLE      | film       | eq_ref | PRIMARY       | PRIMARY           | 4       | test.film_actor.film_id |    1 | NULL        |
+----+-------------+------------+--------+---------------+-------------------+---------+-------------------------+------+-------------+

   ref:相比 eq_ref,不使用唯一索引,而是使用普通索引或者唯一性索引的部分前缀,索引要和某个值相比较,可能会找到多个符合条件的行。

1. 简单 select 查询,name是普通索引(非唯一索引)
mysql> explain select * from film where name = "film1";
+----+-------------+-------+------+---------------+----------+---------+-------+------+--------------------------+
| id | select_type | table | type | possible_keys | key      | key_len | ref   | rows | Extra                    |
+----+-------------+-------+------+---------------+----------+---------+-------+------+--------------------------+
|  1 | SIMPLE      | film  | ref  | idx_name      | idx_name | 33      | const |    1 | Using where; Using index |
+----+-------------+-------+------+---------------+----------+---------+-------+------+--------------------------+

2.关联表查询,idx_film_actor_id是film_id和actor_id的联合索引,这里使用到了film_actor的左边前缀film_id部分。
mysql> explain select * from film left join film_actor on film.id = film_actor.film_id;
+----+-------------+------------+-------+-------------------+-------------------+---------+--------------+------+-------------+
| id | select_type | table      | type  | possible_keys     | key               | key_len | ref          | rows | Extra       |
+----+-------------+------------+-------+-------------------+-------------------+---------+--------------+------+-------------+
|  1 | SIMPLE      | film       | index | NULL              | idx_name          | 33      | NULL         |    3 | Using index |
|  1 | SIMPLE      | film_actor | ref   | idx_film_actor_id | idx_film_actor_id | 4       | test.film.id |    1 | Using index |
+----+-------------+------------+-------+-------------------+-------------------+---------+--------------+------+-------------+

   ref_or_null:类似ref,但是可以搜索值为NULL的行。

mysql> explain select * from film where name = "film1" or name is null;
+----+-------------+-------+-------------+---------------+----------+---------+-------+------+--------------------------+
| id | select_type | table | type        | possible_keys | key      | key_len | ref   | rows | Extra                    |
+----+-------------+-------+-------------+---------------+----------+---------+-------+------+--------------------------+
|  1 | SIMPLE      | film  | ref_or_null | idx_name      | idx_name | 33      | const |    2 | Using where; Using index |
+----+-------------+-------+-------------+---------------+----------+---------+-------+------+--------------------------+

   index_merge:表示使用了索引合并的优化方法。 

      例如下表:id是主键,tenant_id是普通索引。or 的时候没有用 primary key,而是使用了 primary key(id) 和 tenant_id 索引

mysql> explain select * from role where id = 11011 or tenant_id = 8888;
+----+-------------+-------+-------------+-----------------------+-----------------------+---------+------+------+-------------------------------------------------+
| id | select_type | table | type        | possible_keys         | key                   | key_len | ref  | rows | Extra                                           |
+----+-------------+-------+-------------+-----------------------+-----------------------+---------+------+------+-------------------------------------------------+
|  1 | SIMPLE      | role  | index_merge | PRIMARY,idx_tenant_id | PRIMARY,idx_tenant_id | 4,4     | NULL |  134 | Using union(PRIMARY,idx_tenant_id); Using where |
+----+-------------+-------+-------------+-----------------------+-----------------------+---------+------+------+-------------------------------------------------+

   range:范围扫描通常出现在 in(), between ,> ,<, >= 等操作中。使用一个索引来检索给定范围的行。

mysql> explain select * from actor where id > 1;
+----+-------------+-------+-------+---------------+---------+---------+------+------+-------------+
| id | select_type | table | type  | possible_keys | key     | key_len | ref  | rows | Extra       |
+----+-------------+-------+-------+---------------+---------+---------+------+------+-------------+
|  1 | SIMPLE      | actor | range | PRIMARY       | PRIMARY | 4       | NULL |    2 | Using where |
+----+-------------+-------+-------+---------------+---------+---------+------+------+-------------+

   index:和ALL一样,不同就是mysql只需扫描索引树,这通常比ALL快一些。

mysql> explain select count(*) from film;
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+
| id | select_type | table | type  | possible_keys | key      | key_len | ref  | rows | Extra       |
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+
|  1 | SIMPLE      | film  | index | NULL          | idx_name | 33      | NULL |    3 | Using index |
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+

   ALL即全表扫描,意味着mysql需要从头到尾去查找所需要的行。通常情况下这需要增加索引来进行优化了

mysql> explain select * from actor;
+----+-------------+-------+------+---------------+------+---------+------+------+-------+
| id | select_type | table | type | possible_keys | key  | key_len | ref  | rows | Extra |
+----+-------------+-------+------+---------------+------+---------+------+------+-------+
|  1 | SIMPLE      | actor | ALL  | NULL          | NULL | NULL    | NULL |    2 | NULL  |
+----+-------------+-------+------+---------------+------+---------+------+------+-------+

5. possible_keys列

    这一列显示查询可能使用哪些索引来查找。 

    explain 时可能出现 possible_keys 有列,而 key 显示 NULL 的情况,这种情况是因为表中数据不多,mysql认为索引对此查询帮助不大,选择了全表查询。 

    如果该列是NULL,则没有相关的索引。在这种情况下,可以通过检查 where 子句看是否可以创造一个适当的索引来提高查询性能,然后用 explain 查看效果。

6. key列

    这一列显示mysql实际采用哪个索引来优化对该表的访问。

    如果没有使用索引,则该列是 NULL。如果想强制mysql使用或忽视possible_keys列中的索引,在查询中使用 force index、ignore index。

7. key_len列

    这一列显示了mysql在索引里使用的字节数,通过这个值可以算出具体使用了索引中的哪些列。 

    举例来说,film_actor的联合索引 idx_film_actor_id 由 film_id 和 actor_id 两个int列组成,并且每个int是4字节。通过结果中的key_len=4可推断出查询使用了第一个列:film_id列来执行索引查找。

mysql> explain select * from film_actor where film_id = 2;
+----+-------------+------------+------+-------------------+-------------------+---------+-------+------+-------------+
| id | select_type | table      | type | possible_keys     | key               | key_len | ref   | rows | Extra       |
+----+-------------+------------+------+-------------------+-------------------+---------+-------+------+-------------+
|  1 | SIMPLE      | film_actor | ref  | idx_film_actor_id | idx_film_actor_id | 4       | const |    1 | Using index |
+----+-------------+------------+------+-------------------+-------------------+---------+-------+------+-------------+

   key_len计算规则如下:

  • 字符串
    • char(n):n字节长度
    • varchar(n):2字节存储字符串长度,如果是utf-8,则长度 3n + 2
  • 数值类型
    • tinyint:1字节
    • smallint:2字节
    • int:4字节
    • bigint:8字节  
  • 时间类型 
    • date:3字节
    • timestamp:4字节
    • datetime:8字节
  • 如果字段允许为 NULL,需要1字节记录是否为 NULL

   索引最大长度是768字节,当字符串过长时,mysql会做一个类似左前缀索引的处理,将前半部分的字符提取出来做索引。

 8. ref列

     这一列显示了在key列记录的索引中,表查找值所用到的列或常量,常见的有:const(常量),func,NULL,字段名(例:film.id)

 9. rows列

     这一列是mysql估计要读取并检测的行数,注意这个不是结果集里的行数。

 10. Extra列

     这一列展示的是额外信息。常见的重要值如下: 

   distinct: 一旦mysql找到了与行相联合匹配的行,就不再搜索了

mysql> explain select distinct name from film left join film_actor on film.id = film_actor.film_id;
+----+-------------+------------+-------+-------------------+-------------------+---------+--------------+------+------------------------------+
| id | select_type | table      | type  | possible_keys     | key               | key_len | ref          | rows | Extra                        |
+----+-------------+------------+-------+-------------------+-------------------+---------+--------------+------+------------------------------+
|  1 | SIMPLE      | film       | index | idx_name          | idx_name          | 33      | NULL         |    3 | Using index; Using temporary |
|  1 | SIMPLE      | film_actor | ref   | idx_film_actor_id | idx_film_actor_id | 4       | test.film.id |    1 | Using index; Distinct        |
+----+-------------+------------+-------+-------------------+-------------------+---------+--------------+------+------------------------------+

   Using index:这发生在对表的请求列都是同一索引的部分的时候,返回的列数据只使用了索引中的信息,而没有再去访问表中的行记录。是性能高的表现。

mysql> explain select id from film order by id;
+----+-------------+-------+-------+---------------+---------+---------+------+------+-------------+
| id | select_type | table | type  | possible_keys | key     | key_len | ref  | rows | Extra       |
+----+-------------+-------+-------+---------------+---------+---------+------+------+-------------+
|  1 | SIMPLE      | film  | index | NULL          | PRIMARY | 4       | NULL |    3 | Using index |
+----+-------------+-------+-------+---------------+---------+---------+------+------+-------------+

   Using where:mysql服务器将在存储引擎检索行后再进行过滤。就是先读取整行数据,再按 where 条件进行检查,符合就留下,不符合就丢弃。

mysql> explain select * from film where id > 1;
+----+-------------+-------+-------+---------------+----------+---------+------+------+--------------------------+
| id | select_type | table | type  | possible_keys | key      | key_len | ref  | rows | Extra                    |
+----+-------------+-------+-------+---------------+----------+---------+------+------+--------------------------+
|  1 | SIMPLE      | film  | index | PRIMARY       | idx_name | 33      | NULL |    3 | Using where; Using index |
+----+-------------+-------+-------+---------------+----------+---------+------+------+--------------------------+

    Using temporary:mysql需要创建一张临时表来处理查询。出现这种情况一般是要进行优化的,首先是想到用索引来优化。

1. actor.name没有索引,此时创建了张临时表来distinct
mysql> explain select distinct name from actor;
+----+-------------+-------+------+---------------+------+---------+------+------+-----------------+
| id | select_type | table | type | possible_keys | key  | key_len | ref  | rows | Extra           |
+----+-------------+-------+------+---------------+------+---------+------+------+-----------------+
|  1 | SIMPLE      | actor | ALL  | NULL          | NULL | NULL    | NULL |    2 | Using temporary |
+----+-------------+-------+------+---------------+------+---------+------+------+-----------------+

2. film.name建立了idx_name索引,此时查询时extra是using index,没有用临时表
mysql> explain select distinct name from film;
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+
| id | select_type | table | type  | possible_keys | key      | key_len | ref  | rows | Extra       |
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+
|  1 | SIMPLE      | film  | index | idx_name      | idx_name | 33      | NULL |    3 | Using index |
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+

   Using filesort:mysql 会对结果使用一个外部索引排序,而不是按索引次序从表里读取行。此时mysql会根据联接类型浏览所有符合条件的记录,并保存排序关键字和行指针,然后排序关键字并按顺序检索行信息。这种情况下一般也是要考虑使用索引来优化的。

1. actor.name未创建索引,会浏览actor整个表,保存排序关键字name和对应的id,然后排序name并检索行记录
mysql> explain select * from actor order by name;
+----+-------------+-------+------+---------------+------+---------+------+------+----------------+
| id | select_type | table | type | possible_keys | key  | key_len | ref  | rows | Extra          |
+----+-------------+-------+------+---------------+------+---------+------+------+----------------+
|  1 | SIMPLE      | actor | ALL  | NULL          | NULL | NULL    | NULL |    2 | Using filesort |
+----+-------------+-------+------+---------------+------+---------+------+------+----------------+

2. film.name建立了idx_name索引,此时查询时extra是using index
mysql> explain select * from film order by name;
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+
| id | select_type | table | type  | possible_keys | key      | key_len | ref  | rows | Extra       |
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+
|  1 | SIMPLE      | film  | index | NULL          | idx_name | 33      | NULL |    3 | Using index |
+----+-------------+-------+-------+---------------+----------+---------+------+------+-------------+

使用的表

DROP TABLE IF EXISTS `actor`;
CREATE TABLE `actor` (
  `id` int(11) NOT NULL,
  `name` varchar(45) DEFAULT NULL,
  `update_time` datetime DEFAULT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

INSERT INTO `actor` (`id`, `name`, `update_time`) VALUES (1,'a','2017-12-22 15:27:18'), (2,'b','2017-12-22 15:27:18'), (3,'c','2017-12-22 15:27:18');

DROP TABLE IF EXISTS `film`;
CREATE TABLE `film` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `name` varchar(10) DEFAULT NULL,
  PRIMARY KEY (`id`),
  KEY `idx_name` (`name`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

INSERT INTO `film` (`id`, `name`) VALUES (3,'film0'),(1,'film1'),(2,'film2');

DROP TABLE IF EXISTS `film_actor`;
CREATE TABLE `film_actor` (
  `id` int(11) NOT NULL,
  `film_id` int(11) NOT NULL,
  `actor_id` int(11) NOT NULL,
  PRIMARY KEY (`id`),
  KEY `idx_film_actor_id` (`film_id`,`actor_id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

INSERT INTO `film_actor` (`id`, `film_id`, `actor_id`) VALUES (1,1,1),(2,1,2),(3,2,1);

 

posted @ 2019-07-17 19:02  龙福  阅读(389)  评论(0编辑  收藏  举报