MySQL InnoDB 锁 - For Update 加锁分析:

1. InnoDB锁 简单介绍

2. 当前读加锁分析:REPEATABLE-READ 可重复读、READ-COMMITTED 读已提交

3. 锁模式说明及8.0的data_locks表

一、InnoDB锁

1、全局锁

全局读锁,flush tables with read lock,整库处于只读状态。全局锁的一个典型场景:全库逻辑备份,--single-transaction实现一致性读。

2、表级锁

表锁,lock tables…read/write,主动在表上加读锁或写锁;

元数据锁(meta data lock,MDL),访问表时自动加上,防止DDL和DML并发的冲突,保证读写正确性;

自增锁,表中auto_increment字段的自增值生成控制,内存自增计数器,8.0之后通过redo进行持久化;

意向锁,只会和表级锁发生冲突,不会阻止除表锁请求之外的锁,表明有事务即将、或正锁定某N行;

  1. 意向共享锁(IS):SELECT ... LOCK IN SHARE MODE,在对应记录行上加锁之前,在表上加意向共享锁;

  2. 意向排它锁(IX):SELECT .. FOR UPDATE,悲观锁,对表所有扫描过的行都会被加上意向排它锁,若扫描行其中有行锁,则会被阻塞;对SELECT索引加排它锁,阻塞其他事务修改或SELECT ... FOR SHARE(在8.0新增的方式);

3、行锁

行锁,事务锁,只有发生行锁冲突,才会出现事务锁的排队等待。

两阶段锁协议:行锁在需要时加上,事务结束时释放。

行锁的3种算法:record lock、gap lock、next-key lock

  1. 记录锁 record lock:添加在索引上,表中没有索引时会默认添加在默认创建的聚集索引上;

  2. 间隙锁 gap lock:锁定一个范围,可重复读 隔离级别下,行锁会变成gap锁(范围锁),降低并发性,当前读(dml、select for update),若where条件列上有索引,加gap lock在索引上,实现可重复读;

  3. Next-Key Lock:Gap Lock+Record Lock,锁定一个范围,并且锁定记录本身;

    ① 唯一索引或主键,Next-Key Lock 降为 Record Lock,即仅锁住索引本身,而不是范围。

    ② 辅助索引(二级索引),默认使用Next-Key Locking加锁,锁定范围是前一个索引到后一个索引之间范围,左开右闭。

### session 1
root@test 15:51 > begin; root@test 15:51 > show create table student;
+---------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Table | Create Table |
+---------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| student | CREATE TABLE `student` (
`id` int(11) NOT NULL AUTO_INCREMENT,
`name` varchar(20) DEFAULT NULL,
`birthday` datetime DEFAULT NULL,
PRIMARY KEY (`id`),
KEY `ix_name` (`name`),
KEY `ix_birthday` (`birthday`)
) ENGINE=InnoDB AUTO_INCREMENT=7 DEFAULT CHARSET=utf8 |
+---------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ root@test 15:52 > select * from student;
+----+-------+---------------------+
| id | name | birthday |
+----+-------+---------------------+
| 1 | abcd | 1995-06-27 00:00:00 |
| 2 | abef | 1995-01-24 00:00:00 |
| 3 | abg | 1995-07-26 00:00:00 |
| 4 | cdmn | 1995-06-13 00:00:00 |
+----+-------+---------------------+ root@test 15:52 > select * from student where birthday > '1995-06-27 00:00:00' and birthday < '1995-07-26 00:00:00' for update;
Empty set (0.02 sec) ### session 2
root@test 15:51 > begin; # 左开
root@test 15:54 > update student set name = 'abcd' where birthday = "1995-06-27 00:00:00"; # 右闭(阻塞更新)
root@test 15:55 > update student set name = 'abg' where birthday = '1995-07-26 00:00:00';
ERROR 1205 (HY000): Lock wait timeout exceeded; try restarting transaction

二、当前读加锁分析

分析不同隔离级别,当前读(dml、select … for update)的加锁情况

1、REPEATABLE-READ 可重复读

root@test 15:06 > show global variables like "%iso%";
+-----------------------+-----------------+
| Variable_name | Value |
+-----------------------+-----------------+
| transaction_isolation | REPEATABLE-READ |
| tx_isolation | REPEATABLE-READ |
+-----------------------+-----------------+
1.1、表无显式主键和索引
root@test 15:30 > show create table t_student;
+-----------+----------------------------------------------------------------------------------------------------------------------------+
| Table | Create Table |
+-----------+----------------------------------------------------------------------------------------------------------------------------+
| t_student | CREATE TABLE `t_student` (
`id` int(11) NOT NULL,
`name` varchar(10) DEFAULT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8 |
+-----------+----------------------------------------------------------------------------------------------------------------------------+ root@test 15:30 > begin; root@test 15:31 > select * from t_student for update;
+----+-------+
| id | name |
+----+-------+
| 1 | jack |
| 2 | kuzma |
| 3 | linda |
+----+-------+

如上,可重复读,表上没有主键(会自动生成隐式主键聚集组织表),也没有索引,全表SELECT的当前读的加锁情况:

  ① 对表添加 IX 锁

  ② 在"supremum"上添加 Next-Key Lock(supremum表示高于表中任何一个索引的值),即最大索引值之后的间隙锁住

  ③ 在三条记录上分别添加 Next-Key Lock

root@test 16:08 > begin;

# where上带条件 id = 3
root@test 16:08 > select * from t_student where id = 3 for update;
+----+-------+
| id | name |
+----+-------+
| 3 | linda |
+----+-------+ root@test 16:09 > show engine innodb status\G
# 锁信息如上,表上IX,supremum 和 三条记录上添加 Next-Key Lock # 另开一个session
root@test 16:09 > begin; root@test 16:13 > insert into t_student values(2,"tom");
ERROR 1205 (HY000): Lock wait timeout exceeded; try restarting transaction
root@test 16:15 > insert into t_student values(4,"tom");
ERROR 1205 (HY000): Lock wait timeout exceeded; try restarting transaction

如上,insert为什么会被阻塞呢?delete呢?update呢?

每次插入记录时,所生成的聚集索引(DB_ROW_ID)是自增的,每次都会在表的最后插入,因此就有可能插入id=10这条记录,所以需要添加"supremum pseudo-record"防止数据插入。

---TRANSACTION 582122, ACTIVE 3874 sec inserting
mysql tables in use 1, locked 1
LOCK WAIT 2 lock struct(s), heap size 1136, 6 row lock(s)
MySQL thread id 12529, OS thread handle 123145486712832, query id 94463 localhost root update
insert into t_student values(5,"tom")
Trx read view will not see trx with id >= 582123, sees < 582121
------- TRX HAS BEEN WAITING 3 SEC FOR THIS LOCK TO BE GRANTED:
RECORD LOCKS space id 168 page no 3 n bits 72 index GEN_CLUST_INDEX of table `test`.`t_student` trx id 582122 lock_mode X insert intention waiting
Record lock, heap no 1 PHYSICAL RECORD: n_fields 1; compact format; info bits 0
0: len 8; hex 73757072656d756d; asc supremum;; ------------------
TABLE LOCK table `test`.`t_student` trx id 582122 lock mode IX
RECORD LOCKS space id 168 page no 3 n bits 72 index GEN_CLUST_INDEX of table `test`.`t_student` trx id 582122 lock_mode X insert intention waiting
Record lock, heap no 1 PHYSICAL RECORD: n_fields 1; compact format; info bits 0
0: len 8; hex 73757072656d756d; asc supremum;;

即使是不满足where条件的记录上,也会添加Next-Key Lock,目的是为了防止幻读。因此的,其他会话事务执行delete或者update都会造成幻读,也就被阻塞的。

---TRANSACTION 582122, ACTIVE 3788 sec starting index read
mysql tables in use 1, locked 1
LOCK WAIT 2 lock struct(s), heap size 1136, 5 row lock(s)
MySQL thread id 12529, OS thread handle 123145486712832, query id 94461 localhost root updating
update t_student set name = "linda" where id = 3
Trx read view will not see trx with id >= 582123, sees < 582121
------- TRX HAS BEEN WAITING 14 SEC FOR THIS LOCK TO BE GRANTED:
RECORD LOCKS space id 168 page no 3 n bits 72 index GEN_CLUST_INDEX of table `test`.`t_student` trx id 582122 lock_mode X waiting
Record lock, heap no 2 PHYSICAL RECORD: n_fields 5; compact format; info bits 0
0: len 6; hex 00000000090a; asc ;;
1: len 6; hex 00000008e1c8; asc ;;
2: len 7; hex f4000001e40110; asc ;;
3: len 4; hex 80000001; asc ;;
4: len 4; hex 6a61636b; asc jack;; ------------------
TABLE LOCK table `test`.`t_student` trx id 582122 lock mode IX
RECORD LOCKS space id 168 page no 3 n bits 72 index GEN_CLUST_INDEX of table `test`.`t_student` trx id 582122 lock_mode X waiting
Record lock, heap no 2 PHYSICAL RECORD: n_fields 5; compact format; info bits 0
0: len 6; hex 00000000090a; asc ;;
1: len 6; hex 00000008e1c8; asc ;;
2: len 7; hex f4000001e40110; asc ;;
3: len 4; hex 80000001; asc ;;
4: len 4; hex 6a61636b; asc jack;;
1.2、表有显式主键无索引
  1. 不带where条件,表上IX,主键最大索引值之后的间隙锁住,表所有记录对应主键加上记录锁

  2. where条件是主键,表上IX,主键添加记录锁(X,REC_NOT_GAP),并且只锁住条件记录,因为主键保证唯一,不需要间隙锁

---TRANSACTION 582139, ACTIVE 12 sec
2 lock struct(s), heap size 1136, 1 row lock(s)
MySQL thread id 12528, OS thread handle 123145486434304, query id 94472 localhost root
TABLE LOCK table `test`.`t_student` trx id 582139 lock mode IX
RECORD LOCKS space id 169 page no 3 n bits 72 index PRIMARY of table `test`.`t_student` trx id 582139 lock_mode X locks rec but not gap
Record lock, heap no 3 PHYSICAL RECORD: n_fields 4; compact format; info bits 0
0: len 4; hex 80000002; asc ;;
1: len 6; hex 00000008e1c8; asc ;;
2: len 7; hex f4000001e4011f; asc ;;
3: len 5; hex 6b757a6d61; asc kuzma;;
1.3、表无显式主键有索引
  1. 不带where条件,表上IX,id最大索引值之后的间隙锁住,表所有记录对应索引加上记录锁

  2. where条件是普通索引字段

root@test 22:01 > show create table t_student;
+-----------+--------------------------------------------------------------------------------------------------------------------------------------------------+
| Table | Create Table |
+-----------+--------------------------------------------------------------------------------------------------------------------------------------------------+
| t_student | CREATE TABLE `t_student` (
`id` int(11) NOT NULL,
`name` varchar(10) DEFAULT NULL,
KEY `ix_id` (`id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8 |
+-----------+--------------------------------------------------------------------------------------------------------------------------------------------------+ root@test 22:10 > begin; root@test 22:11 > select * from t_student where id = 2 for update;
+----+-------+
| id | name |
+----+-------+
| 2 | kuzma |
+----+-------+ root@test 22:11 > show engine innodb status\G
---TRANSACTION 582176, ACTIVE 14 sec
4 lock struct(s), heap size 1136, 3 row lock(s)
MySQL thread id 12534, OS thread handle 123145487269888, query id 94485 localhost root
TABLE LOCK table `test`.`t_student` trx id 582176 lock mode IX
RECORD LOCKS space id 170 page no 4 n bits 72 index ix_id of table `test`.`t_student` trx id 582176 lock_mode X
Record lock, heap no 3 PHYSICAL RECORD: n_fields 2; compact format; info bits 0
0: len 4; hex 80000002; asc ;;
1: len 6; hex 000000000912; asc ;; RECORD LOCKS space id 170 page no 3 n bits 72 index GEN_CLUST_INDEX of table `test`.`t_student` trx id 582176 lock_mode X locks rec but not gap
Record lock, heap no 3 PHYSICAL RECORD: n_fields 5; compact format; info bits 0
0: len 6; hex 000000000912; asc ;;
1: len 6; hex 00000008e200; asc ;;
2: len 7; hex be00000146011f; asc F ;;
3: len 4; hex 80000002; asc ;;
4: len 5; hex 6b757a6d61; asc kuzma;; RECORD LOCKS space id 170 page no 4 n bits 72 index ix_id of table `test`.`t_student` trx id 582176 lock_mode X locks gap before rec
Record lock, heap no 4 PHYSICAL RECORD: n_fields 2; compact format; info bits 0
0: len 4; hex 80000003; asc ;;
1: len 6; hex 000000000913; asc ;;

如上,过滤一个普通索引时的加锁情况是:

  ① 对表添加 IX锁

  ② 对id=2对应的索引添加 Next-Key Lock锁,区间是(-∞, 2]

  ③ 对索引对应的聚集索引添加 X记录锁

  ④ 为防止幻读(因为是普通索引,可重复插入id=2的记录),对索引记录区间(2,3)添加间隙锁(lock_mode X locks gap before rec)

也就是说,(测试用例有些许不恰当)如果说放大到10~20~30测试,id直到29之间的记录插入都会被阻塞,而插入id=30因为不在间隙锁范围,不会被阻塞。

1.4、表有显式主键和索引
  1. 无where条件,如1.2.1描述

  2. 有where条件,其实,无论是主键,还是唯一键索引,只要能准确定位的,都是表上IX,主键或唯一键添加记录锁(X,REC_NOT_GAP),并且只锁住条件记录

2、READ-COMMITTED 读已提交

root@test 23:57 > show global variables like "tx_isolation";
+---------------+----------------+
| Variable_name | Value |
+---------------+----------------+
| tx_isolation | READ-COMMITTED |
+---------------+----------------+
2.1、表无显式主键和索引
root@test 23:57 > show create table t_people;
+----------+-------------------------------------------------------------------------------------------------------------------------------+
| Table | Create Table |
+----------+-------------------------------------------------------------------------------------------------------------------------------+
| t_people | CREATE TABLE `t_people` (
`id` int(11) DEFAULT NULL,
`name` varchar(10) DEFAULT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8 |
+----------+-------------------------------------------------------------------------------------------------------------------------------+ root@test 23:58 > select * from t_people;
+------+-------+
| id | name |
+------+-------+
| 1 | jack |
| 2 | kuzma |
| 3 | linda |
+------+-------+

如下,表t_people上加 IX意向排它锁,表中所有行的隐藏主键上(行格式里第三个就是隐藏主键,在表中没有显示主键的时候自动生成用于组织表数据)加 X记录锁,只锁定记录本身,非范围间隙锁。

如果带上where条件呢?

root@test 00:44 > begin;

root@test 00:45 > select * from t_people where id = 2 for update;
+------+-------+
| id | name |
+------+-------+
| 2 | kuzma |
+------+-------+ root@test 00:45 > show engine innodb status;
......
---TRANSACTION 582053, ACTIVE 4 sec
2 lock struct(s), heap size 1136, 1 row lock(s)
MySQL thread id 12521, OS thread handle 123145487269888, query id 94339 localhost root
TABLE LOCK table `test`.`t_people` trx id 582053 lock mode IX
RECORD LOCKS space id 166 page no 3 n bits 72 index GEN_CLUST_INDEX of table `test`.`t_people` trx id 582053 lock_mode X locks rec but not gap
Record lock, heap no 3 PHYSICAL RECORD: n_fields 5; compact format; info bits 0
0: len 6; hex 000000000908; asc ;;
1: len 6; hex 00000008e19e; asc ;;
2: len 7; hex d2000001580110; asc X ;;
3: len 4; hex 80000002; asc ;;
4: len 5; hex 6b757a6d61; asc kuzma;;
......
# 只是在 id = 2 的记录上加了X记录锁
2.2、表有显式主键无索引
  1. 不带where条件,如上的,表中所有行上加 X记录锁,不锁定范围

  2. where条件是主键字段时,对表加 IX锁,对主键添加记录锁(X, REC_NOTGAP),where了主键,主键已经保证唯一,非范围锁,锁加在具体的记录上

root@test 00:49 > show engine innodb  status;
---TRANSACTION 582071, ACTIVE 7 sec
2 lock struct(s), heap size 1136, 1 row lock(s)
MySQL thread id 12521, OS thread handle 123145487269888, query id 94353 localhost root
TABLE LOCK table `test`.`t_people` trx id 582071 lock mode IX
RECORD LOCKS space id 167 page no 3 n bits 72 index PRIMARY of table `test`.`t_people` trx id 582071 lock_mode X locks rec but not gap
Record lock, heap no 3 PHYSICAL RECORD: n_fields 4; compact format; info bits 0
0: len 4; hex 80000002; asc ;;
1: len 6; hex 00000008e19e; asc ;;
2: len 7; hex d2000001580110; asc X ;;
3: len 5; hex 6b757a6d61; asc kuzma;;
  1. where条件包含主键字段和非主键字段,和上面是一样的,因为主键已经定位了加锁。

2.3、表无显示主键有索引
  1. 不带where条件,同样的,表中所有行上加 X记录锁,不锁定范围

  2. where条件是普通索引字段,唯一索引亦如是

root@test 20:24 > show create table t_student;
+-----------+------------------------------------------------------------------------------------------------------------------------------------------------------+
| Table | Create Table |
+-----------+------------------------------------------------------------------------------------------------------------------------------------------------------+
| t_student | CREATE TABLE `t_student` (
`id` int(11) NOT NULL,
`name` varchar(10) DEFAULT NULL,
KEY `ix_name` (`name`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8 |
+-----------+------------------------------------------------------------------------------------------------------------------------------------------------------+ root@test 20:25 > begin; root@test 20:27 > select * from t_student where name = 'kuzma' for update;
+----+-------+
| id | name |
+----+-------+
| 2 | kuzma |
+----+-------+ root@test 20:27 > show engine innodb status;
---TRANSACTION 582093, ACTIVE 57 sec
3 lock struct(s), heap size 1136, 2 row lock(s)
MySQL thread id 12525, OS thread handle 123145486712832, query id 94388 localhost root
TABLE LOCK table `test`.`t_student` trx id 582093 lock mode IX
RECORD LOCKS space id 168 page no 4 n bits 72 index ix_name of table `test`.`t_student` trx id 582093 lock_mode X locks rec but not gap
Record lock, heap no 3 PHYSICAL RECORD: n_fields 2; compact format; info bits 0
0: len 5; hex 6b757a6d61; asc kuzma;;
1: len 6; hex 00000000090b; asc ;; RECORD LOCKS space id 168 page no 3 n bits 72 index GEN_CLUST_INDEX of table `test`.`t_student` trx id 582093 lock_mode X locks rec but not gap
Record lock, heap no 3 PHYSICAL RECORD: n_fields 5; compact format; info bits 0
0: len 6; hex 00000000090b; asc ;;
1: len 6; hex 00000008e1c8; asc ;;
2: len 7; hex f4000001e4011f; asc ;;
3: len 4; hex 80000002; asc ;;
4: len 5; hex 6b757a6d61; asc kuzma;;

如上,当where条件上是普通索引字段时,加锁情况如下:

  ① 表上加 IX,意向排它锁

  ② name='kuzma' 对应的索引上添加 X 记录锁

  ③ GEN_CLUST_INDEX,对应的(自动生成的)聚集索引上添加 X 记录锁

2.4、表有显式主键有索引
  1. 不带where条件,所有行记录添加记录锁,并没有间隙范围锁

  2. where条件是普通索引或主键索引,如前面的,先是表上加 IX 意向排它锁,然后在对应的普通索引上添加 X 记录锁(如果是主键则无需),最后在对应的聚集索引(主键)上添加 X 记录锁

三、锁模式说明及8.0的data_locks表

3.1、锁模式LOCK_MODE

show engine innodb status中见到的 lock_mode,如下整理说明:

锁模式 说明
IX   意向排它锁
X   Next-Key Lock锁定记录和记录之前的间隙(X)
S   Next-Key Lock锁定记录和记录之前的间隙(S)
X, REC_NOT_GAP   只锁定记录本身(X)
S, REC_NOT_GAP   只锁定记录本身(S)
X, GAP   间隙锁,不锁定记录本身(X)
S, GAP   间隙锁,不锁定记录本身(S)
X, GAP, INSERT_INTENTION   插入意向锁,间隙范围,排它

3.2、8.0的data_locks表

在8.0之前,查看锁信息可以通过设置innodb_status_output_locks=ON,然后在 show engine innodb status的输出里,看到详细的锁信息打印,如前面展示。

8.0之后,performance_schema.data_locks,新增的,记录表加锁情况,可将之前的innodb status锁信息打印更好的以表格的形式记录展示。

For Update 加锁分析的更多相关文章

  1. MySQL的并发控制与加锁分析

    本文主要是针对MySQL/InnoDB的并发控制和加锁技术做一个比较深入的剖析,并且对其中涉及到的重要的概念,如多版本并发控制(MVCC),脏读(dirty read),幻读(phantom read ...

  2. (转)mysql、innodb和加锁分析

    mysql.innodb和加锁分析 原文:https://liuzhengyang.github.io/2016/09/25/mysqlinnodb/ 介绍 本文主要介绍MySQL和InnoDB存储引 ...

  3. MySQL中一条SQL的加锁分析

    MySQL中一条SQL的加锁分析 id主键 + RC id唯一索引 + RC id非唯一索引 + RC id无索引 + RC id主键 + RR id唯一索引 + RR id非唯一索引 + RR id ...

  4. mysql InnoDB加锁分析

    文章转载自:http://www.fanyilun.me/2017/04/20/MySQL%E5%8A%A0%E9%94%81%E5%88%86%E6%9E%90/ 以下实验数据基于MySQL 5.7 ...

  5. select加锁分析(Mysql)

    [原创]惊!史上最全的select加锁分析(Mysql) 前言 大家在面试中有没遇到面试官问你下面六句Sql的区别呢 select * from table where id = ? select * ...

  6. 解决死锁之路3 - 常见 SQL 语句的加锁分析 (转)

    出处:https://www.aneasystone.com/archives/2017/12/solving-dead-locks-three.html 这篇博客将对一些常见的 SQL 语句进行加锁 ...

  7. MySQL加锁分析

    参考:MySQL 加锁处理分析.该文已经讲的很详尽了,也易懂,下面仅仅是个人做的总结. 一. 背景 1.1 隔离级别 1.2 加锁过程 逐条处理,逐条加锁. 1.3 两阶段锁2PL 1.4 gap锁 ...

  8. MyISAM加锁分析

    为什么加锁 你正在读着你喜欢的女孩递给你的信,看到一半的时候,她的好闺蜜过来瞄了一眼(假设她会隐身术,你看不到她),她想把"我很喜欢你"改成"我不喜欢你",刚把 ...

  9. 史上最全的select加锁分析(Mysql)

    引言 大家在面试中有没遇到面试官问你下面六句Sql的区别呢 select * from table where id = ? select * from table where id < ? s ...

随机推荐

  1. win10使用照片查看器查看图片

    1.关于 演示环境: win10 1909 2.习惯win7的照片查看器 如果你习惯使用win7的照片查看器在win10查看照片,可以通过下面的注册表代码实现.方法:1.创建 后缀名为 .reg的文件 ...

  2. 【LeetCode】1042. Flower Planting With No Adjacent 解题报告(Python & C++)

    作者: 负雪明烛 id: fuxuemingzhu 个人博客: http://fuxuemingzhu.cn/ 目录 题目描述 题目大意 解题方法 图 日期 题目地址:https://leetcode ...

  3. 【九度OJ】题目1064:反序数 解题报告

    [九度OJ]题目1064:反序数 解题报告 标签(空格分隔): 九度OJ 原题地址:http://ac.jobdu.com/problem.php?pid=1064 题目描述: 设N是一个四位数,它的 ...

  4. 【LeetCode】1001. Grid Illumination 解题报告(C++)

    作者: 负雪明烛 id: fuxuemingzhu 个人博客: http://fuxuemingzhu.cn/ 目录 题目描述 题目大意 解题方法 哈希 日期 题目地址:https://leetcod ...

  5. 【LeetCode】598. Range Addition II 解题报告(Python)

    作者: 负雪明烛 id: fuxuemingzhu 个人博客: http://fuxuemingzhu.cn/ 目录 题目描述 题目大意 解题方法 日期 题目地址:https://leetcode.c ...

  6. Java生成随机数的4种方式

    Random Random 类诞生于 JDK 1.0,它产生的随机数是伪随机数,也就是有规则的随机数.Random 使用的随机算法为 linear congruential pseudorandom ...

  7. 使用zTree插件实现可拖拽的树

    在目前接触到的树插件中,我觉得zTree比较简单,也容易上手.有一次业务需求是将某对象分组树上的对象可以随意拖拽,相当于改变了对象的分组,因此我用到了zTree,对其进行了一些列学习.         ...

  8. A Deep Neural Network’s Loss Surface Contains Every Low-dimensional Pattern

    目录 概 相关工作 主要内容 引理1 定理1 定理2 A Deep Neural Network's Loss Surface Contains Every Low-dimensional Patte ...

  9. [高数]高数部分-Part II 导数与微分

    Part II 导数与微分 回到总目录 Part II 导数与微分 一元函数微分的定义 一元函数定义注意点 基本求导公式 基本求导方法 复合函数求导 隐函数求导 对数求导法 反函数求导 参数方程求导 ...

  10. WinForm应用程序的开机自启、记住密码,自动登录的实现

    一.思路: 1.开机自启,自然是需要用到注册表,我们需要把程序添加到电脑的注册表中去 2.记住密码,自动登录,开机自启,在页面的呈现我们都使用复选框按钮来呈现 3.数据持久化,不能是数据库,可以是sq ...