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HomeDatabaseMysql TutorialMySQL Basics Tutorial 10 - Function Full-text Search Function

Grammar:

  • MATCH (col1,col2,...) AGAINST (expr [IN BOOLEAN MODE | WITH QUERY EXPANSION])

MySQL supports full-text indexing and search functions. The full-text index type FULLTEXT index in MySQL. FULLTEXT indexes are only available on MyISAM tables; they can be created from CHAR, VARCHAR, or TEXT columns as part of a CREATE TABLE statement, or added later using ALTER TABLE or CREATE INDEX. For larger data sets, entering your data into a table that does not have a FULLTEXT index and then creating the index is faster than entering the data into an existing FULLTEXT index.

Full text search is performed with the MATCH() function.

mysql> CREATE TABLE articles (    
->   id INT UNSIGNED AUTO_INCREMENT NOT NULL PRIMARY KEY,    
->   title VARCHAR(200),    
->   body TEXT,    
->   FULLTEXT (title,body)    
-> );Query OK, 0 rows affected (0.00 sec)

mysql> INSERT INTO articles (title,body) VALUES    
-> ('MySQL Tutorial','DBMS stands for DataBase ...'),    
-> ('How To Use MySQL Well','After you went through a ...'),    
-> ('Optimizing MySQL','In this tutorial we will show ...'),    
-> ('1001 MySQL Tricks','1. Never run mysqld as root. 2. ...'),    
-> ('MySQL vs. YourSQL','In the following database comparison ...'),    
-> ('MySQL Security','When configured properly, MySQL ...');Query OK, 6 rows affected (0.00 sec)
Records: 6  Duplicates: 0  Warnings: 0

mysql> SELECT * FROM articles    
-> WHERE MATCH (title,body) AGAINST ('database');
+----+-------------------+------------------------------------------+
| id | title             | body          |
+----+-------------------+------------------------------------------+
|  5 | MySQL vs. YourSQL | In the following database comparison ... |
|  1 | MySQL Tutorial    | DBMS stands for DataBase ...            |
+----+-------------------+------------------------------------------+
2 rows in set (0.00 sec)

The MATCH() function performs a natural language search within the database for a string. A database is a set of 1 or 2 columns contained in FULLTEXT. The search string is given as a parameter to AGAINST(). For each row in the table, MATCH() returns a correlation value, that is, a similarity measure between the search string and the text in that row in the specified column in the MATCH() table.

By default, the search is performed in a case-insensitive manner. However, you can perform a case-sensitive full-text search by using a binary sort on the indexed columns. For example, you can give a latin1_bin sorting method to a column that uses the latin1 character set, making full-text searches case-sensitive.

As in the above example, when MATCH() is used in a WHERE statement, the relevant value is a non-negative floating point number. Zero correlation means no similarity. The correlation is calculated based on the number of words in the line, the number of uniques in the line, the total number of words in the database, and the number of files (lines) that contain the unique word.

For natural language full-text search, it is required that the columns named in the MATCH() function are the same as the columns contained in some FULLTEXT indexes in your table. For the above query, please note that the columns named in the MATCH() function (title and full text) are the same as the columns in the FULLTEXT index of the article table. If you want to search the title and full text separately, you should create a FULLTEXT index on each column.

Alternatively you can run a Boolean search or search using query expansion.

The above example basically shows how to use the MATCH() function that returns rows in a decreasing order of correlation. The following example shows how to retrieve the relevant value explicitly. The order of the returned rows is uncertain because the SELECT statement does not contain a WHERE or ORDER BY clause:

mysql> SELECT id, MATCH (title,body) AGAINST ('Tutorial')    
-> FROM articles;
+----+-----------------------------------------+
| id | MATCH (title,body) AGAINST ('Tutorial') |
+----+-----------------------------------------+
|  1 |                        0.65545833110809 |
|  2 |                                       0 |
|  3 |                        0.66266459226608 |
|  4 |                                       0 |
|  5 |                                       0 |
|  6 |                                       0 |
+----+-----------------------------------------+
6 rows in set (0.00 sec)

The following example is more complicated. The query returns the relevant values, sorting the rows in order of decreasing relevance. To achieve this result, you should specify MATCH() twice: once in the SELECT list and once in the WHERE clause. This causes no additional housekeeping because the MySQL optimizer notices that the two MATCH() calls are identical and activates the full-text search code only once.

mysql> SELECT id, body, MATCH (title,body) AGAINST    
-> ('Security implications of running MySQL as root') AS score    
-> FROM articles WHERE MATCH (title,body) AGAINST    
-> ('Security implications of running MySQL as root');
+----+-------------------------------------+-----------------+
| id | body                                | score           |
+----+-------------------------------------+-----------------+
|  4 | 1. Never run mysqld as root. 2. ... | 1.5219271183014 |
|  6 | When configured properly, MySQL ... | 1.3114095926285 |
+----+-------------------------------------+-----------------+
2 rows in set (0.00 sec)

There are 2 rows in the table (0.00 seconds)

MySQL FULLTEXT execution treats any sequence of single-word character prototypes (letters, numbers, and underscore parts) as a word. This sequence may also contain single quotes ('), but there will be no more than one on a line. This means aaa'bbb will be treated as one word, while aaa''bbb will be treated as 2 words. Single quotes before or after a word will be removed by the FULLTEXT parser; 'aaa'bbb' will become aaa'bbb.

The FULLTEXT parser determines where a word begins and ends by looking for certain delimiters, such as ' ' (space mark), , (comma), and . (period). If words are not separated by delimiters (such as in Chinese), the FULLTEXT parser cannot determine the start and end positions of a word. In order to be able to add words or other indexed terms to a FULLTEXT index in such a language, you must preprocess them so that they are separated by some arbitrary delimiter such as ".

Some words will be ignored in full-text searches:

  • ##Any words that are too short will be ignored. The default minimum length of words found by full-text searches is 4 characters.

  • Words in stop words are ignored. A stop word is a word like "the" or "some" that is too common to be considered semantic, but there is a built-in stop word. It can be overridden through user-defined lists
  • ## Each correct word in the vocabulary and query is measured according to its importance in the vocabulary and query. In this way, a word that appears in many documents has a lower importance (and even many words have zero importance) because of its lower semantic value in this particular vocabulary. On the contrary, if the word is rare, Then it gets a higher importance. The importance of the words is then combined and used to calculate the relevance of the row.

    这项技术最适合同大型词库一起使用 (事实上, 此时它经过仔细的调整 )。对于很小的表,单词分布并不能充分反映它们的语义价值, 而这个模式有时可能会产生奇特的结果。例如, 虽然单词 “MySQL” 出现在文章表中的每一行,但对这个词的搜索可能得不到任何结果:

    mysql> SELECT * FROM articles

    -> WHERE MATCH (title,body) AGAINST ('MySQL');

    找不到搜索的词(0.00 秒)

    这个搜索的结果为空,原因是单词 “MySQL” 出现在至少全文的50%的行中。 因此, 它被列入停止字。对于大型数据集,使用这个操作最合适不过了----一个自然语言问询不会从一个1GB 的表每隔一行返回一次。对于小型数据集,它的用处可能比较小。

    一个符合表中所有行的内容的一半的单词查找相关文档的可能性较小。事实上, 它更容易找到很多不相关的内容。我们都知道,当我们在因特网上试图使用搜索引擎寻找资料的时候,这种情况发生的频率颇高。可以推论,包含该单词的行因其所在特别数据集 而被赋予较低的语义价值。 一个给定的词有可能在一个数据集中拥有超过其50%的域值,而在另一个数据集却不然。

    当你第一次尝试使用全文搜索以了解其工作过程时,这个50% 的域值提供重要的蕴涵操作:若你创建了一个表,并且只将文章的1、2行插入其中, 而文中的每个单词在所有行中出现的机率至少为  50% 。那么结果是你什么也不会搜索到。一定要插入至少3行,并且多多益善。需要绕过该50% 限制的用户可使用布尔搜索代码。

    1. 布尔全文搜索

    利用IN BOOLEAN MODE修改程序, MySQL 也可以执行布尔全文搜索:

    mysql> SELECT * FROM articles WHERE MATCH (title,body)    
    -> AGAINST ('+MySQL -YourSQL' IN BOOLEAN MODE);
    +----+-----------------------+-------------------------------------+
    | id | title                 | body                                |
    +----+-----------------------+-------------------------------------+
    |  1 | MySQL Tutorial        | DBMS stands for DataBase ...        |
    |  2 | How To Use MySQL Well | After you went through a ...        |
    |  3 | Optimizing MySQL      | In this tutorial we will show ...   |
    |  4 | 1001 MySQL Tricks     | 1. Never run mysqld as root. 2. ... |
    |  6 | MySQL Security        | When configured properly, MySQL ... |
    +----+-----------------------+-------------------------------------+

    这个问询检索所有包含单词“MySQL”的行,但检索包含单词“YourSQL”的行。

    布尔全文搜索具有以下特点:

    • 它们不使用 50% 域值。.

    • 它们不会按照相关性渐弱的顺序将行进行分类。你可以从上述问询结果中看到这一点:相关性最高的行是一个包含两个“MySQL” 的行,但它被列在最后的位置,而不是开头位置。

    • 即使没有FULLTEXT,它们仍然可以工作,尽管这种方式的搜索执行的速度非常之慢。

    • 最小单词长度全文参数和最大单词长度全文参数均适用。

    • 停止字适用。

    布尔全文搜索的性能支持以下操作符:

    • +

    一个前导的加号表示该单词必须 出现在返回的每一行的开头位置。

    • -

    一个前导的减号表示该单词一定不能出现在任何返回的行中。

    • (无操作符)

    在默认状态下(当没有指定 + 或–的情况下),该单词可有可无,但含有该单词的行等级较高。这和MATCH() ... AGAINST()不使用IN BOOLEAN MODE修改程序时的运作很类似。

    • >

    这两个操作符用来改变一个单词对赋予某一行的相关值的影响。 > 操作符增强其影响,而 

    • ( )

    括号用来将单词分成子表达式。括入括号的部分可以被嵌套。

    • ~

    一个前导的代字号用作否定符, 用来否定单词对该行相关性的影响。 这对于标记“noise(无用信息)”的单词很有用。包含这类单词的行较其它行等级低,但因其可能会和-号同时使用,因而不会在任何时候都派出所有无用信息行。

    • *

    星号用作截断符。于其它符号不同的是,它应当被追加到要截断的词上。

    • "

    一个被括入双引号的短语 (‘"’) 只和字面上包含该短语输入格式的行进行匹配。全文引擎将短语拆分成单词,在FULLTEXT索引中搜索该单词。   非单词字符不需要严密的匹配:短语搜索只要求符合搜索短语包含的单词且单词的排列顺序相同的内容。例如, "test phrase" 符合 "test, phrase"。

    若索引中不存在该短语包含的单词,则结果为空。例如,若所有单词都是禁用词,或是长度都小于编入索引单词的最小长度,则结果为空。

    以下例子展示了一些使用布尔全文符号的搜索字符串:

    • 'apple banana'

    寻找包含至少两个单词中的一个的行。

    • '+apple +juice'

    寻找两个单词都包含的行。

    • '+apple macintosh'

    寻找包含单词“apple”的行,若这些行也包含单词“macintosh”, 则列为更高等级。

    • '+apple -macintosh'

    寻找包含单词“apple” 但不包含单词 “macintosh”的行。

    • '+apple +(>turnover

    寻找包含单词“apple”和“turnover” 的行,或包含“apple” 和“strudel”的行 (无先后顺序),然而包含 “apple turnover”的行较包含“apple strudel”的行排列等级更为高。

    • 'apple*'

    寻找包含“apple”、“apples”、“applesauce”或“applet”的行。

    • '"some words"'

    寻找包含原短语“some words”的行 (例如,包含“some words of wisdom” 的行,而非包含  “some noise words”的行)。注意包围词组的‘"’ 符号是界定短语的操作符字符。它们不是包围搜索字符串本身的引号。

    2. 全文搜索带查询扩展

    全文搜索支持查询扩展功能 (特别是其多变的“盲查询扩展功能” )。若搜索短语的长度过短, 那么用户则需要依靠全文搜索引擎通常缺乏的内隐知识进行查询。这时,查询扩展功能通常很有用。例如, 某位搜索 “database” 一词的用户,可能认为“MySQL”、“Oracle”、“DB2” and “RDBMS”均为符合 “databases”的项,因此都应被返回。这既为内隐知识。

    在下列搜索短语后添加WITH QUERY EXPANSION,激活盲查询扩展功能(即通常所说的自动相关性反馈)。它将执行两次搜索,其中第二次搜索的搜索短语是同第一次搜索时找到的少数顶层文件连接的原始搜索短语。这样,假如这些文件中的一个 含有单词 “databases” 以及单词 “MySQL”, 则第二次搜索会寻找含有单词“MySQL” 的文件,即使这些文件不包含单词 “database”。下面的例子显示了这个不同之处:

    mysql> SELECT * FROM articles   
     -> WHERE MATCH (title,body) AGAINST ('database');
    +----+-------------------+------------------------------------------+
    | id | title             | body                                     |
    +----+-------------------+------------------------------------------+
    |  5 | MySQL vs. YourSQL | In the following database comparison ... |
    |  1 | MySQL Tutorial    | DBMS stands for DataBase ...             |
    +----+-------------------+------------------------------------------+
    2 rows in set (0.00 sec)
    
    mysql> SELECT * FROM articles    
    -> WHERE MATCH (title,body)    
    -> AGAINST ('database' WITH QUERY EXPANSION);
    +----+-------------------+------------------------------------------+
    | id | title             | body                                     |
    +----+-------------------+------------------------------------------+
    |  1 | MySQL Tutorial    | DBMS stands for DataBase ...             |
    |  5 | MySQL vs. YourSQL | In the following database comparison ... |
    |  3 | Optimizing MySQL  | In this tutorial we will show ...        |
    +----+-------------------+------------------------------------------+
    3 rows in set (0.00 sec)

    另一个例子是Georges Simenon 搜索关于Maigret的书籍, 这个用户不确定“Maigret”一词的拼法。若不使用查询扩展而搜索“Megre and the reluctant witnesses” 得到的结果只能是的“Maigret and the Reluctant Witnesses” 。 而带有查询扩展的搜索会在第二遍得到带有“Maigret”一词的所有书名。

    注释:  盲查询扩展功能很容易返回非相关文件而增加无用信息,因此只有在查询一个长度很短的短语时才有必要使用这项功能。

    3. 全文停止字

    以下表列出了默认的全文停止字:

    a's able about above according
    accordingly across actually after afterwards
    again against ain't all allow
    allows almost alone along already
    also although always am among
    amongst an and another any
    anybody anyhow anyone anything anyway
    anyways anywhere apart appear appreciate
    appropriate are aren't around as
    aside ask asking associated at
    available away awfully be became
    because become becomes becoming been
    before beforehand behind being believe
    below beside besides best better
    between beyond both brief but
    by c'mon c's came can
    can't cannot cant cause causes
    certain certainly changes clearly co
    com come comes concerning consequently
    consider considering contain containing contains
    corresponding could couldn't course currently
    definitely described despite did didn't
    different do does doesn't doing
    don't done down downwards during
    each edu eg eight either
    else elsewhere enough entirely especially
    et etc even ever every
    everybody everyone everything everywhere ex
    exactly example except far few
    fifth first five followed following
    follows for former formerly forth
    four from further furthermore get
    gets getting given gives go
    goes going gone got gotten
    greetings had hadn't happens hardly
    has hasn't have haven't having
    he he's hello help hence
    her here here's hereafter hereby
    herein hereupon hers herself hi
    him himself his hither hopefully
    how howbeit however i'd i'll
    i'm i've ie if ignored
    immediate in inasmuch inc indeed
    indicate indicated indicates inner insofar
    instead into inward is isn't
    it it'd it'll it's its
    itself just keep keeps kept
    know knows known last lately
    later latter latterly least less
    lest let let's like liked
    likely little look looking looks
    ltd mainly many may maybe
    me mean meanwhile merely might
    more moreover most mostly much
    must my myself name namely
    nd near nearly necessary need
    needs neither never nevertheless new
    next nine no nobody non
    none noone nor normally not
    nothing novel now nowhere obviously
    of off often oh ok
    okay old on once one
    ones only onto or other
    others otherwise ought our ours
    ourselves out outside over overall
    own particular particularly per perhaps
    placed please plus possible presumably
    probably provides que quite qv
    rather rd re really reasonably
    regarding regardless regards relatively respectively
    right said same saw say
    saying says second secondly see
    seeing seem seemed seeming seems
    seen self selves sensible sent
    serious seriously seven several shall
    she should shouldn't since six
    so some somebody somehow someone
    something sometime sometimes somewhat somewhere
    soon sorry specified specify specifying
    still sub such sup sure
    t's take taken tell tends
    th than thank thanks thanx
    that that's thats the their
    theirs them themselves then thence
    there there's thereafter thereby therefore
    therein theres thereupon these they
    they'd they'll they're they've think
    third this thorough thoroughly those
    though three through throughout thru
    thus to together too took
    toward towards tried tries truly
    try trying twice two un
    under unfortunately unless unlikely until
    unto up upon us use
    used useful uses using usually
    value various very via viz
    vs want wants was wasn't
    way we we'd we'll we're
    we've welcome well went were
    weren't what what's whatever when
    whence whenever where where's whereafter
    whereas whereby wherein whereupon wherever
    whether which while whither who
    who's whoever whole whom whose
    why will willing wish with
    within without won't wonder would
    would wouldn't yes yet you
    you'd you'll you're you've your
    yours yourself yourselves zero


    4. Full-text qualification

    • Full-text search only applies to MyISAM tables.

    • Full-text search can be used with most multi-byte character sets. Unicode is an exception; the utf8 character set can be used instead of the ucs2 character set.

    • Ideographic languages ​​such as Chinese and Japanese do not have custom delimiters. Therefore, the FULLTEXT parser cannot determine where words begin and end in these or other such languages.

    • If multiple character sets are supported in a single table, all columns in the FULLTEXT index must use the same character set and library.

    • MATCH() column list must exactly match the column list in some FULLTEXT index definitions in the table, unless MATCH() is in IN BOOLEAN MODE.

    • The parameter to AGAINST() must be a constant string.


    MySQL’s full-text search capacity has almost no user-tunable parameters. If you have a MySQL source distribution, you can exercise more control over full-text search performance, since some changes require source code modifications.

    Note that in order to be more effective, full-text searches need to be carefully tuned. In fact, modifying the default performance will only reduce its performance in most cases. Do not change the MySQL source unless you know what you are doing.

    Most of the full-text variables described below must be set when the server starts. In order to change them, the server must be restarted; they will not be changed while the server is running.

    Changes to some variables require you to rebuild the FULLTEXT index in the table. The relevant operating instructions are given at the end of this chapter.

    • ft_min_word_len and ft_max_word_len system arguments specify the minimum and maximum length of indexed words. The default minimum value is four characters; the default maximum value depends on the version of MySQL used. If you change any value, you must rebuild your FULLTEXT index. For example, if you want a 3-character word to be searchable, you can set the ft_min_word_len variable by moving the following line into a selection file:

    · [mysqld ]

    · ft_min_word_len=3

    Then restart the server and rebuild your FULLTEXT index. At the same time, pay special attention to the comments about myisamchk in the description behind the table.

    • To override the default stop word, you can set the ft_stopword_file system variable. The variable value should be a file pathname containing stop words, or an empty string used to stop stop word filtering. Rebuild your FULLTEXT index after changing the value of this variable or the contents of the stopword file.

    Stop words are free form, that is, you can use any non-alphanumeric character such as newline, space, or comma to separate stop words. The exceptions are the underscore character (_) and the single quote (') which are considered part of a word. The stop word character set is the server's default character set.

    • The 50% threshold for natural language queries is determined by the particular trade-off chosen. To prevent it, look for the following line in myisam/ftdefs.h:

    · #define GWS_IN_USE GWS_PROB

    Change the line to:

    #define GWS_IN_USE GWS_FREQ

    Then recompile MySQL. There is no need to rebuild the index at this time. Note: By doing this you will seriously reduce MySQL's ability to provide appropriate correlation values ​​for the MATCH() function. If you need to search for such common words, it is better to use IN BOOLEAN MODE instead because it does not follow the 50% threshold.

      To change the operator used for Boolean full-text searches, set the ft_boolean_syntax system variable. This variable can also be changed while the server is running, but you must have SUPER privileges to do so. There is no need to rebuild the index in this case.
    • If you change the full-text variables that affect indexing (ft_min_word_len, ft_max_word_len, or ft_stopword_file), or if you change the stopword file itself, you must rebuild after changing and restarting the server Your FULLTEXT index. At this time, to rebuild the index, you only need to perform a QUICK repair operation:

    mysql>

    REPAIR TABLE

    tbl_name QUICK;Note that if you Using

    myisamchk

    to perform an operation that modifies the table index (such as repair or analysis), the FULLTEXT index is rebuilt using the default full-text parameter values ​​for minimum and maximum word length and stop words, unless you specify otherwise . This will cause the query to fail.

    发生这个问题的原因是只有服务器认识这些参数。它们的存储位置不在  MyISAM 索引文件中。若你已经修改了最小单词长度或最大单词长度或服务器中的停止字,为避免这个问题,为你对mysqld所使用的myisamchk 指定同样的ft_min_word_len、 ft_max_word_len和ft_stopword_file值。例如,假如你已经将最小单词长度设置为 3, 则你可以这样修改一个带有myisamchk的表:

    shell> myisamchk --recover --ft_min_word_len=3 tbl_name.MYI

    为保证 myisamchk 及服务器对全文参数使用相同的值, 可将每一项都放在供选文件中的 [mysqld]和 [myisamchk] 部分:

    [mysqld]
    ft_min_word_len=3
    [myisamchk]
    ft_min_word_len=3

    使用 REPAIR TABLE、 ANALYZE TABLE、OPTIMIZE TABLE或ALTER TABLE来代替使用 myisamchk 。这些语句通过服务器来执行,服务器知道使用哪个全文参数值更加合适。

     以上就是MySQL基础教程10 —— 函数之全文搜索功能的内容,更多相关内容请关注PHP中文网(www.php.cn)!


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MySQL asynchronous master-slave replication enables data synchronization through binlog, improving read performance and high availability. 1) The master server record changes to binlog; 2) The slave server reads binlog through I/O threads; 3) The server SQL thread applies binlog to synchronize data.

MySQL: Simple Concepts for Easy LearningMySQL: Simple Concepts for Easy LearningApr 10, 2025 am 09:29 AM

MySQL is an open source relational database management system. 1) Create database and tables: Use the CREATEDATABASE and CREATETABLE commands. 2) Basic operations: INSERT, UPDATE, DELETE and SELECT. 3) Advanced operations: JOIN, subquery and transaction processing. 4) Debugging skills: Check syntax, data type and permissions. 5) Optimization suggestions: Use indexes, avoid SELECT* and use transactions.

MySQL: A User-Friendly Introduction to DatabasesMySQL: A User-Friendly Introduction to DatabasesApr 10, 2025 am 09:27 AM

The installation and basic operations of MySQL include: 1. Download and install MySQL, set the root user password; 2. Use SQL commands to create databases and tables, such as CREATEDATABASE and CREATETABLE; 3. Execute CRUD operations, use INSERT, SELECT, UPDATE, DELETE commands; 4. Create indexes and stored procedures to optimize performance and implement complex logic. With these steps, you can build and manage MySQL databases from scratch.

How does the InnoDB Buffer Pool work and why is it crucial for performance?How does the InnoDB Buffer Pool work and why is it crucial for performance?Apr 09, 2025 am 12:12 AM

InnoDBBufferPool improves the performance of MySQL databases by loading data and index pages into memory. 1) The data page is loaded into the BufferPool to reduce disk I/O. 2) Dirty pages are marked and refreshed to disk regularly. 3) LRU algorithm management data page elimination. 4) The read-out mechanism loads the possible data pages in advance.

MySQL: The Ease of Data Management for BeginnersMySQL: The Ease of Data Management for BeginnersApr 09, 2025 am 12:07 AM

MySQL is suitable for beginners because it is simple to install, powerful and easy to manage data. 1. Simple installation and configuration, suitable for a variety of operating systems. 2. Support basic operations such as creating databases and tables, inserting, querying, updating and deleting data. 3. Provide advanced functions such as JOIN operations and subqueries. 4. Performance can be improved through indexing, query optimization and table partitioning. 5. Support backup, recovery and security measures to ensure data security and consistency.

When might a full table scan be faster than using an index in MySQL?When might a full table scan be faster than using an index in MySQL?Apr 09, 2025 am 12:05 AM

Full table scanning may be faster in MySQL than using indexes. Specific cases include: 1) the data volume is small; 2) when the query returns a large amount of data; 3) when the index column is not highly selective; 4) when the complex query. By analyzing query plans, optimizing indexes, avoiding over-index and regularly maintaining tables, you can make the best choices in practical applications.

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