MySQL实现嵌套集合模型
译文主要是介绍如何用MySQL来存储嵌套集合数据。在其中会增加一些自己的理解，也会删除掉一些自认为无用的废话。
这篇文章主要讲的是嵌套集合模型，所以邻接表不是本文的重点，简单略过就好。
也许这是，因为我也不知道这是不是原文。
介绍
什么是分层数据？
类似于树形结构，除了根节点和叶子节点外，所有节点都有用一个父节点和多个子节点。
那么，在MySQL中如何处理分层数据呢？
原文中介绍了两种分层结构模型：邻接表模型和嵌套集合模型。
邻接表模型(The Adjacency List Model)
首先，建立测试表，导入测试数据，
CREATE TABLE category( category_id INT AUTO_INCREMENT PRIMARY KEY, name VARCHAR(20) NOT NULL, parent INT DEFAULT NULL);INSERT INTO category VALUES (1,'ELECTRONICS',NULL), (2,'TELEVISIONS',1), (3,'TUBE',2), (4,'LCD',2), (5,'PLASMA',2), (6,'PORTABLE ELECTRONICS',1), (7,'MP3 PLAYERS',6), (8,'FLASH',7), (9,'CD PLAYERS',6), (10,'2 WAY RADIOS',6);SELECT * FROM category ORDER BY category_id;+-------------+----------------------+--------+| category_id | name | parent |+-------------+----------------------+--------+| 1 | ELECTRONICS | NULL || 2 | TELEVISIONS | 1 || 3 | TUBE | 2 || 4 | LCD | 2 || 5 | PLASMA | 2 || 6 | PORTABLE ELECTRONICS | 1 || 7 | MP3 PLAYERS | 6 || 8 | FLASH | 7 || 9 | CD PLAYERS | 6 || 10 | 2 WAY RADIOS | 6 |+-------------+----------------------+--------+10 rows in set (0.00 sec)
在邻接表中，所有的数据均拥有一个Parent字段，用来存储它的父节点。当前节点为根节点的话，它的父节点则为NULL。
那么在遍历的时候，可以使用递归来实现查询整棵树，从根节点开始，不断寻找子节点（父节点->子节点->父节点->子节点）。检索分层路径
一般需要获取一个分层结构的路径问题，那么
SELECT t1.name AS lev1, t2.name as lev2, t3.name as lev3, t4.name as lev4FROM category AS t1LEFT JOIN category AS t2 ON t2.parent = t1.category_idLEFT JOIN category AS t3 ON t3.parent = t2.category_idLEFT JOIN category AS t4 ON t4.parent = t3.category_idWHERE t1.name = 'ELECTRONICS';+-------------+----------------------+--------------+-------+| lev1 | lev2 | lev3 | lev4 |+-------------+----------------------+--------------+-------+| ELECTRONICS | TELEVISIONS | TUBE | NULL || ELECTRONICS | TELEVISIONS | LCD | NULL || ELECTRONICS | TELEVISIONS | PLASMA | NULL || ELECTRONICS | PORTABLE ELECTRONICS | MP3 PLAYERS | FLASH || ELECTRONICS | PORTABLE ELECTRONICS | CD PLAYERS | NULL || ELECTRONICS | PORTABLE ELECTRONICS | 2 WAY RADIOS | NULL |+-------------+----------------------+--------------+-------+6 rows in set (0.00 sec)
检索叶子节点
SELECT t1.name FROMcategory AS t1 LEFT JOIN category as t2ON t1.category_id = t2.parentWHERE t2.category_id IS NULL;+--------------+| name |+--------------+| TUBE || LCD || PLASMA || FLASH || CD PLAYERS || 2 WAY RADIOS |+--------------+
检索指定路径
SELECT t1.name AS lev1, t2.name as lev2, t3.name as lev3, t4.name as lev4FROM category AS t1LEFT JOIN category AS t2 ON t2.parent = t1.category_idLEFT JOIN category AS t3 ON t3.parent = t2.category_idLEFT JOIN category AS t4 ON t4.parent = t3.category_idWHERE t1.name = 'ELECTRONICS' AND t4.name = 'FLASH';+-------------+----------------------+-------------+-------+| lev1 | lev2 | lev3 | lev4 |+-------------+----------------------+-------------+-------+| ELECTRONICS | PORTABLE ELECTRONICS | MP3 PLAYERS | FLASH |+-------------+----------------------+-------------+-------+1 row in set (0.01 sec)
邻接表的缺点
在检索路径的过程中，除了本层外，每一层都会对应一个LEFT JOIN，那么如果层数不定怎么办？或者层数过多？
嵌套集合模型Nested Set Model
原文中主要的目的是介绍嵌套集合模型，如下
通过集合的包含关系，嵌套结合模型可以表示分层结构，每一个分层可以用一个Set来表示（一个圈），父节点所在的圈包含所有子节点所在的圈。
为了用MySQL来表示集合关系，需要定义连个字段left和right（表示一个集合的范围）。
CREATE TABLE nested_category ( category_id INT AUTO_INCREMENT PRIMARY KEY, name VARCHAR(20) NOT NULL, lft INT NOT NULL, rgt INT NOT NULL);INSERT INTO nested_category VALUES (1,'ELECTRONICS',1,20), (2,'TELEVISIONS',2,9), (3,'TUBE',3,4), (4,'LCD',5,6), (5,'PLASMA',7,8), (6,'PORTABLE ELECTRONICS',10,19), (7,'MP3 PLAYERS',11,14), (8,'FLASH',12,13), (9,'CD PLAYERS',15,16), (10,'2 WAY RADIOS',17,18);SELECT * FROM nested_category ORDER BY category_id;+-------------+----------------------+-----+-----+| category_id | name | lft | rgt |+-------------+----------------------+-----+-----+| 1 | ELECTRONICS | 1 | 20 || 2 | TELEVISIONS | 2 | 9 || 3 | TUBE | 3 | 4 || 4 | LCD | 5 | 6 || 5 | PLASMA | 7 | 8 || 6 | PORTABLE ELECTRONICS | 10 | 19 || 7 | MP3 PLAYERS | 11 | 14 || 8 | FLASH | 12 | 13 || 9 | CD PLAYERS | 15 | 16 || 10 | 2 WAY RADIOS | 17 | 18 |+-------------+----------------------+-----+-----+
由于left和right是MySQL的保留字，因此，字段名称用lft和rgt代替。每一个集合都是从lft开始到rgt结束，也就是集合的两个边界。
在树中也同样适用，
当为树状结构编号时，我们从左到右，一次一层，赋值按照从左到右的顺序遍历其子节点，这种方法称为先序遍历算法。
检索分层路径
由于子节点的lft值总在父节点的lft和rgt值之间，所以可以通过父节点连接到子节点上来检索整棵树。
SELECT node.nameFROM nested_category AS node, nested_category AS parentWHERE node.lft BETWEEN parent.lft AND parent.rgt AND parent.name = 'ELECTRONICS'ORDER BY node.lft;+----------------------+| name |+----------------------+| ELECTRONICS || TELEVISIONS || TUBE || LCD || PLASMA || PORTABLE ELECTRONICS || MP3 PLAYERS || FLASH || CD PLAYERS || 2 WAY RADIOS |+----------------------+
这个方法并不需要考虑层数，而且不需要考虑节点的rgt。
检索所有叶子节点
由于每一个叶子节点的rgt=lft+1，那么只需要这一个条件即可。
SELECT nameFROM nested_categoryWHERE rgt = lft + 1;+--------------+| name |+--------------+| TUBE || LCD || PLASMA || FLASH || CD PLAYERS || 2 WAY RADIOS |+--------------+
检索节点路径
不再需要多个join连接操作。
SELECT parent.nameFROM nested_category AS node, nested_category AS parentWHERE node.lft BETWEEN parent.lft AND parent.rgt AND node.name = 'FLASH'ORDER BY node.lft;+----------------------+| name |+----------------------+| ELECTRONICS || PORTABLE ELECTRONICS || MP3 PLAYERS || FLASH |+----------------------+
检索节点深度
通过COUNT和GROUP BY函数来获取父节点的个数。
SELECT node.name, (COUNT(parent.name) - 1) AS depthFROM nested_category AS node, nested_category AS parentWHERE node.lft BETWEEN parent.lft AND parent.rgtGROUP BY node.nameORDER BY node.lft;+----------------------+-------+| name | depth |+----------------------+-------+| ELECTRONICS | 0 || TELEVISIONS | 1 || TUBE | 2 || LCD | 2 || PLASMA | 2 || PORTABLE ELECTRONICS | 1 || MP3 PLAYERS | 2 || FLASH | 3 || CD PLAYERS | 2 || 2 WAY RADIOS | 2 |+----------------------+-------+
甚至可以得到分层的缩进结果，
SELECT CONCAT( REPEAT(' ', COUNT(parent.name) - 1), node.name) AS nameFROM nested_category AS node, nested_category AS parentWHERE node.lft BETWEEN parent.lft AND parent.rgtGROUP BY node.nameORDER BY node.lft;+-----------------------+| name |+-----------------------+| ELECTRONICS || TELEVISIONS || TUBE || LCD || PLASMA || PORTABLE ELECTRONICS || MP3 PLAYERS || FLASH || CD PLAYERS || 2 WAY RADIOS |+-----------------------+ 检索子树的深度
考虑到检索中需要自连接的node或parent，因此需要增加一个额外的连接来作为子查询来限制子树。
SELECT node.name, (COUNT(parent.name) - (sub_tree.depth + 1)) AS depthFROM nested_category AS node, nested_category AS parent, nested_category AS sub_parent, ( SELECT node.name, (COUNT(parent.name) - 1) AS depth FROM nested_category AS node, nested_category AS parent WHERE node.lft BETWEEN parent.lft AND parent.rgt AND node.name = 'PORTABLE ELECTRONICS' GROUP BY node.name ORDER BY node.lft )AS sub_treeWHERE node.lft BETWEEN parent.lft AND parent.rgt AND node.lft BETWEEN sub_parent.lft AND sub_parent.rgt AND sub_parent.name = sub_tree.nameGROUP BY node.nameORDER BY node.lft;+----------------------+-------+| name | depth |+----------------------+-------+| PORTABLE ELECTRONICS | 0 || MP3 PLAYERS | 1 || FLASH | 2 || CD PLAYERS | 1 || 2 WAY RADIOS | 1 |+----------------------+-------+
检索节点的直接子节点
假设一个场景，当用户点击网站上电子产品的一个分类时，将呈现该分类下的产品，同时需要列出所有子分类，并不是全部分类。
为了限制显示分类的层数，需要使用HAVING字句， SELECT node.name, (COUNT(parent.name) - (sub_tree.depth + 1)) AS depthFROM nested_category AS node, nested_category AS parent, nested_category AS sub_parent, ( SELECT node.name, (COUNT(parent.name) - 1) AS depth FROM nested_category AS node, nested_category AS parent WHERE node.lft BETWEEN parent.lft AND parent.rgt AND node.name = 'PORTABLE ELECTRONICS' GROUP BY node.name ORDER BY node.lft )AS sub_treeWHERE node.lft BETWEEN parent.lft AND parent.rgt AND node.lft BETWEEN sub_parent.lft AND sub_parent.rgt AND sub_parent.name = sub_tree.nameGROUP BY node.nameHAVING depth <= 1ORDER BY node.lft;+----------------------+-------+| name | depth |+----------------------+-------+| PORTABLE ELECTRONICS | 0 || MP3 PLAYERS | 1 || CD PLAYERS | 1 || 2 WAY RADIOS | 1 |+----------------------+-------+
增加新节点
上面已经介绍了如何检索结果，那么如何才能增加新的节点呢？
如果希望在TELEVISIONS和PROTABLE ELECTRONICS节点之间增加一个新的节点，那么新节点的lft和rgt的值应该是10和11，那么所有大于10的节点（新节点右侧的节点）的lft和rgt都应该加2，如上图所示。
LOCK TABLE nested_category WRITE;SELECT @myRight := rgt FROM nested_categoryWHERE name = 'TELEVISIONS';UPDATE nested_category SET rgt = rgt + 2 WHERE rgt > @myRight;UPDATE nested_category SET lft = lft + 2 WHERE lft > @myRight;INSERT INTO nested_category(name, lft, rgt) VALUES('GAME CONSOLES', @myRight + 1, @myRight + 2);UNLOCK TABLES 如果希望在叶子节点下增加节点，需要修改下查询语句，
LOCK TABLE nested_category WRITE;SELECT @myLeft := lft FROM nested_categoryWHERE name = '2 WAY RADIOS';UPDATE nested_category SET rgt = rgt + 2 WHERE rgt > @myLeft;UPDATE nested_category SET lft = lft + 2 WHERE lft > @myLeft;INSERT INTO nested_category(name, lft, rgt) VALUES('FRS', @myLeft + 1, @myLeft + 2);UNLOCK TABLES;```###删除节点删除叶子节点比较容易，只需要删除自己，而删除一个中间层节点就需要删除其所有子节点。在这个模型中，所有子节点的节点正好在lft和rgt之间。 LOCK TABLE nested_category WRITE;
SELECT @myLeft := lft, @myRight := rgt, @myWidth := rgt - lft + 1
FROM nested_category WHERE name = 'GAME CONSOLES';DELETE FROM nested_category WHERE lft BETWEEN @myLeft AND @myRight;
UPDATE nested_category SET rgt = rgt - @myWidth WHERE rgt > @myRight;
UPDATE nested_category SET lft = lft - @myWidth WHERE lft > @myRight;UNLOCK TABLES;
在某些情况下，只需要删除某个节点，但是并不希望删除该节点下的子节点数据。通过把右侧所有节点的左右值-2，当前节点的子节点左右值-1
LOCK TABLE nested_category WRITE;
SELECT @myLeft := lft, @myRight := rgt, @myWidth := rgt - lft + 1
FROM nested_category WHERE name = 'PORTABLE ELECTRONICS';DELETE FROM nested_category WHERE lft = @myLeft;
UPDATE nested_category SET rgt = rgt - 1, lft = lft - 1 WHERE lft BETWEEN @myLeft AND @myRight;
UPDATE nested_category SET rgt = rgt - 2 WHERE rgt > @myRight; UPDATE nested_category SET lft = lft - 2 WHERE lft > @myRight;UNLOCK TABLES;
```最后的思考
原作者推荐了一本名为《Joe Celko's Trees and Hierarchies in SQL for Smarties》的书籍，该书的作者是SQL领域的大神Joe Celko（嵌套几何模型的创造者）。这本书涵盖了本文中未涉及到的一些高级话题。