Tree关系或者说层次结构是开发过程中遇到的普遍的问题，如何把这种关系持久化到数据库中，并能支持高效的SQL查询，这方面有不少讨论和解决方案，这边文章是对这主题相关内容的总结，介绍的比较肤浅，有兴趣的同学可以阅读一下我在参考资料中列举的文章和书籍。
Adjacency List Model（邻接列表模式）
样例表结构和数据准备SQL
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 |
+-------------+----------------------+--------+
在Adjacency List Model中，每一项都要保留一个指针指向它的父项，最顶层的用NULL或者其他的特殊值来表示。
下面我们来看看Adjacency List Model中主要其中应用场景下SQL的写法：
获取整棵树
SELECT t1.name AS lev1, t2.name as lev2, t3.name as lev3, t4.name as lev4
FROM category AS t1
LEFT JOIN category AS t2 ON t2.parent = t1.category_id
LEFT JOIN category AS t3 ON t3.parent = t2.category_id
LEFT JOIN category AS t4 ON t4.parent = t3.category_id
WHERE 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)
查找树中的全部叶子节点
SELECT t1.name FROM
category AS t1 LEFT JOIN category as t2
ON t1.category_id = t2.parent
WHERE t2.category_id IS NULL;
+--------------+
| name |
+--------------+
| TUBE |
| LCD |
| PLASMA |
| FLASH |
| CD PLAYERS |
| 2 WAY RADIOS |
+--------------+
获取单一路径
SELECT t1.name AS lev1, t2.name as lev2, t3.name as lev3, t4.name as lev4
FROM category AS t1
LEFT JOIN category AS t2 ON t2.parent = t1.category_id
LEFT JOIN category AS t3 ON t3.parent = t2.category_id
LEFT JOIN category AS t4 ON t4.parent = t3.category_id
WHERE t1.name = 'ELECTRONICS' AND t4.name = 'FLASH';
+-------------+----------------------+-------------+-------+
| lev1 | lev2 | lev3 | lev4 |
+-------------+----------------------+-------------+-------+
| ELECTRONICS | PORTABLE ELECTRONICS | MP3 PLAYERS | FLASH |
+-------------+----------------------+-------------+-------+
1 row in set (0.01 sec)
Adjacency List Model的局限性
- 普通的SQL很难处理Adjacency List Model，例如想要获取某个目录的全路径就必须知道目录所在的目录层级。
- 另外，删除某个节点的时候也必须要小心，否则容易造成该节点的子节点成为孤儿节点。
- 通过客户端代码或者存储过程可以解决其中的一些问题。通过过程语句，我们可以从顶层迭代从而获取整个树路径和单一路径；也可以在删除节点的时候，重置子节点的父节点值。
路径实体化（Materialized Path）模式
这种方式用的也很多，就是将节点的层次路径加以保存。
| ENAME |
PATH |
| KING |
1 |
| JONES |
1.1 |
| SCOTT |
1.1.1 |
| ADAMS |
1.1.1.1 |
| FORD |
1.1.2 |
| SMITH |
1.1.2.1 |
| BLAKE |
1.2 |
| ALLEN |
1.2.1 |
| WARD |
1.2.2 |
| CLARK |
1.3 |
| MILLER |
1.3.1 |
各种查询通过借助PATH值来实现，例如
获取某个节点的全部父节点
Nested Set Model（嵌套集合）模式
在嵌套集合模式父节点会包含它的子节点，这种层次关系通过节点的左、右值来体现的，如下图。
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 |
+-------------+----------------------+-----+-----+
树状的显示如下图
左、右值的赋值逻辑是“When working with a tree, we work from left to right, one layer at a time, descending to each node’s children before assigning a right-hand number and moving on to the right. This approach is called the modified preorder tree traversal algorithm.”
在给某个节点右值进行赋值之前，先降低到该节点的子节点，
获取整棵树
SELECT node.name
FROM nested_category AS node,
nested_category AS parent
WHERE 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 |
+----------------------+
跟Adjacency List Model的不同之处是查询不需要关注树的深度
查找树中的全部叶子节点
SELECT name
FROM nested_category
WHERE rgt = lft + 1;
+--------------+
| name |
+--------------+
| TUBE |
| LCD |
| PLASMA |
| FLASH |
| CD PLAYERS |
| 2 WAY RADIOS |
+--------------+
获取单一路径
SELECT parent.name
FROM nested_category AS node,
nested_category AS parent
WHERE node.lft BETWEEN parent.lft AND parent.rgt
AND node.name = 'FLASH'
ORDER BY parent.lft;
+----------------------+
| name |
+----------------------+
| ELECTRONICS |
| PORTABLE ELECTRONICS |
| MP3 PLAYERS |
| FLASH |
+----------------------+
获取节点深度
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
GROUP BY node.name
ORDER 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 |
+----------------------+-------+
如果新增节点
如果想要在“TELEVISIONS”和“PORTABLE ELECTRONICS”节点间新增一个节点，新节点的左、右值就是10和11，该节点右边节点的左、右值都要加2,MYSQL 4.x的实现如下！
LOCK TABLE nested_category WRITE;
SELECT @myRight := rgt FROM nested_category
WHERE 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;
如果要给一个没有子节点的节点增加一个子节点，上面的SQL要稍作调整。
LOCK TABLE nested_category WRITE;
SELECT @myLeft := lft FROM nested_category
WHERE 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
如果删除的是一个叶子节点，除了删除节点本身，还要修改该节点右边节点的左、右值。SQL如下
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;
如果要删除某个节点以及它的子节点。SQL如下
LOCK TABLE nested_category WRITE;
SELECT @myLeft := lft, @myRight := rgt, @myWidth := rgt - lft + 1
FROM nested_category
WHERE name = 'MP3 PLAYERS';
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;
如果删除父节点的时候，不要求删除子节点，而是将子节点提升到删除节点的级别。SQL如下
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;
参考资料
Storing Hierarchical Data in a Database
Managing Hierarchical Data in MySQL
一种理想的在关系数据库中存储树型结构数据的方法
Joe Celko’s Trees and Hierarchies in SQL for Smarties
A Nested Set Implementation in Java and PostgreSQL
Text Based Nested Set Implementation
Trees in SQL: Nested Sets and Materialized Path
