递归CTE问题

6

我将尝试在SQL Server中使用递归CTE从包含底层树结构的表中建立谓词公式。

例如,我的表如下:

Id  |  Operator/Val |  ParentId
--------------------------
1   | 'OR'          |  NULL 
2   | 'AND'         |  1
3   | 'AND'         |  1
4   | '>'           |  2
5   | 'a'           |  4
6   | 'alpha'       |  4
...

...它代表着 ((a > alpha) AND (b > beta)) OR ((c > gamma) AND (a < delta))。

ParentId 是指向同一表中父节点的 Id 的引用。

我想编写一个查询,从表中构建这个字符串。这是可能的吗?

谢谢。


请在原始数据和期望输出之间添加一些中间步骤,以更好地解释。很抱歉我看不出它们之间的联系。 - gbn
我需要时间为您创建一张图片 - 基本上它代表谓词作为树形结构,然后在表格中被展开,每个节点都有指向其父节点的指针。 - Chris
酷!我经常在典型类别的大纲上做这种事情,但我从来没有想过对语法树使用CTE。 - harpo
你打算如何处理假设 Id 列足以指定树结构中左右排序的假设? - Nat
不错的观点,Nat - 我原本计划在树中添加另一列用于左/右排序,但是想保持问题简单,然后再进行扩展。 - Chris
@Chris:你找到了你一直在寻找的答案吗?请接受答案并投票,这是让SO运转的关键。 - Lucero
4个回答

5

对于生产环境,如果性能和递归深度限制(32级)不是问题,您可能希望选择递归函数以简化操作。

然而,这里提供了一种相当干净和高效的解决方案,使用公共表达式(CTEs)。请注意,它将接受任意数量的“树”,并为每个没有父元素的项目返回一个结果:

DECLARE @tbl TABLE
  (
   id int PRIMARY KEY
          NOT NULL,
   op nvarchar(max) NOT NULL,
   parent int
  ) ;
INSERT INTO @tbl
    SELECT 1, 'OR', NULL    UNION ALL
    SELECT 2, 'AND', 1    UNION ALL
    SELECT 3, 'AND', 1    UNION ALL
    SELECT 4, '>', 2    UNION ALL
    SELECT 5, 'a', 4    UNION ALL
    SELECT 6, 'alpha', 4    UNION ALL
    SELECT 7, '>', 2    UNION ALL
    SELECT 8, 'b', 7    UNION ALL
    SELECT 9, 'beta', 7    UNION ALL
    SELECT 10, '>', 3    UNION ALL
    SELECT 11, 'c', 10    UNION ALL
    SELECT 12, 'gamma', 10    UNION ALL
    SELECT 13, '>', 3    UNION ALL
    SELECT 14, 'd', 13    UNION ALL
    SELECT 15, 'delta', 13 ;

WITH  nodes -- A CTE which sets a flag to 1 for non-leaf nodes
        AS (
            SELECT t.*, CASE WHEN p.parent IS NULL THEN 0
                             ELSE 1
                        END node
              FROM @tbl t 
              LEFT JOIN (
                         SELECT DISTINCT parent
                          FROM @tbl
                        ) p ON p.parent = T.id
           ),
      rec -- the main recursive run to determine the sort order and add meta information
        AS (
            SELECT id rootId, node lvl, CAST(0 AS float) sort, CAST(0.5 AS float) offset, *
              FROM nodes
              WHERE parent IS NULL
            UNION ALL
            SELECT r.rootId, r.lvl+t.node, r.sort+r.offset*CAST((ROW_NUMBER() OVER (ORDER BY t.id)-1)*2-1 AS float),
                r.offset/2, t.*
              FROM rec r 
              JOIN 
                nodes t ON r.id = t.parent
           ),
      ranked -- ranking of the result to sort and find the last item
        AS (
            SELECT rootId, ROW_NUMBER() OVER (PARTITION BY rootId ORDER BY sort) ix,
                COUNT(1) OVER (PARTITION BY rootId) cnt, lvl, op
              FROM rec
           ),
      concatenated -- concatenate the string, adding ( and ) as needed
        AS (
            SELECT rootId, ix, cnt, lvl, CAST(REPLICATE('(', lvl)+op AS nvarchar(max)) txt
              FROM ranked
              WHERE ix = 1
            UNION ALL
            SELECT r.rootId, r.ix, r.cnt, r.lvl,
                c.txt+COALESCE(REPLICATE(')', c.lvl-r.lvl), '')+' '+COALESCE(REPLICATE('(', r.lvl-c.lvl), '')+r.op
                +CASE WHEN r.ix = r.cnt THEN REPLICATE(')', r.lvl)
                      ELSE ''
                 END
              FROM ranked r 
              JOIN 
                concatenated c ON (r.rootId = c.rootId)
                                  AND (r.ix = c.ix+1)
           )
  SELECT rootId id, txt
    FROM concatenated
    WHERE ix = cnt
    OPTION (MAXRECURSION 0);

1
感谢您的反馈!如果能点个赞,这个答案就能排在那两个不完整/不可用的答案之上了。 ;) - Lucero

2

我发现了一些东西,但看起来相当恶心。使用递归函数可以更轻松地完成这个任务...

DECLARE @Table TABLE(
        ID INT,
        Op VARCHAR(20),
        ParentID INT
)

INSERT INTO @Table SELECT 1,'OR',NULL 
INSERT INTO @Table SELECT 2,'AND',1
INSERT INTO @Table SELECT 3,'AND',1

INSERT INTO @Table SELECT 4,'>',2
INSERT INTO @Table SELECT 5,'a',4
INSERT INTO @Table SELECT 6,'alpha',4
INSERT INTO @Table SELECT 7,'>',2
INSERT INTO @Table SELECT 8,'b',7
INSERT INTO @Table SELECT 9,'beta',7

INSERT INTO @Table SELECT 10,'>',3
INSERT INTO @Table SELECT 11,'c',10
INSERT INTO @Table SELECT 12,'gamma',10
INSERT INTO @Table SELECT 13,'<',3
INSERT INTO @Table SELECT 14,'a',13
INSERT INTO @Table SELECT 15,'delta',13

;WITH Vals AS (
        SELECT  t.*,
                1 Depth
        FROM    @Table t LEFT JOIN
                @Table parent ON t.ID = parent.ParentID
        WHERE   parent.ParentID IS NULL 
        UNION ALL
        SELECT  t.*,
                v.Depth + 1
        FROM    @Table t INNER JOIN
                Vals v ON v.ParentID = t.ID
),
ValLR AS(
        SELECT  DISTINCT 
                vLeft.ID LeftID,
                vLeft.Op LeftOp,
                vRight.ID RightID,
                vRight.Op RightOp,
                vLeft.ParentID OperationID,
                vLeft.Depth
        FROM    Vals vLeft INNER JOIN
                Vals vRight ON  vLeft.ParentID = vRight.ParentID
                            AND vLeft.ID < vRight.ID
        WHERE   (vRight.ID IS NOT NULL)
),
ConcatVals AS(
        SELECT  CAST('(' + LeftOp + ' ' + Op + ' ' + RightOp + ')' AS VARCHAR(500)) ConcatOp,
                t.ID OpID,
                v.Depth,
                1 CurrentDepth
        FROM    ValLR v INNER JOIN
                @Table t ON v.OperationID = t.ID
        WHERE   v.Depth = 1
        
        UNION ALL       
        SELECT  CAST('(' + cL.ConcatOp + ' ' + t.Op + ' {' + CAST(v.RightID AS VARCHAR(10)) + '})' AS VARCHAR(500)) ConcatOp,
                t.ID OpID,
                v.Depth,
                cL.CurrentDepth + 1
        FROM    ValLR v INNER JOIN
                @Table t ON v.OperationID = t.ID INNER JOIN
                ConcatVals cL ON v.LeftID = cL.OpID
        WHERE   v.Depth = cL.CurrentDepth + 1
),
Replaces AS(
        SELECT  REPLACE(
                            c.ConcatOp,
                            SUBSTRING(c.ConcatOp,PATINDEX('%{%', c.ConcatOp), PATINDEX('%}%', c.ConcatOp) - PATINDEX('%{%', c.ConcatOp) + 1),
                            (SELECT ConcatOp FROM ConcatVals WHERE OpID = CAST(SUBSTRING(c.ConcatOp,PATINDEX('%{%', c.ConcatOp) + 1, PATINDEX('%}%', c.ConcatOp) - PATINDEX('%{%', c.ConcatOp) - 1)  AS INT))
                        ) ConcatOp,
                1 Num
        FROM    ConcatVals c
        WHERE   Depth = (SELECT MAX(Depth) FROM ConcatVals)
        UNION ALL
        SELECT  REPLACE(
                            r.ConcatOp,
                            SUBSTRING(r.ConcatOp,PATINDEX('%{%', r.ConcatOp), PATINDEX('%}%', r.ConcatOp) - PATINDEX('%{%', r.ConcatOp) + 1),
                            (SELECT ConcatOp FROM ConcatVals WHERE OpID = CAST(SUBSTRING(r.ConcatOp,PATINDEX('%{%', r.ConcatOp) + 1, PATINDEX('%}%', r.ConcatOp) - PATINDEX('%{%', r.ConcatOp) - 1)  AS INT))
                        ) ConcatOp,
                Num + 1
        FROM    Replaces r
        WHERE   PATINDEX('%{%', r.ConcatOp) > 0
)
SELECT  TOP 1
        *
FROM    Replaces
ORDER BY Num DESC

输出

ConcatOp                                                        
----------------------------------------------------------------
(((a > alpha) AND (b > beta)) OR ((c > gamma) AND (a < delta))) 

如果你更喜欢看递归函数,请告诉我,我们可以一起看看。

编辑:递归函数

看看这个有多简单。

CREATE TABLE TableValues (
        ID INT,
        Op VARCHAR(20),
        ParentID INT
)

INSERT INTO TableValues SELECT 1,'OR',NULL 
INSERT INTO TableValues SELECT 2,'AND',1
INSERT INTO TableValues SELECT 3,'AND',1

INSERT INTO TableValues SELECT 4,'>',2
INSERT INTO TableValues SELECT 5,'a',4
INSERT INTO TableValues SELECT 6,'alpha',4
INSERT INTO TableValues SELECT 7,'>',2
INSERT INTO TableValues SELECT 8,'b',7
INSERT INTO TableValues SELECT 9,'beta',7

INSERT INTO TableValues SELECT 10,'>',3
INSERT INTO TableValues SELECT 11,'c',10
INSERT INTO TableValues SELECT 12,'gamma',10
INSERT INTO TableValues SELECT 13,'<',3
INSERT INTO TableValues SELECT 14,'a',13
INSERT INTO TableValues SELECT 15,'delta',13

GO

CREATE FUNCTION ReturnMathVals (@ParentID INT, @Side VARCHAR(1))
RETURNS VARCHAR(500)
AS 
BEGIN
    DECLARE @RetVal VARCHAR(500)

    IF (@ParentID IS NULL)
    BEGIN
        SELECT  @RetVal = ' (' + dbo.ReturnMathVals(ID,'L') + Op + dbo.ReturnMathVals(ID,'R') + ') '
        FROM    TableValues 
        WHERE   ParentID IS NULL
    END
    ELSE
    BEGIN
        SELECT  TOP 1 @RetVal = ' (' + dbo.ReturnMathVals(ID,'L') + Op + dbo.ReturnMathVals(ID,'R') + ') '
        FROM    TableValues 
        WHERE   ParentID = @ParentID
        ORDER BY CASE WHEN @Side = 'L' THEN ID ELSE -ID END
        
        SET @RetVal = ISNULL(@RetVal, (SELECT TOP 1 Op FROM TableValues WHERE ParentID = @ParentID ORDER BY CASE WHEN @Side = 'L' THEN ID ELSE -ID END))
    END
    
    RETURN @RetVal
END
GO

SELECT  dbo.ReturnMathVals(NULL, NULL)
GO
DROP FUNCTION ReturnMathVals
DROP TABLE TableValues

1
看起来非常不错,谢谢你。我明天需要进一步测试它。我之前没有考虑过只使用递归函数,但似乎这是更好的解决方案。 - Chris
请注意,标量函数的递归深度仅限于32(不可更改),而CTE的递归深度默认为100,并且可以增加甚至禁用。另请参阅http://msdn.microsoft.com/en-us/library/ms186755.aspx和http://msdn.microsoft.com/en-us/library/ms175972.aspx。 - Lucero

0

我无法理解如何进行双重递归,但希望本文中的其中一个中间CTE可以为您指明正确的方向:

SET NOCOUNT ON

DECLARE @tree AS TABLE
    (
     Id int NOT NULL
    ,Operator varchar(10) NOT NULL
    ,ParentId int
    )

INSERT  INTO @tree
VALUES  (1, 'OR', NULL)
INSERT  INTO @tree
VALUES  (2, 'AND', 1)
INSERT  INTO @tree
VALUES  (3, 'AND', 1)
INSERT  INTO @tree
VALUES  (4, '>', 2)
INSERT  INTO @tree
VALUES  (5, 'a', 4)
INSERT  INTO @tree
VALUES  (6, 'alpha', 4)
INSERT  INTO @tree
VALUES  (7, '>', 2)
INSERT  INTO @tree
VALUES  (8, 'b', 7)
INSERT  INTO @tree
VALUES  (9, 'beta', 7)
INSERT  INTO @tree
VALUES  (10, '>', 3)
INSERT  INTO @tree
VALUES  (11, 'c', 10)
INSERT  INTO @tree
VALUES  (12, 'gamma', 10)
INSERT  INTO @tree
VALUES  (13, '>', 3)
INSERT  INTO @tree
VALUES  (14, 'd', 13)
INSERT  INTO @tree
VALUES  (15, 'delta', 13) ;
WITH    lhs_selector
          AS (
              SELECT    ParentId
                       ,MIN(Id) AS Id
              FROM      @tree
              GROUP BY  ParentId
             ),
        rhs_selector
          AS (
              SELECT    ParentId
                       ,MAX(Id) AS Id
              FROM      @tree
              GROUP BY  ParentId
             ),
        leaf_selector
          AS (
              SELECT    Id
              FROM      @tree AS leaf
              WHERE     NOT EXISTS ( SELECT *
                                     FROM   @tree
                                     WHERE  ParentId = leaf.Id )
             ),
        recurse
          AS (
              SELECT    operator.Id
                       ,CASE WHEN lhs_is_leaf.Id IS NOT NULL THEN NULL
                             ELSE lhs.Id
                        END AS LhsId
                       ,CASE WHEN rhs_is_leaf.Id IS NOT NULL THEN NULL
                             ELSE rhs.Id
                        END AS RhsId
                       ,CASE WHEN COALESCE(lhs_is_leaf.Id, rhs_is_leaf.Id) IS NULL
                             THEN '({' + CAST(lhs.Id AS varchar) + '} ' + operator.Operator + ' {'
                                  + CAST(rhs.Id AS varchar) + '})'
                             ELSE '(' + lhs.Operator + ' ' + operator.Operator + ' ' + rhs.Operator + ')'
                        END AS expression
              FROM      @tree AS operator
              INNER JOIN lhs_selector
                        ON lhs_selector.ParentID = operator.Id
              INNER JOIN rhs_selector
                        ON rhs_selector.ParentID = operator.Id
              INNER JOIN @tree AS lhs
                        ON lhs.Id = lhs_selector.Id
              INNER JOIN @tree AS rhs
                        ON rhs.Id = rhs_selector.Id
              LEFT JOIN leaf_selector AS lhs_is_leaf
                        ON lhs_is_leaf.Id = lhs.Id
              LEFT JOIN leaf_selector AS rhs_is_leaf
                        ON rhs_is_leaf.Id = rhs.Id
             )
    SELECT  *
           ,REPLACE(REPLACE(op.expression, '{' + CAST(op.LhsId AS varchar) + '}', lhs.expression),
                    '{' + CAST(op.RhsId AS varchar) + '}', rhs.expression) AS final_expression
    FROM    recurse AS op
    LEFT JOIN recurse AS lhs
            ON lhs.Id = op.LhsId
    LEFT JOIN recurse AS rhs
            ON rhs.Id = op.RhsId

0

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