如何获得总和等于给定值的行

Question

有表包含

ID     Qty
----------
1       2
2       4
3       1
4       5

现在，如果我必须选择数量总和等于 10 的行， 我该怎么做？

喜欢 2+4+1 = 7 但如果我加 5 那么 12

所以忽略 2，然后 4+1+5 = 10

我怎样才能做到这一点？

编辑：

我想要总结出价值的任何可能的组合。 假设 7 然后总和为 7 的任何行 同样，如果为 8，则任何行的总和为 8

希望行/行的组合等于给定值。

Answer 1

您要解决的问题称为subset sum 问题。不幸的是，它是NP-complete。

这意味着，无论您使用 SQL 还是任何其他语言来解决它，您都只能解决问题的非常小的实例，即表中只有几个条目的实例。否则，运行时间将变得过多，因为它随着表中的行数呈指数增长。这样做的原因是，基本上没有比尝试所有可能的组合更好的方法来找到解决方案。

如果一个近似解是可以接受的，有一个多项式时间算法，在维基百科页面上有描述。

Answer 2

如果你希望它总是三个加 10 的数字，那么这个

SELECT
  *
FROM 
  MyTable t1
  JOIN
  MyTable t2 ON t1.ID <> t2.ID 
  JOIN
  MyTable t3 ON t1.ID <> t3.ID AND t2.ID <> t3.ID
WHERE
  t1.Qty + t2.Qty + t3.Qty = 10

如果你想要 2 个或 4 个或 5 个数字，那么你不能在 SQL 中真正做到

编辑：

• 更新为按 ID 而非数量忽略
• 再说一遍：如果您想要 2 个或 4 个或 5 个数字，那么您无法在 SQL 中真正做到这一点

Answer 3

当您在 SQL 中处理此类任务时，您需要使用游标方法。

游标让您可以逐行执行操作，而这正是您所需要的，例如：

• 您想将总和为 10 的组进行分组

这是任务

• 选择所有表进入临时表#TBL_ALL
• 逐行循环，当行总和为 10 时，从临时表中删除并插入到最终临时表中 #TBL_FINAL
• 执行此操作直到无法执行 #TBL_ALL 总和

一个例子：

测试表：

/****** Object:  Table [dbo].[tblExample]    Script Date: 06/09/2011 11:25:27 ******/
SET ANSI_NULLS ON
GO

SET QUOTED_IDENTIFIER ON
GO

CREATE TABLE [dbo].[tblExample](
    [Id] [int] IDENTITY(1,1) NOT NULL,
    [Qty] [int] NOT NULL,
 CONSTRAINT [PK_tblExample] PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX  = OFF, STATISTICS_NORECOMPUTE  = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS  = ON, ALLOW_PAGE_LOCKS  = ON) ON [PRIMARY]
) ON [PRIMARY]

GO

测试数据：

INSERT INTO tblExample SELECT 2;
INSERT INTO tblExample SELECT 4;
INSERT INTO tblExample SELECT 1;
INSERT INTO tblExample SELECT 5;
INSERT INTO tblExample SELECT 5;
INSERT INTO tblExample SELECT 11;
INSERT INTO tblExample SELECT 1;
INSERT INTO tblExample SELECT 2;
INSERT INTO tblExample SELECT 3;
INSERT INTO tblExample SELECT 4;
INSERT INTO tblExample SELECT 7;
INSERT INTO tblExample SELECT 9;
INSERT INTO tblExample SELECT 1;
INSERT INTO tblExample SELECT 2;

存储过程：

http://pastebin.com/EFeZcKXf

结果：

分组表：

ids qty group
12  9   1
7   1   1
11  7   2
9   3   2
4   5   3
5   5   3
2   4   4
10  4   4
14  2   4

未使用的数字：

id  qty 
1   2
8   2
3   1
13  1
6   11

希望对你有帮助

---

SP 给那些无法访问 PasteBin 的人

CREATE PROCEDURE getGroups
(
    @groupByQty int, -- grouping number
    @numberRuns int  -- how many loops

    -- usage: getGroups 10, 10
)
AS

SET NOCOUNT ON;

-- declare all variables
DECLARE  @rowId      int,
         @rowQty     int,
         @rowTotal   int,
         @groupId    int,
         @totalRuns  int,
         @continue   bit

-- set up our final temporary table
CREATE TABLE #TBL_COUNT
(
  ids NVARCHAR(4000),
  qty int,
  [group] int
)

-- initializate variable
SET @groupId = 1;
SET @continue = 1;
SET @totalRuns = 0;
SELECT Id, Qty INTO #TBL_ALL FROM tblExample ORDER BY Qty DESC;

WHILE @totalRuns <= @numberRuns 
BEGIN
    -- declare the cursor
    DECLARE Product CURSOR FOR SELECT Id, Qty FROM #TBL_ALL ORDER BY Qty DESC;

    OPEN Product;
    FETCH Product INTO @rowId, @rowQty;

    PRINT ' ';
    PRINT '### Run: ' + CAST(@totalRuns AS nvarchar(10)) + ' #################################################################';
    PRINT 'Grouping Table by ' + CAST(@groupByQty AS nvarchar(10)) + ' | group id = ' + CAST(@groupId AS nvarchar(10));

    -- Retrieve and process the first row

    SELECT Top 1 @rowId = Id, @rowQty = Qty FROM #TBL_ALL ORDER BY Qty DESC;
    PRINT 'First Row: id = ' + CAST(@rowId AS nvarchar(10)) + ' | qty = ' + CAST(@rowQty AS nvarchar(10));

    -- sum it up and see if we have @groupByQty
    SELECT @rowTotal = ISNULL(SUM(qty),0) FROM #TBL_COUNT WHERE [group] = @groupId;
    PRINT 'Current sum in #TBL_COUNT: @groupId = '+ CAST(@groupId AS nvarchar(10)) +' | @rowTotal = ' + CAST(@rowTotal AS nvarchar(10)) + ' | (@rowTotal + @rowQty) = ' + CAST((@rowTotal + @rowQty) AS nvarchar(10));

    IF @rowQty > @groupByQty
    BEGIN
        PRINT '  x First row has an unused number';
    END
    ELSE
    BEGIN
      -- handle result
      IF (@rowTotal + @rowQty) = @groupByQty
      BEGIN

        PRINT '+++ Current sum is ' + CAST(@groupByQty AS nvarchar(10)) + ' +++';

        -- save number
        INSERT INTO #TBL_COUNT SELECT @rowId, @rowQty, @groupId;
        PRINT '### Inserted final # into #TBL_COUNT : id = ' + CAST(@rowId AS nvarchar(10)) + ' | qty = ' + CAST(@rowQty AS nvarchar(10)) + ' | group = ' + CAST(@groupId AS nvarchar(10));

        -- remove from table as we use it already
        DELETE FROM #TBL_ALL WHERE Id = @rowId;

        -- we got 10, let's change our Groupping
        SET @groupId = (@groupId + 1);

        PRINT 'New group id: ' + CAST(@groupId AS nvarchar(10));

      END
      ELSE 
      BEGIN   
        IF (@rowTotal + @rowQty) < @groupByQty
        BEGIN
            PRINT '### Inserted into #TBL_COUNT : id = ' + CAST(@rowId AS nvarchar(10)) + ' | qty = ' + CAST(@rowQty AS nvarchar(10)) + ' | group = ' + CAST(@groupId AS nvarchar(10));

            -- save number 
            INSERT INTO #TBL_COUNT SELECT @rowId, @rowQty, @groupId;

            -- remove from table as we use it already
            DELETE FROM #TBL_ALL WHERE Id = @rowId;
        END
        ELSE
        BEGIN
            PRINT '  x Unmatch number, will handle this latter';
        END
      END
    END 

    -- start the main processing loop
    WHILE @@Fetch_Status = 0
       BEGIN

          FETCH Product INTO @rowId, @rowQty;
          PRINT '@@Fetch_Status = ' + CAST(@@Fetch_Status AS nvarchar(100));

          IF @@Fetch_Status < 0
          BEGIN
            BREAK
          END

          -- we have the values of our row, let's use them
          PRINT 'Fetched Row: id = ' + CAST(@rowId AS nvarchar(10)) + ' | qty = ' + CAST(@rowQty AS nvarchar(10));

          -- sum it up and see if we have @groupByQty
          SELECT @rowTotal = ISNULL(SUM(qty),0) FROM #TBL_COUNT WHERE [group] = @groupId;
          PRINT 'Current sum in #TBL_COUNT: @groupId = '+ CAST(@groupId AS nvarchar(10)) +' | @rowTotal = ' + CAST(@rowTotal AS nvarchar(10)) + ' | (@rowTotal + @rowQty) = ' + CAST((@rowTotal + @rowQty) AS nvarchar(10));

          -- handle result
          IF (@rowTotal + @rowQty) = @groupByQty
          BEGIN

            PRINT '+++ Current sum is ' + CAST(@groupByQty AS nvarchar(10)) + ' +++';

            -- save number
            INSERT INTO #TBL_COUNT SELECT @rowId, @rowQty, @groupId;
            PRINT '### Inserted final # into #TBL_COUNT : id = ' + CAST(@rowId AS nvarchar(10)) + ' | qty = ' + CAST(@rowQty AS nvarchar(10)) + ' | group = ' + CAST(@groupId AS nvarchar(10));

            -- remove from table as we use it already
            DELETE FROM #TBL_ALL WHERE Id = @rowId;

            -- we got 10, let's change our Groupping
            SET @groupId = (@groupId + 1);

            PRINT 'New group id: ' + CAST(@groupId AS nvarchar(10));

            -- start again
            BREAK; 

          END
          ELSE 
          BEGIN   
            IF (@rowTotal + @rowQty) < @groupByQty
            BEGIN
                PRINT '### Inserted into #TBL_COUNT : id = ' + CAST(@rowId AS nvarchar(10)) + ' | qty = ' + CAST(@rowQty AS nvarchar(10)) + ' | group = ' + CAST(@groupId AS nvarchar(10));

                -- save number 
                INSERT INTO #TBL_COUNT SELECT @rowId, @rowQty, @groupId;

                -- remove from table as we use it already
                DELETE FROM #TBL_ALL WHERE Id = @rowId;
            END
            ELSE
            BEGIN
                PRINT '  x Unmatch number, will handle this latter';
            END
          END

       END -- END WHILE @@Fetch_Status = 0

       SET @totalRuns = @totalRuns + 1;

       -- Close and dealocate
       CLOSE Product;
       DEALLOCATE Product;

   END -- END WHILE totalRuns <= @numberRuns

   -- let's sum our last group and remove it if it's not @groupByQty
   SELECT @rowTotal = ISNULL(SUM(qty),0) FROM #TBL_COUNT WHERE [group] = @groupId;
   IF @rowTotal <> @groupByQty
   BEGIN
    SET IDENTITY_INSERT #TBL_ALL ON
    INSERT INTO #TBL_ALL (Id, Qty) SELECT Ids, Qty FROM #TBL_COUNT WHERE [group] = @groupId;
    DELETE FROM #TBL_COUNT WHERE [group] = @groupId;
   END

SET NOCOUNT OFF;

-- Show and Delete temp tables
SELECT * FROM #TBL_COUNT;
SELECT * FROM #TBL_ALL;
DROP TABLE #TBL_COUNT;
DROP TABLE #TBL_ALL;

P.S.我不是 SQL 专业人士，所以如果我做了一些奇怪的事情，请多多包涵，并记住这是一种性能浪费，也许有人可以使用没有游标的循环， more in this page

Answer 4

如果你总是添加 3 个数字，就像 gbn 说的那样，如果不是，那么你必须检查你的行的每个组合，这给你 2 到 number_of_rows 电源组合，我不知道如何在一个查询中在 sql 上完成它。如果你在 sql 中使用循环确定它是可能的，但你应该找到一些好的算法来完成这个任务。