Consulta SQL para combinações sem repetição

Para valores relativamente pequenos de n(20 neste exemplo), você pode usar um método que explora o fato de que os inteiros naturais são combinações de bits.

Solução T-SQL

Dados de amostra:

DECLARE @Sample AS TABLE 
(
    item_id     tinyint IDENTITY(1,1) PRIMARY KEY NONCLUSTERED,
    item        nvarchar(500) NOT NULL,
    bit_value   AS 
                CONVERT
                (
                    integer, 
                    POWER(2, item_id - 1)
                )
                PERSISTED UNIQUE CLUSTERED
);    

INSERT @Sample
    (item)
VALUES
    (N'Ann'),
    (N'Bob'),
    (N'Charles'),
    (N'Darren'),
    (N'Eric'),
    (N'Fred'),
    (N'George'),
    (N'Harry'),
    (N'Ian'),
    (N'John'),
    (N'Keith'),
    (N'Larry'),
    (N'Mark'),
    (N'Nathan'),
    (N'Owen'),
    (N'Paul'),
    (N'Quentin'),
    (N'Ryan'),
    (N'Steve'),
    (N'Terry');

Solução:

-- Maximum integer we need
-- for all combinations of 'n' bits
DECLARE 
    @max integer = 
    POWER(2,
        (
            SELECT COUNT(*) 
            FROM @Sample AS s
        )
    ) - 1;

SELECT
    combination =
        STUFF
        (
            (
                -- Choose items where the bit is set
                -- and concatenate all matches
                SELECT ',' + s.item 
                FROM @Sample AS s
                WHERE
                    n.n & s.bit_value = s.bit_value
                ORDER BY
                    s.bit_value
                FOR XML 
                    PATH (''),
                    TYPE                    
            ).value('(./text())[1]', 'varchar(8000)'), 1, 1, ''
        )
-- A standard numbers table
-- (single column, integers from 1 to 1048576, indexed)
FROM dbo.Numbers AS N
WHERE
    N.n BETWEEN 1 AND @max;

Amostra de saída:

╔════════════════════════╗
║      combination       ║
╠════════════════════════╣
║ Ann                    ║
║ Bob                    ║
║ Ann,Bob                ║
║ Charles                ║
║ Ann,Charles            ║
║ Bob,Charles            ║
║ Ann,Bob,Charles        ║
║ Darren                 ║
║ Ann,Darren             ║
║ Bob,Darren             ║
║ Ann,Bob,Darren         ║
║ Charles,Darren         ║
║ Ann,Charles,Darren     ║
║ Bob,Charles,Darren     ║
║ Ann,Bob,Charles,Darren ║
║ ...                    ║
╚════════════════════════╝

Plano de execução:

Leva 41 segundos para gravar as 1.048.576 combinações em uma variável no meu laptop. Com o paralelismo forçado, consegui diminuir o tempo de execução DOP 8para 13 segundos.

Se você precisar de uma tabela Numbers, esta é uma maneira rápida de produzir uma:

SELECT TOP (1048576)
    n = ISNULL(CONVERT(integer, ROW_NUMBER() OVER (ORDER BY (SELECT NULL))), 0)
INTO dbo.Numbers
FROM sys.columns AS c
CROSS JOIN sys.columns AS c2
CROSS JOIN sys.columns AS c3;

CREATE UNIQUE CLUSTERED INDEX cuq
ON dbo.Numbers (n)
WITH (MAXDOP = 1, SORT_IN_TEMPDB = ON);

Solução SQLCLR

Uma implementação muito mais eficiente é possível no SQLCLR (SQL Server 2005 em diante):

CREATE ASSEMBLY [Demo]
    AUTHORIZATION [dbo]
    FROM 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
GO
CREATE FUNCTION dbo.Combinations
(
    @ElementsCSV nvarchar (4000)
)
RETURNS TABLE
(
    Combination nvarchar (4000) NULL
)
AS EXTERNAL NAME Demo.UserDefinedFunctions.Permute;

Exemplo de uso:

SELECT 
    f.Combination
FROM dbo.Combinations('A,B,C,D') AS f;

Resultado:

╔═════════════╗
║ Combination ║
╠═════════════╣
║ A           ║
║ B           ║
║ A,B         ║
║ C           ║
║ A,C         ║
║ B,C         ║
║ A,B,C       ║
║ D           ║
║ A,D         ║
║ B,D         ║
║ A,B,D       ║
║ C,D         ║
║ A,C,D       ║
║ B,C,D       ║
║ A,B,C,D     ║
╚═════════════╝

Usando o conjunto de 20 elementos de antes:

DECLARE @Sample AS TABLE 
(
    item_id     tinyint IDENTITY(1,1) PRIMARY KEY CLUSTERED,
    item        nvarchar(50) NOT NULL
);

INSERT @Sample
    (item)
VALUES
    (N'Ann'),
    (N'Bob'),
    (N'Charles'),
    (N'Darren'),
    (N'Eric'),
    (N'Fred'),
    (N'George'),
    (N'Harry'),
    (N'Ian'),
    (N'John'),
    (N'Keith'),
    (N'Larry'),
    (N'Mark'),
    (N'Nathan'),
    (N'Owen'),
    (N'Paul'),
    (N'Quentin'),
    (N'Ryan'),
    (N'Steve'),
    (N'Terry');

Solução SQLCLR:

-- Create CSV input
DECLARE 
    @Elements nvarchar(4000) =
        STUFF
        (
            (
                SELECT ',' + s.item 
                FROM @Sample AS s
                ORDER BY
                    s.item_id
                FOR XML 
                    PATH (''),
                    TYPE                    
            ).value('(./text())[1]', 'varchar(8000)'), 1, 1, ''
        );

DECLARE
    @bitbucket nvarchar(4000);

SELECT
    @bitbucket = combination
FROM dbo.Combinations(@Elements);

O tempo de execução é de 2,5 segundos para as 1.048.576 combinações no meu laptop em DOP 1.

Criando a entrada CSV:

Encontrando as combinações:

Código fonte C#:

using System;
using System.Collections;
using Microsoft.SqlServer.Server;

public partial class UserDefinedFunctions
{
    [SqlFunction
        (
        DataAccess=DataAccessKind.None, 
        SystemDataAccess=SystemDataAccessKind.None,
        FillRowMethodName="FillRow",
        TableDefinition="Permutation nvarchar(4000)"
        )
    ]
    public static IEnumerable Permute(string ElementsCSV)
    {
        // Split CSV
        string[] elements = ElementsCSV.Split(new char[] { ',' });

        // Highest integer needed
        int count = (int)Math.Pow(2, elements.Length) - 1;

        // Pre-computed array of 2^n values
        int[] powers = new int[elements.Length];

        for (int i = 0; i < powers.Length; i++)
        {
            powers[i] = (int)Math.Pow(2, i);
        }

        // Test integers
        for (int i = 1; i <= count; i++)
        {
            // Reset output
            string s = string.Empty;

            // Test each bit that could be set
            for (int bit = 0; bit < powers.Length && i >= powers[bit]; bit++)
            {
                if ((i & powers[bit]) == powers[bit])
                {
                    // Add the element corresponding to the set bit
                    s += elements[bit] + ',';
                }
            }

            // Return a row via enumeration
            yield return s.Substring(0, s.Length - 1);
        }
    }

    // Called by SQL Server to fetch a row
    public static void FillRow(object o, out string Permutation)
    {
        Permutation = (string)o;
    }
}