Consulta SQL para combinaciones sin repetición

Necesito una consulta que pueda usarse en (o como) una función y recupere todas las combinaciones de n valores. Y necesito todas las combinaciones de longitud k donde k = 1..n.

Entrada y resultado de muestra extendidos para que la entrada tenga 3 valores en lugar de 2; sin embargo, el número de valores de entrada puede variar de 1 a n.

Ejemplo: Entrada: tabla con valores en una columna en varias filas

Value  (nvarchar(500))
------
Ann
John
Mark

Salida # 1: tabla con valores concatenados en una columna

    Ann
    John
    Mark
    Ann,John
    John,Mark
    Ann,Mark
    Ann,John,Mark

Para valores relativamente pequeños de n(20 en este ejemplo), puede usar un método que explota el hecho de que los enteros naturales son combinaciones de bits.

Solución T-SQL

Data de muestra:

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');

Solución:

-- 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;

Muestra de salida:

╔════════════════════════╗
║      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 ║
║ ...                    ║
╚════════════════════════╝

Plan de ejecución:

Me lleva 41 segundos escribir las 1,048,576 combinaciones en una variable en mi computadora portátil. Con paralelismo forzado, pude reducir el tiempo de ejecución DOP 8a 13 segundos.

Si necesita una tabla de Números, esta es una forma rápida de producir una:

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);

Solución SQLCLR

Una implementación mucho más eficiente es posible en SQLCLR (SQL Server 2005 en adelante):

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;

Ejemplo de uso:

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

Salida:

╔═════════════╗
║ 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 el 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');

Solución 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);

El tiempo de ejecución es de 2.5 segundos para las 1,048,576 combinaciones en mi computadora portátil en DOP 1.

Crear la entrada CSV:

Encontrar las combinaciones:

Código fuente de 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;
    }
}