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agrupar y cambiar las columnas y filas

Puedes hacer esto con PIVOT dinámico y el ROW_NUMBER() función:

DECLARE @cols AS VARCHAR(1000),
        @query  AS VARCHAR(8000)
SELECT @cols = STUFF((SELECT ',' +   QUOTENAME(Name) 
                    FROM (SELECT DISTINCT Name
                          FROM #test
                          )sub
                    ORDER BY Name
                    FOR XML PATH(''), TYPE).value('.', 'VARCHAR(MAX)') 
                    ,1,1,'')
PRINT @cols

SET @query = '
WITH cte AS (SELECT DISTINCT *
             FROM  #test)
    ,cte2 AS (SELECT *,ROW_NUMBER() OVER(PARTITION BY Name ORDER BY Apt)RowRank
             FROM  cte)
SELECT * 
FROM  cte2 
PIVOT (max(Apt) for Name in ('[email protected]+')) p
            '
EXEC (@query)

SQL Fiddle - Lista distinta, orden específico

Editar:si no desea que la lista sea distinta, elimine el primer cte anterior, y si desea mantener un orden arbitrario, cambie ORDER BY a (SELECT 1) :

DECLARE @cols AS VARCHAR(1000),
        @query  AS VARCHAR(8000)
SELECT @cols = STUFF((SELECT ',' +   QUOTENAME(Name) 
                    FROM (SELECT DISTINCT Name
                          FROM #test
                          )sub
                          ORDER BY Name
                    FOR XML PATH(''), TYPE).value('.', 'VARCHAR(MAX)') 
                    ,1,1,'')
PRINT @cols

SET @query = '
WITH cte AS (SELECT *,ROW_NUMBER() OVER(PARTITION BY Name ORDER BY (SELECT 1))RowRank
             FROM  #test)
SELECT * 
FROM  cte 
PIVOT (max(Apt) for Name in ('[email protected]+')) p
            '
EXEC (@query)

SQL Fiddle:lista completa, orden arbitrario

Y finalmente, si no querías el RowRank en sus resultados, simplemente reutilice el @cols variable en su SELECT :

SET @query = '
WITH cte AS (SELECT *,ROW_NUMBER() OVER(PARTITION BY Name ORDER BY (SELECT 1))RowRank
             FROM  #test)
SELECT '[email protected]+' 
FROM  cte 
PIVOT (max(Apt) for Name in ('[email protected]+')) p
            '
EXEC (@query)