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cuente el número de filas que ocurren para cada fecha en el rango de fechas de la columna

WITH    q AS
        (
        SELECT  (
                SELECT  MIN(start_date)
                FROM    mytable
                ) + level - 1 AS mydate
        FROM    dual
        CONNECT BY
                level <= (
                SELECT  MAX(end_date) - MIN(start_date)
                FROM    mytable
                )
        )
SELECT  group, mydate,
        (
        SELECT  COUNT(*)
        FROM    mytable mi
        WHERE   mi.group = mo.group
                AND q BETWEEN mi.start_date AND mi.end_date
        ) 
FROM    q
CROSS JOIN
        (
        SELECT  DISTINCT group
        FROM    mytable
        ) mo

Actualización:

Una consulta mejor y más rápida haciendo uso de funciones analíticas.

La idea principal es que la cantidad de rangos que contienen cada fecha es la diferencia antes de que el conteo de rangos comenzara antes de esa fecha y el conteo de rangos que terminaron antes.

SELECT  cur_date,
        grouper,
        SUM(COALESCE(scnt, 0) - COALESCE(ecnt, 0)) OVER (PARTITION BY grouper ORDER BY cur_date) AS ranges
FROM    (
        SELECT  (
                SELECT  MIN(start_date)
                FROM    t_range
                ) + level - 1 AS cur_date
        FROM    dual
        CONNECT BY
                level <=
                (
                SELECT  MAX(end_date)
                FROM    t_range
                ) -
                (
                SELECT  MIN(start_date)
                FROM    t_range
                ) + 1
        ) dates
CROSS JOIN
        (
        SELECT  DISTINCT grouper AS grouper
        FROM    t_range
        ) groups
LEFT JOIN
        (
        SELECT  grouper AS sgrp, start_date, COUNT(*) AS scnt
        FROM    t_range
        GROUP BY
                grouper, start_date
        ) starts
ON      sgrp = grouper
        AND start_date = cur_date
LEFT JOIN
        (
        SELECT  grouper AS egrp, end_date, COUNT(*) AS ecnt
        FROM    t_range
        GROUP BY
                grouper, end_date
        ) ends
ON      egrp = grouper
        AND end_date = cur_date - 1
ORDER BY
        grouper, cur_date

Esta consulta se completa en 1 segundo en 1,000,000 filas.

Ver esta entrada en mi blog para más detalles: