Flattening intersecting timespans

Question

I have lots of data with start and stop times for a given ID and I need to flatten all intersecting and adjacent timespans into one combined timespan. The sample data posted below is all for the same ID so I didn't list it.

To make things a bit clearer, take a look at the sample data for 03.06.2009:

The following timespans are overlapping or contiunous and need to merge into one timespan

• 05:54:48 - 10:00:13
• 09:26:45 - 09:59:40

The resulting timespan would be from 05:54:48 to 10:00:13. Since there's a gap between 10:00:13 and 10:12:50 we also have the following timespans:

• 10:12:50 - 10:27:25
• 10:13:12 - 11:14:56
• 10:27:25 - 10:27:31
• 10:27:39 - 13:53:38
• 11:14:56 - 11:15:03
• 11:15:30 - 14:02:14
• 13:53:38 - 13:53:43
• 14:02:14 - 14:02:31

which result in one merged timespan from 10:12:50 to 14:02:31, since they're overlapping or adjacent.

Below you will find the sample data and the flattened data as I would need it. The duration column is just informative.

Any solution - be it SQL or not - is appreciated.

---

EDIT: Since there are lots of different and interesting solutions I'm refining my original question by adding constraints to see the "best" (if there is one) solution bubble up:

• I'm getting the data via ODBC from another system. There's no way to change the table layout for me or adding indexes
• The data is indexed only by the date column (the time part isn't)
• There are about 2.5k rows for every day
• The estimated usage pattern of the data is roughly as follows:
  • Most of the time (lets say 90%) the user will query just one or two days (2.5k - 5k rows)
  • Sometimes (9%) the range will be up to a month (~75k rows)
  • Rarely (1%) the range will be up to a year (~900k rows)
• The query should be fast for the typical case and not "last forever" for the rare case.
• Querying a year worth of data takes about 5 minutes (plain select without joins)

Within these constraints, what would be the best solution? I'm afraid that most of the solutions will be horribly slow since they join on the combination of date and time, which is not an index field in my case.

Would you do all the merging on the client or the server side? Would you first create an optimized temp table and use one of the proposed solutions with that table? I didn't have the time to test the solutions until now but I will keep you informed what works best for me.

---

Sample data:

Date       | Start    | Stop
-----------+----------+---------
02.06.2009 | 05:55:28 | 09:58:27
02.06.2009 | 10:15:19 | 13:58:24
02.06.2009 | 13:58:24 | 13:58:43
03.06.2009 | 05:54:48 | 10:00:13
03.06.2009 | 09:26:45 | 09:59:40
03.06.2009 | 10:12:50 | 10:27:25
03.06.2009 | 10:13:12 | 11:14:56
03.06.2009 | 10:27:25 | 10:27:31
03.06.2009 | 10:27:39 | 13:53:38
03.06.2009 | 11:14:56 | 11:15:03
03.06.2009 | 11:15:30 | 14:02:14
03.06.2009 | 13:53:38 | 13:53:43
03.06.2009 | 14:02:14 | 14:02:31
04.06.2009 | 05:48:27 | 09:58:59
04.06.2009 | 06:00:00 | 09:59:07
04.06.2009 | 10:15:52 | 13:54:52
04.06.2009 | 10:16:01 | 13:24:20
04.06.2009 | 13:24:20 | 13:24:24
04.06.2009 | 13:24:32 | 14:00:39
04.06.2009 | 13:54:52 | 13:54:58
04.06.2009 | 14:00:39 | 14:00:49
05.06.2009 | 05:53:58 | 09:59:12
05.06.2009 | 10:16:05 | 13:59:08
05.06.2009 | 13:59:08 | 13:59:16
06.06.2009 | 06:04:00 | 10:00:00
06.06.2009 | 10:16:54 | 10:18:40
06.06.2009 | 10:18:40 | 10:18:45
06.06.2009 | 10:23:00 | 13:57:00
06.06.2009 | 10:23:48 | 13:57:54
06.06.2009 | 13:57:21 | 13:57:38
06.06.2009 | 13:57:54 | 13:57:58
07.06.2009 | 21:59:30 | 01:58:49
07.06.2009 | 22:12:16 | 01:58:39
07.06.2009 | 22:12:25 | 01:58:28
08.06.2009 | 02:10:33 | 05:56:11
08.06.2009 | 02:10:43 | 05:56:23
08.06.2009 | 02:10:49 | 05:55:59
08.06.2009 | 05:55:59 | 05:56:01
08.06.2009 | 05:56:11 | 05:56:14
08.06.2009 | 05:56:23 | 05:56:27

Flattened result:

Date       | Start    | Stop     | Duration
-----------+----------+----------+---------
02.06.2009 | 05:55:28 | 09:58:27 | 04:02:59
02.06.2009 | 10:15:19 | 13:58:43 | 03:43:24
03.06.2009 | 05:54:48 | 10:00:13 | 04:05:25
03.06.2009 | 10:12:50 | 14:02:31 | 03:49:41
04.06.2009 | 05:48:27 | 09:59:07 | 04:10:40
04.06.2009 | 10:15:52 | 14:00:49 | 03:44:58
05.06.2009 | 05:53:58 | 09:59:12 | 04:05:14
05.06.2009 | 10:16:05 | 13:59:16 | 03:43:11
06.06.2009 | 06:04:00 | 10:00:00 | 03:56:00
06.06.2009 | 10:16:54 | 10:18:45 | 00:01:51
06.06.2009 | 10:23:00 | 13:57:58 | 03:34:58
07.06.2009 | 21:59:30 | 01:58:49 | 03:59:19
08.06.2009 | 02:10:33 | 05:56:27 | 03:45:54

Answer 1

I needed to do something similar and wanted a solution that made sense to me:

I start by creating a table of the "smallest time intervals", each one being the interval between successive time points (regardless of whether the pairs of time points are contained within a single time span or not):

create table Time_Pairs
as
select d1, 
       lead(d1) over (order by d1) as d2
from ( -- all time points
    select d1
    from (select d1 from Test_Time_Spans union all select d2 from Test_Time_Spans)
    group by 1
    )

I then keep only the pairs which are within a single time span, and flag whether the small time span is contiguous with the previous and next time span:

create table Non_Overlapping_Time_Spans
as
select s.d1,
       s.d2,
       case
           when s.d1=lag(s.d2) over (order by s.d1) then 1 -- prev time interval is contiguous with this one
           else 0
       end as merge_prev,
       case
           when s.d2=lead(s.d1) over (order by s.d1) then 1 -- next time interval is contiguous with this one
           else 0
       end as merge_next
from Test_Time_Spans t inner join
     Time_Pairs s
on s.d1>=t.d1
and s.d2<=t.d2
group by 1,2

Finally, I keep only the start time and end time of each block by picking only the times where merge_prev or merge_next are equal to 0:

select distinct -- need to de-dupe
       case 
           when merge_prev=0 then d1
           else lag(d1) over (order by d1)
       end as d1,
       case 
           when merge_next=0 then d2
           else lead(d2) over (order by d1)
       end as d2
from Non_Overlapping_Time_Spans
where merge_prev=0 or merge_next=0
order by 1

Answer 2

Extending on MahlerFive answer I wrote a swift extension to DateTools. So far it has passed all my tests.

extension DTTimePeriodCollection {

    func flatten() {

        self.sortByStartAscending()

        guard let periods = self.periods() else { return }
        if periods.count < 1 { return }

        var flattenedPeriods = [DTTimePeriod]()
        let flatdate = DTTimePeriod()

        for period in periods {

            guard let periodStart = period.StartDate, let periodEnd = period.EndDate else { continue }

            if !flatdate.hasStartDate() { flatdate.StartDate = periodStart }
            if !flatdate.hasEndDate() { flatdate.EndDate = periodEnd }

            if periodStart.isEarlierThanOrEqualTo(flatdate.EndDate) && periodEnd.isGreaterThanOrEqualTo(flatdate.EndDate) {

                flatdate.EndDate = periodEnd

            } else {

                flattenedPeriods.append(flatdate.copy())
                flatdate.StartDate = periodStart
                flatdate.EndDate = periodEnd
            }
        }

        flattenedPeriods.append(flatdate.copy())

        // delete all periods
        for var i = 0 ; i < periods.count ; i++ { self.removeTimePeriodAtIndex(0) }

        // add flattened periods to self
        for flat in flattenedPeriods { self.addTimePeriod(flat) }
    }

Answer 3

In MySQL:

SELECT  grouper, MIN(start) AS group_start, MAX(end) AS group_end
FROM    (
        SELECT  start,
                end,
                @r := @r + (@edate < start) AS grouper,
                @edate := GREATEST(end, CAST(@edate AS DATETIME))
        FROM    (
                SELECT  @r := 0,
                        @edate := CAST('0000-01-01' AS DATETIME)
                ) vars,
                (
                SELECT  rn_date + INTERVAL TIME_TO_SEC(rn_start) SECOND AS start,
                        rn_date + INTERVAL TIME_TO_SEC(rn_end) SECOND + INTERVAL (rn_start > rn_end) DAY AS end
                FROM    t_ranges
                ) q
        ORDER BY
                start
        ) q
GROUP BY
        grouper
ORDER BY
        group_start

Same decision for SQL Server is described in the following article in my blog:

• Flattening timespans: SQL Server

Here's the function to do this:

DROP FUNCTION fn_spans
GO
CREATE FUNCTION fn_spans(@p_from DATETIME, @p_till DATETIME)
RETURNS @t TABLE
        (
        q_start DATETIME NOT NULL,
        q_end DATETIME NOT NULL
        )
AS
BEGIN
        DECLARE @qs DATETIME
        DECLARE @qe DATETIME
        DECLARE @ms DATETIME
        DECLARE @me DATETIME
        DECLARE cr_span CURSOR FAST_FORWARD
        FOR
        SELECT  s_date + s_start AS q_start,
                s_date + s_stop + CASE WHEN s_start < s_stop THEN 0 ELSE 1 END AS q_end
        FROM    t_span
        WHERE   s_date BETWEEN @p_from - 1 AND @p_till
                AND s_date + s_start >= @p_from
                AND s_date + s_stop <= @p_till
        ORDER BY
                q_start
        OPEN    cr_span
        FETCH   NEXT
        FROM    cr_span
        INTO    @qs, @qe
        SET @ms = @qs
        SET @me = @qe
        WHILE @@FETCH_STATUS = 0
        BEGIN
                FETCH   NEXT
                FROM    cr_span
                INTO    @qs, @qe
                IF @qs > @me
                BEGIN
                        INSERT
                        INTO    @t
                        VALUES (@ms, @me)
                        SET @ms = @qs
                END
                SET @me = CASE WHEN @qe > @me THEN @qe ELSE @me END
        END
        IF @ms IS NOT NULL 
        BEGIN
                INSERT
                INTO    @t
                VALUES  (@ms, @me)
        END
        CLOSE   cr_span
        RETURN
END

Since SQL Server lacks an easy way to refer to previously selected rows in a resultset, this is one of rare cases when cursors in SQL Server work faster than set-based decisions.

Tested on 1,440,000 rows, works for 24 seconds for the full set, and almost instant for a range of day or two.

Note the additional condition in the SELECT query:

s_date BETWEEN @p_from - 1 AND @p_till

This seems to be redundant, but it is actually a coarse filter to make your index on s_date usable.

Answer 4

To help answer the question, here is the sample data given in the question in a table variable like Hainstech used:

declare @T1 table (d1 datetime, d2 datetime)

insert @T1 (d1,d2)
select           '02 June 2009 05:55:28','02 June 2009 09:58:27'
union all select '02 June 2009 10:15:19','02 June 2009 13:58:24'
union all select '02 June 2009 13:58:24','02 June 2009 13:58:43'
union all select '03 June 2009 05:54:48','03 June 2009 10:00:13'
union all select '03 June 2009 09:26:45','03 June 2009 09:59:40'
union all select '03 June 2009 10:12:50','03 June 2009 10:27:25'
union all select '03 June 2009 10:13:12','03 June 2009 11:14:56'
union all select '03 June 2009 10:27:25','03 June 2009 10:27:31'
union all select '03 June 2009 10:27:39','03 June 2009 13:53:38'
union all select '03 June 2009 11:14:56','03 June 2009 11:15:03'
union all select '03 June 2009 11:15:30','03 June 2009 14:02:14'
union all select '03 June 2009 13:53:38','03 June 2009 13:53:43'
union all select '03 June 2009 14:02:14','03 June 2009 14:02:31'
union all select '04 June 2009 05:48:27','04 June 2009 09:58:59'
union all select '04 June 2009 06:00:00','04 June 2009 09:59:07'
union all select '04 June 2009 10:15:52','04 June 2009 13:54:52'
union all select '04 June 2009 10:16:01','04 June 2009 13:24:20'
union all select '04 June 2009 13:24:20','04 June 2009 13:24:24'
union all select '04 June 2009 13:24:32','04 June 2009 14:00:39'
union all select '04 June 2009 13:54:52','04 June 2009 13:54:58'
union all select '04 June 2009 14:00:39','04 June 2009 14:00:49'
union all select '05 June 2009 05:53:58','05 June 2009 09:59:12'
union all select '05 June 2009 10:16:05','05 June 2009 13:59:08'
union all select '05 June 2009 13:59:08','05 June 2009 13:59:16'
union all select '06 June 2009 06:04:00','06 June 2009 10:00:00'
union all select '06 June 2009 10:16:54','06 June 2009 10:18:40'
union all select '06 June 2009 10:18:40','06 June 2009 10:18:45'
union all select '06 June 2009 10:23:00','06 June 2009 13:57:00'
union all select '06 June 2009 10:23:48','06 June 2009 13:57:54'
union all select '06 June 2009 13:57:21','06 June 2009 13:57:38'
union all select '06 June 2009 13:57:54','06 June 2009 13:57:58'
union all select '07 June 2009 21:59:30','07 June 2009 01:58:49'
union all select '07 June 2009 22:12:16','07 June 2009 01:58:39'
union all select '07 June 2009 22:12:25','07 June 2009 01:58:28'
union all select '08 June 2009 02:10:33','08 June 2009 05:56:11'
union all select '08 June 2009 02:10:43','08 June 2009 05:56:23'
union all select '08 June 2009 02:10:49','08 June 2009 05:55:59'
union all select '08 June 2009 05:55:59','08 June 2009 05:56:01'
union all select '08 June 2009 05:56:11','08 June 2009 05:56:14'
union all select '08 June 2009 05:56:23','08 June 2009 05:56:27'

Answer 5

Here is a recursive CTE solution, but I took the liberty of assigning a date and time to each column rather than pulling the date out separately. Helps to avoid some messy special case code. If you must store the date separately, I would use a view of CTE to make it look like two datetime columns and go with this approach.

create test data:

create table t1 (d1 datetime, d2 datetime)

insert t1 (d1,d2)
    select           '2009-06-03 10:00:00', '2009-06-03 14:00:00'
    union all select '2009-06-03 13:55:00', '2009-06-03 18:00:00'
    union all select '2009-06-03 17:55:00', '2009-06-03 23:00:00'
    union all select '2009-06-03 22:55:00', '2009-06-04 03:00:00'

    union all select '2009-06-04 03:05:00', '2009-06-04 07:00:00'

    union all select '2009-06-04 07:05:00', '2009-06-04 10:00:00'
    union all select '2009-06-04 09:55:00', '2009-06-04 14:00:00'

Recursive CTE:

;with dateRanges (ancestorD1, parentD1, d2, iter) as
(
--anchor is first level of collapse
    select
        d1 as ancestorD1,
        d1 as parentD1,
        d2,
        cast(0 as int) as iter
    from t1

--recurse as long as there is another range to fold in
    union all select
        tLeft.ancestorD1,
        tRight.d1 as parentD1,
        tRight.d2,
        iter + 1  as iter
    from dateRanges as tLeft join t1 as tRight
        --join condition is that the t1 row can be consumed by the recursive row
        on tLeft.d2 between tRight.d1 and tRight.d2
            --exclude identical rows
            and not (tLeft.parentD1 = tRight.d1 and tLeft.d2 = tRight.d2)
)
select
    ranges1.*
from dateRanges as ranges1
where not exists (
    select 1
    from dateRanges as ranges2
    where ranges1.ancestorD1 between ranges2.ancestorD1 and ranges2.d2
        and ranges1.d2 between ranges2.ancestorD1 and ranges2.d2
        and ranges2.iter > ranges1.iter
)

Gives output:

ancestorD1              parentD1                d2                      iter
----------------------- ----------------------- ----------------------- -----------
2009-06-04 03:05:00.000 2009-06-04 03:05:00.000 2009-06-04 07:00:00.000 0
2009-06-04 07:05:00.000 2009-06-04 09:55:00.000 2009-06-04 14:00:00.000 1
2009-06-03 10:00:00.000 2009-06-03 22:55:00.000 2009-06-04 03:00:00.000 3

Answer 6

Here is a SQL only solution. I used DATETIME for the columns. Storing the time separate is a mistake in my opinion, as you will have problems when the times go past midnight. You can adjust this to handle that situation though if you need to. The solution also assumes that the start and end times are NOT NULL. Again, you can adjust as needed if that's not the case.

The general gist of the solution is to get all of the start times that don't overlap with any other spans, get all of the end times that don't overlap with any spans, then match the two together.

The results match your expected results except in one case, which checking by hand looks like you have a mistake in your expected output. On the 6th there should be a span that ends at 2009-06-06 10:18:45.000.

SELECT
     ST.start_time,
     ET.end_time
FROM
(
     SELECT
          T1.start_time
     FROM
          dbo.Test_Time_Spans T1
     LEFT OUTER JOIN dbo.Test_Time_Spans T2 ON
          T2.start_time < T1.start_time AND
          T2.end_time >= T1.start_time
     WHERE
          T2.start_time IS NULL
) AS ST
INNER JOIN
(
     SELECT
          T3.end_time
     FROM
          dbo.Test_Time_Spans T3
     LEFT OUTER JOIN dbo.Test_Time_Spans T4 ON
          T4.end_time > T3.end_time AND
          T4.start_time <= T3.end_time
     WHERE
          T4.start_time IS NULL
) AS ET ON
     ET.end_time > ST.start_time
LEFT OUTER JOIN
(
     SELECT
          T5.end_time
     FROM
          dbo.Test_Time_Spans T5
     LEFT OUTER JOIN dbo.Test_Time_Spans T6 ON
          T6.end_time > T5.end_time AND
          T6.start_time <= T5.end_time
     WHERE
          T6.start_time IS NULL
) AS ET2 ON
     ET2.end_time > ST.start_time AND
     ET2.end_time < ET.end_time
WHERE
     ET2.end_time IS NULL

Answer 7

Similar question on SO here:

Min effective and termdate for contiguous dates

FWIW I up-voted the one that recommended Joe Celko's SQL For Smarties, Third Edition -- repeat: Third Edition (2005) -- which discusses various approaches, set base and procedural.

Answer 8

Assuming you:

• have some sort of simple custom Date object that stores a start date/time and end date/time
• get the rows back in sorted order (by start date/time) as a list, L, of these Dates
• want to create a flattened list of Dates, F

Do the following:

first = first row in L
flat_date.start = first.start, flat_date.end = first.end
For each row in L:
    if row.start < flat_date.end and row.end > flat_date.end: // adding on to a timespan
        flat_date.end = row.end
    else: // ending a timespan and starting a new one
        add flat_date to F
        flat_date.start = row.start, flat_date.end = row.end
add flat_date to F // adding the last timespan to the flattened list