Merge overlapping date intervals - sql

Question

Is there a better way of merging overlapping date intervals?
The solution I came up with is so simple that now I wonder if someone else has a better idea of how this could be done.
/***** DATA EXAMPLE *****/
DECLARE #T TABLE (d1 DATETIME, d2 DATETIME)
INSERT INTO #T (d1, d2)
SELECT '2010-01-01','2010-03-31' UNION SELECT '2010-04-01','2010-05-31'
UNION SELECT '2010-06-15','2010-06-25' UNION SELECT '2010-06-26','2010-07-10'
UNION SELECT '2010-08-01','2010-08-05' UNION SELECT '2010-08-01','2010-08-09'
UNION SELECT '2010-08-02','2010-08-07' UNION SELECT '2010-08-08','2010-08-08'
UNION SELECT '2010-08-09','2010-08-12' UNION SELECT '2010-07-04','2010-08-16'
UNION SELECT '2010-11-01','2010-12-31' UNION SELECT '2010-03-01','2010-06-13'
/***** INTERVAL ANALYSIS *****/
WHILE (1=1) BEGIN
UPDATE t1 SET t1.d2 = t2.d2
FROM #T AS t1 INNER JOIN #T AS t2 ON
DATEADD(day, 1, t1.d2) BETWEEN t2.d1 AND t2.d2
IF ##ROWCOUNT = 0 BREAK
END
/***** RESULT *****/
SELECT StartDate = MIN(d1) , EndDate = d2
FROM #T
GROUP BY d2
ORDER BY StartDate, EndDate
/***** OUTPUT *****/
/*****
StartDate EndDate
2010-01-01 2010-06-13
2010-06-15 2010-08-16
2010-11-01 2010-12-31
*****/

Answer 1

I was looking for the same solution and came across this post on Combine overlapping datetime to return single overlapping range record.
There is another thread on Packing Date Intervals.
I tested this with various date ranges, including the ones listed here, and it works correctly every time.
SELECT
s1.StartDate,
--t1.EndDate
MIN(t1.EndDate) AS EndDate
FROM #T s1
INNER JOIN #T t1 ON s1.StartDate <= t1.EndDate
AND NOT EXISTS(SELECT * FROM #T t2
WHERE t1.EndDate >= t2.StartDate AND t1.EndDate < t2.EndDate)
WHERE NOT EXISTS(SELECT * FROM #T s2
WHERE s1.StartDate > s2.StartDate AND s1.StartDate <= s2.EndDate)
GROUP BY s1.StartDate
ORDER BY s1.StartDate
The result is:
StartDate | EndDate
2010-01-01 | 2010-06-13
2010-06-15 | 2010-06-25
2010-06-26 | 2010-08-16
2010-11-01 | 2010-12-31

Answer 2

You asked this back in 2010 but don't specify any particular version.
An answer for people on SQL Server 2012+
WITH T1
AS (SELECT *,
MAX(d2) OVER (ORDER BY d1) AS max_d2_so_far
FROM #T),
T2
AS (SELECT *,
CASE
WHEN d1 <= DATEADD(DAY, 1, LAG(max_d2_so_far) OVER (ORDER BY d1))
THEN 0
ELSE 1
END AS range_start
FROM T1),
T3
AS (SELECT *,
SUM(range_start) OVER (ORDER BY d1) AS range_group
FROM T2)
SELECT range_group,
MIN(d1) AS d1,
MAX(d2) AS d2
FROM T3
GROUP BY range_group
Which returns
+-------------+------------+------------+
| range_group | d1 | d2 |
+-------------+------------+------------+
| 1 | 2010-01-01 | 2010-06-13 |
| 2 | 2010-06-15 | 2010-08-16 |
| 3 | 2010-11-01 | 2010-12-31 |
+-------------+------------+------------+
DATEADD(DAY, 1 is used because your desired results show you want a period ending on 2010-06-25 to be collapsed into one starting 2010-06-26. For other use cases this may need adjusting.

Answer 3

Here is a solution with just three simple scans. No CTEs, no recursion, no joins, no table updates in a loop, no "group by" — as a result, this solution should scale the best (I think).
I think number of scans can be reduced to two, if min and max dates are known in advance;
the logic itself just needs two scans — find gaps, applied twice.
declare #datefrom datetime, #datethru datetime
DECLARE #T TABLE (d1 DATETIME, d2 DATETIME)
INSERT INTO #T (d1, d2)
SELECT '2010-01-01','2010-03-31'
UNION SELECT '2010-03-01','2010-06-13'
UNION SELECT '2010-04-01','2010-05-31'
UNION SELECT '2010-06-15','2010-06-25'
UNION SELECT '2010-06-26','2010-07-10'
UNION SELECT '2010-08-01','2010-08-05'
UNION SELECT '2010-08-01','2010-08-09'
UNION SELECT '2010-08-02','2010-08-07'
UNION SELECT '2010-08-08','2010-08-08'
UNION SELECT '2010-08-09','2010-08-12'
UNION SELECT '2010-07-04','2010-08-16'
UNION SELECT '2010-11-01','2010-12-31'
select #datefrom = min(d1) - 1, #datethru = max(d2) + 1 from #t
SELECT
StartDate, EndDate
FROM
(
SELECT
MAX(EndDate) OVER (ORDER BY StartDate) + 1 StartDate,
LEAD(StartDate ) OVER (ORDER BY StartDate) - 1 EndDate
FROM
(
SELECT
StartDate, EndDate
FROM
(
SELECT
MAX(EndDate) OVER (ORDER BY StartDate) + 1 StartDate,
LEAD(StartDate) OVER (ORDER BY StartDate) - 1 EndDate
FROM
(
SELECT d1 StartDate, d2 EndDate from #T
UNION ALL
SELECT #datefrom StartDate, #datefrom EndDate
UNION ALL
SELECT #datethru StartDate, #datethru EndDate
) T
) T
WHERE StartDate <= EndDate
UNION ALL
SELECT #datefrom StartDate, #datefrom EndDate
UNION ALL
SELECT #datethru StartDate, #datethru EndDate
) T
) T
WHERE StartDate <= EndDate
The result is:
StartDate EndDate
2010-01-01 2010-06-13
2010-06-15 2010-08-16
2010-11-01 2010-12-31

Answer 4

The idea is to simulate the scanning algorithm for merging intervals. My solution makes sure it works across a wide range of SQL implementations. I've tested it on MySQL, Postgres, SQL-Server 2017, SQLite and even Hive.
Assuming the table schema is the following.
CREATE TABLE t (
a DATETIME,
b DATETIME
);
We also assume the interval is half-open like [a,b).
When (a,i,j) is in the table, it shows that there are j intervals covering a, and there are i intervals covering the previous point.
CREATE VIEW r AS
SELECT a,
Sum(d) OVER (ORDER BY a ROWS BETWEEN UNBOUNDED PRECEDING AND 1 PRECEDING) AS i,
Sum(d) OVER (ORDER BY a ROWS UNBOUNDED PRECEDING) AS j
FROM (SELECT a, Sum(d) AS d
FROM (SELECT a, 1 AS d FROM t
UNION ALL
SELECT b, -1 AS d FROM t) e
GROUP BY a) f;
We produce all the endpoints in the union of the intervals and pair up adjacent ones. Finally, we produce the set of intervals by only picking the odd-numbered rows.
SELECT a, b
FROM (SELECT a,
Lead(a) OVER (ORDER BY a) AS b,
Row_number() OVER (ORDER BY a) AS n
FROM r
WHERE j=0 OR i=0 OR i is null) e
WHERE n%2 = 1;
I've created a sample DB-fiddle and SQL-fiddle. I also wrote a blog post on union intervals in SQL.

Answer 5

A Geometric Approach
Here and elsewhere I've noticed that date packing questions don't provide a geometric approach to this problem. After all, any range, date-ranges included, can be interpreted as a line. So why not convert them to a sql geometry type and utilize geometry::UnionAggregate to merge the ranges.
Why?
This has the advantage of handling all types of overlaps, including fully nested ranges. It also works like any other aggregate query, so it's a little more intuitive in that respect. You also get the bonus of a visual representation of your results if you care to use it. Finally, it is the approach I use for simultaneous range packing (you work with rectangles instead of lines in that case, and there are many more considerations). I just couldn't get the existing approaches to work in that scenario.
This has the disadvantage of requiring more recent versions of SQL Server. It also requires a numbers table and it's annoying to extract the individually produced lines from the aggregated shape. But hopefully in the future Microsoft adds a TVF that allows you to do this easily without a numbers table (or you can just build one yourself). Also, geometrical objects work with floats, so you have conversion annoyances and precision concerns to keep in mind.
Performance-wise I don't know how it compares, but I've done a few things (not shown here) to make it work for me even with large datasets.
Code Description
In 'numbers':
I build a table representing a sequence
Swap it out with your favorite way to make a numbers table.
For a union operation, you won't ever need more rows than in
your original table, so I just use it as the base to build it.
In 'mergeLines':
I convert the dates to floats and use those floats
to create geometrical points.
In this problem, we're working in
'integer space,' meaning there are no time considerations, and so
an begin date in one range that is one day apart from an end date
in another should be merged with that other. In order to make
that merge happen, we need to convert to 'real space.', so we
add 1 to the tail of all ranges (we undo this later).
I then connect these points via STUnion and STEnvelope.
Finally, I merge all these lines via UnionAggregate. The resulting
'lines' geometry object might contain multiple lines, but if they
overlap, they turn into one line.
In the outer query:
I use the numbers CTE to extract the individual lines inside 'lines'.
I envelope the lines which here ensures that the lines are stored
only as its two endpoints.
I read the endpoint x values and convert them back to their time
representations, ensuring to put them back into 'integer space'.
The Code
with
numbers as (
select row_number() over (order by (select null)) i
from #t
),
mergeLines as (
select lines = geometry::UnionAggregate(line)
from #t
cross apply (select line =
geometry::Point(convert(float, d1), 0, 0).STUnion(
geometry::Point(convert(float, d2) + 1, 0, 0)
).STEnvelope()
) l
)
select ap.StartDate,
ap.EndDate
from mergeLines ml
join numbers n on n.i between 1 and ml.lines.STNumGeometries()
cross apply (select line = ml.lines.STGeometryN(i).STEnvelope()) l
cross apply (select
StartDate = convert(datetime,l.line.STPointN(1).STX),
EndDate = convert(datetime,l.line.STPointN(3).STX) - 1
) ap
order by ap.StartDate;

Answer 6

In this solution, I created a temporary Calendar table which stores a value for every day across a range. This type of table can be made static. In addition, I'm only storing 400 some odd dates starting with 2009-12-31. Obviously, if your dates span a larger range, you would need more values.
In addition, this solution will only work with SQL Server 2005+ in that I'm using a CTE.
With Calendar As
(
Select DateAdd(d, ROW_NUMBER() OVER ( ORDER BY s1.object_id ), '1900-01-01') As [Date]
From sys.columns as s1
Cross Join sys.columns as s2
)
, StopDates As
(
Select C.[Date]
From Calendar As C
Left Join #T As T
On C.[Date] Between T.d1 And T.d2
Where C.[Date] >= ( Select Min(T2.d1) From #T As T2 )
And C.[Date] <= ( Select Max(T2.d2) From #T As T2 )
And T.d1 Is Null
)
, StopDatesInUse As
(
Select D1.[Date]
From StopDates As D1
Left Join StopDates As D2
On D1.[Date] = DateAdd(d,1,D2.Date)
Where D2.[Date] Is Null
)
, DataWithEariestStopDate As
(
Select *
, (Select Min(SD2.[Date])
From StopDatesInUse As SD2
Where T.d2 < SD2.[Date] ) As StopDate
From #T As T
)
Select Min(d1), Max(d2)
From DataWithEariestStopDate
Group By StopDate
Order By Min(d1)
EDIT The problem with using dates in 2009 has nothing to do with the final query. The problem is that the Calendar table is not big enough. I started the Calendar table at 2009-12-31. I have revised it start at 1900-01-01.

Answer 7

Try this
;WITH T1 AS
(
SELECT d1, d2, ROW_NUMBER() OVER(ORDER BY (SELECT 0)) AS R
FROM #T
), NUMS AS
(
SELECT ROW_NUMBER() OVER(ORDER BY (SELECT 0)) AS R
FROM T1 A
CROSS JOIN T1 B
CROSS JOIN T1 C
), ONERANGE AS
(
SELECT DISTINCT DATEADD(DAY, ROW_NUMBER() OVER(PARTITION BY T1.R ORDER BY (SELECT 0)) - 1, T1.D1) AS ELEMENT
FROM T1
CROSS JOIN NUMS
WHERE NUMS.R <= DATEDIFF(DAY, d1, d2) + 1
), SEQUENCE AS
(
SELECT ELEMENT, DATEDIFF(DAY, '19000101', ELEMENT) - ROW_NUMBER() OVER(ORDER BY ELEMENT) AS rownum
FROM ONERANGE
)
SELECT MIN(ELEMENT) AS StartDate, MAX(ELEMENT) as EndDate
FROM SEQUENCE
GROUP BY rownum
The basic idea is to first unroll the existing data, so you get a separate row for each day. This is done in ONERANGE
Then, identify the relationship between how dates increment and the way the row numbers do.
The difference remains constant within an existing range/island. As soon as you get to a new data island, the difference between them increases because the date increments by more than 1, while the row number increments by 1.

Answer 8

This Solution is similar to the 1st solution with additional Deletion Condition.
This will sort the data in the main table itself instead of using different table to store the result.
DROP TABLE IF EXISTS #SampleTable;
CREATE TABLE #SampleTable (StartTime DATETIME NULL, EndTime DATETIME NULL);
INSERT INTO #SampleTable(StartTime, EndTime)
VALUES
(N'2010-01-01T00:00:00', N'2010-03-31T00:00:00'),
(N'2010-03-01T00:00:00', N'2010-06-13T00:00:00'),
(N'2010-04-01T00:00:00', N'2010-05-31T00:00:00'),
(N'2010-06-15T00:00:00', N'2010-06-25T00:00:00'),
(N'2010-06-26T00:00:00', N'2010-07-10T00:00:00'),
(N'2010-07-04T00:00:00', N'2010-08-16T00:00:00'),
(N'2010-08-01T00:00:00', N'2010-08-05T00:00:00'),
(N'2010-08-01T00:00:00', N'2010-08-09T00:00:00'),
(N'2010-08-02T00:00:00', N'2010-08-07T00:00:00'),
(N'2010-08-08T00:00:00', N'2010-08-08T00:00:00'),
(N'2010-08-09T00:00:00', N'2010-08-12T00:00:00'),
(N'2010-11-01T00:00:00', N'2010-12-31T00:00:00');
--
DECLARE #RowCount INT=0;
WHILE(1=1) --
BEGIN
SET #RowCount=0;
--
UPDATE T1
SET T1.EndTime=T2.EndTime
FROM dbo.#SampleTable AS T1
INNER JOIN dbo.#SampleTable AS T2 ON DATEADD(DAY, 1, T1.EndTime) BETWEEN T2.StartTime AND T2.EndTime;
--
SET #RowCount=#RowCount+##ROWCOUNT;
--
DELETE T1
FROM dbo.#SampleTable AS T1
INNER JOIN dbo.#SampleTable AS T2 ON T1.EndTime=T2.EndTime AND T1.StartTime>T2.StartTime;
--
SET #RowCount=#RowCount+##ROWCOUNT;
--
IF #RowCount=0 --
BREAK;
END;
SELECT * FROM #SampleTable

Answer 9

I was inspired by the Geometric Approach given by pwilcox, but wanted to try a different approach. This is using Trino, but I hope the functions used can also be found in other versions of SQL.
WITH Geo AS (
SELECT
transform( -- 6) See Below~
ST_Geometries( -- 5) Extracts an array of individual lines from the union.
geometry_union( -- 4) Returns the union of aggregated lines, melding all lines together into a single geometric multi-line.
array_agg( -- 3) Aggregation function that joins all lines together.
ST_LineString( -- 2) Makes the pairs of geometric points into lines.
ARRAY[ST_Point(0, to_unixtime(d1)), ST_Point(0, to_unixtime(d2))] -- 1) Takes unix time start and end values and makes them into an array of geometric points.
)
)
)
)
, x -> (ST_YMin(x), ST_Length(x))) AS timestamp_duration -- 6) From the array of lines, The minimum value and length of each line is extracted.
FROM #T -- The miniumum value is a timestamp, length is duration.
WHERE d1 <> d2 -- I had errors any time this was the case.
)
-- 7) Finally, I unnest the produced array and convert the values back into timestamps.
SELECT from_unixtime(timestamp) AS StartDate
, from_unixtime(timestamp + duration) AS EndDate
FROM Geo
CROSS JOIN UNNEST(timestamp_duration) AS t(timestamp, duration)
For reference, this took my company cluster about 2 minutes to make 400k start/end timestamps into 700 distinct start/end timestamps.
It also runs in just 2 stages.