Combine chain of dates where dates are less than few seconds apart

I have a list of timestamps for data acquisition. timestamps close together belong to a cycle. I want to enumerate these cycles. So whenever between two timestamps is more then 100 seconds then it will create the next cycle.

CREATE TABLE [Cycles](
    [Cycle] [int] NOT NULL,
    [CycleStart] [datetime] NOT NULL,
    [CycleEnd] [datetime] NOT NULL,
 CONSTRAINT [PK_Cycles] PRIMARY KEY CLUSTERED 
(
    [Cycle] DESC
))
INSERT INTO [Cycles] VALUES
(10,'2023-12-04T9:00:00','2023-12-04T10:00:00'),
(11,'2023-12-04T21:00:00','2023-12-04T22:00:00'),
(12,'2023-12-04T23:00:00','2023-12-05T00:00:00')

CREATE TABLE [Data](
    [datatimestamp] [datetime] NOT NULL,
 CONSTRAINT [PK_Data] PRIMARY KEY NONCLUSTERED 
(
    [datatimestamp] ASC
))
INSERT INTO [Data] VALUES
('2023-12-05T00:05:20'),
('2023-12-05T00:05:21'),
('2023-12-05T00:05:22'),
('2023-12-05T00:10:01'),
('2023-12-05T00:10:02'),
('2023-12-05T00:10:03')

So I would need to add to Cycles 13 and 14

Here is what I could do as a Select:

DECLARE @lastCycle int = (SELECT TOP 1 Cycle FROM Cycles ORDER BY Cycle DESC);
DECLARE @lastCycleEnd datetime = (SELECT TOP 1 CycleEnd FROM Cycles ORDER BY Cycle DESC);
WITH marks AS (
    SELECT datatimestamp, 
    CASE 
        WHEN DATEDIFF(Second, LAG(datatimestamp, 1, DATEADD(Second, -101, datatimestamp)) OVER (ORDER BY datatimestamp), datatimestamp) > 100 
        THEN 1 ELSE 0 
    END AS NextC
    FROM [Data] 
    WHERE datatimestamp > @lastCycleEnd 
)
SELECT @lastCycle + ROW_NUMBER() OVER (ORDER BY d.datatimestamp) AS Cycle, d.datatimestamp AS CycleBegin 
FROM [Data] d
INNER JOIN marks m On m.datatimestamp = d.datatimestamp
WHERE m.NextC = 1

Which will return the new Cycles and their CycleStarts, as the result for the example data would look like this:

How can I get the CycleEnd aswell as the third column?

Instead of filtering on NextC as the final step, once you have your data from the marks CTE. i.e.

You need to then do SUM(NextC) OVER(ORDER BY datatimestamp), which will give you a value for each group by timestamps, i.e.

You can then group on this column and get the min and max datetimes to get your start/end. So your final query would be:

DECLARE @lastCycle int = (SELECT TOP 1 Cycle FROM Cycles ORDER BY Cycle DESC);
DECLARE @lastCycleEnd datetime = (SELECT TOP 1 CycleEnd FROM Cycles ORDER BY Cycle DESC);
WITH marks AS (
    SELECT datatimestamp, 
   CASE 
        WHEN DATEDIFF(Second, LAG(datatimestamp, 1, DATEADD(Second, -101, datatimestamp)) OVER (ORDER BY datatimestamp), datatimestamp) > 100 
        THEN 1 ELSE 0 
    END AS NextC
    FROM [Data] 
    WHERE datatimestamp > @lastCycleEnd 
), marks2 AS (
  SELECT m.DataTimeStamp, SUM(m.NextC) OVER (ORDER BY m.DataTimeStamp) AS Cycle
  FROM marks AS m)
SELECT @lastCycle + ROW_NUMBER() OVER (ORDER BY m.Cycle) AS Cycle, 
  MIN(m.datatimestamp) AS CycleBegin ,
  MAX(m.datatimestamp) AS CycleEnd
FROM marks2 m 
GROUP BY m.Cycle;

Example on db<>fiddle