Sql-server – Group daily schedule into [Start date; End date] intervals with the list of week days

gaps-and-islandssql serversql-server-2008

I need to convert data between two systems.

First system stores schedules as a plain list of dates. Each date that is included in the schedule is one row.
There can be various gaps in the sequence of dates (weekends, public holidays and longer pauses, some days of the week may be excluded from the schedule). There can be no gaps at all, even weekends can be included. The schedule can be up to 2 years long. Usually it is few weeks long.

Here is a simple example of a schedule that spans two weeks excluding weekends (there are more complicated examples in the script below):

+----+------------+------------+---------+--------+
| ID | ContractID |     dt     | dowChar | dowInt |
+----+------------+------------+---------+--------+
| 10 |          1 | 2016-05-02 | Mon     |      2 |
| 11 |          1 | 2016-05-03 | Tue     |      3 |
| 12 |          1 | 2016-05-04 | Wed     |      4 |
| 13 |          1 | 2016-05-05 | Thu     |      5 |
| 14 |          1 | 2016-05-06 | Fri     |      6 |
| 15 |          1 | 2016-05-09 | Mon     |      2 |
| 16 |          1 | 2016-05-10 | Tue     |      3 |
| 17 |          1 | 2016-05-11 | Wed     |      4 |
| 18 |          1 | 2016-05-12 | Thu     |      5 |
| 19 |          1 | 2016-05-13 | Fri     |      6 |
+----+------------+------------+---------+--------+

ID is unique, but it is not necessarily sequential (it is primary key).
Dates are unique within each Contract (there is unique index on (ContractID, dt)).

Second system stores schedules as intervals with the list of week days that are part of the schedule. Each interval is defined by its start and end dates (inclusive) and a list of week days that are included in the schedule. In this format you can efficiently define repetitive weekly patterns, such as Mon-Wed, but it becomes a pain when a pattern is disrupted, for example by public holiday.

Here is how the simple example above will look like:

+------------+------------+------------+----------+----------------------+
| ContractID |  StartDT   |   EndDT    | DayCount |       WeekDays       |
+------------+------------+------------+----------+----------------------+
|          1 | 2016-05-02 | 2016-05-13 |       10 | Mon,Tue,Wed,Thu,Fri, |
+------------+------------+------------+----------+----------------------+

[StartDT;EndDT] intervals that belong to the same Contract should not overlap.

I need to convert data from the first system into the format used by the second system.
At the moment I'm solving this on the client side in C# for the single given Contract,
but I'd like to do it in T-SQL on the server side for bulk processing and export/import between servers.
Most likely, it could be done using CLR UDF, but at this stage I can't use SQLCLR.

The challenge here is to make the list of intervals as short and human-friendly as possible.

For example, this schedule:

+-----+------------+------------+---------+--------+
| ID  | ContractID |     dt     | dowChar | dowInt |
+-----+------------+------------+---------+--------+
| 223 |          2 | 2016-05-05 | Thu     |      5 |
| 224 |          2 | 2016-05-06 | Fri     |      6 |
| 225 |          2 | 2016-05-09 | Mon     |      2 |
| 226 |          2 | 2016-05-10 | Tue     |      3 |
| 227 |          2 | 2016-05-11 | Wed     |      4 |
| 228 |          2 | 2016-05-12 | Thu     |      5 |
| 229 |          2 | 2016-05-13 | Fri     |      6 |
| 230 |          2 | 2016-05-16 | Mon     |      2 |
| 231 |          2 | 2016-05-17 | Tue     |      3 |
+-----+------------+------------+---------+--------+

should become this:

+------------+------------+------------+----------+----------------------+
| ContractID |  StartDT   |   EndDT    | DayCount |       WeekDays       |
+------------+------------+------------+----------+----------------------+
|          2 | 2016-05-05 | 2016-05-17 |        9 | Mon,Tue,Wed,Thu,Fri, |
+------------+------------+------------+----------+----------------------+

,not this:

+------------+------------+------------+----------+----------------------+
| ContractID |  StartDT   |   EndDT    | DayCount |       WeekDays       |
+------------+------------+------------+----------+----------------------+
|          2 | 2016-05-05 | 2016-05-06 |        2 | Thu,Fri,             |
|          2 | 2016-05-09 | 2016-05-13 |        5 | Mon,Tue,Wed,Thu,Fri, |
|          2 | 2016-05-16 | 2016-05-17 |        2 | Mon,Tue,             |
+------------+------------+------------+----------+----------------------+

I tried to apply a gaps-and-islands approach to this problem. I tried to do it in two passes. In the first pass I find islands of simple consecutive days, i.e. the end of the island is any gap in the sequence of days, be it weekend, public holiday or something else. For each such found island I build a comma-separated list of distinct WeekDays. In the second pass I group found islands further by looking at the gap in the sequence of week numbers or a change in the WeekDays.

With this approach each partial week ends up as an extra interval as shown above, because even though week numbers are consecutive, the WeekDays change. Besides, there can be regular gaps within a week (see ContractID=3 in sample data, which has data only for Mon,Wed,Fri,) and this approach would generate separate intervals for each day in such schedule. On the bright side, it generates one interval if the schedule doesn't have any gaps at all (see ContractID=7 in the sample data that includes weekends) and in that case it doesn't matter if the start or end week is partial.

Please see other examples in the script below to get a better idea of what I'm after. You can see that quite often weekends are excluded, but any other days of the week could also be excluded. In example 3 only Mon, Wed and Fri are part of the schedule. Besides, weekends can be included, as in example 7. The solution should treat all days of the week equally. Any day of the week can be included or excluded from the schedule.

To verify that the generated list of intervals describes the given schedule correctly you can use the following pseudo-code:

  • loop through all intervals
  • for each interval loop through all calendar dates between Start and End dates (inclusive).
  • for each date check if its day of the week is listed in the WeekDays. If yes, then this date is included in the schedule.

Hopefully, this clarifies in what cases a new interval should be created. In examples 4 and 5 one Monday (2016-05-09) is removed from the middle of the schedule and such schedule can't be represented by a single interval. In example 6 there is a long gap in the schedule, so two intervals are needed.

Intervals represent weekly patterns in the schedule and when a pattern is disrupted/changed the new interval has to be added. In example 11 first three weeks have a pattern Tue, then this pattern changes to Thu. As a result we need two intervals to describe such schedule.

I'm using SQL Server 2008 at the moment, so solution should work in this version.
If a solution for SQL Server 2008 can be simplified/improved using features from later versions, that's a bonus, please show it as well.

I have a Calendar table (list of dates) and Numbers table (list of integer numbers starting from 1), so it is OK to use them, if needed. It is also OK to create temporary tables and have several queries that process data in several stages. The number of stages in an algorithm has to be fixed though, cursors and explicit WHILE loops are not OK.

Script for sample data and expected results

-- @Src is sample data
-- @Dst is expected result

DECLARE @Src TABLE (ID int PRIMARY KEY, ContractID int, dt date, dowChar char(3), dowInt int);
INSERT INTO @Src (ID, ContractID, dt, dowChar, dowInt) VALUES

-- simple two weeks (without weekend)
(110, 1, '2016-05-02', 'Mon', 2),
(111, 1, '2016-05-03', 'Tue', 3),
(112, 1, '2016-05-04', 'Wed', 4),
(113, 1, '2016-05-05', 'Thu', 5),
(114, 1, '2016-05-06', 'Fri', 6),
(115, 1, '2016-05-09', 'Mon', 2),
(116, 1, '2016-05-10', 'Tue', 3),
(117, 1, '2016-05-11', 'Wed', 4),
(118, 1, '2016-05-12', 'Thu', 5),
(119, 1, '2016-05-13', 'Fri', 6),

-- a partial end of the week, the whole week, partial start of the week (without weekends)
(223, 2, '2016-05-05', 'Thu', 5),
(224, 2, '2016-05-06', 'Fri', 6),
(225, 2, '2016-05-09', 'Mon', 2),
(226, 2, '2016-05-10', 'Tue', 3),
(227, 2, '2016-05-11', 'Wed', 4),
(228, 2, '2016-05-12', 'Thu', 5),
(229, 2, '2016-05-13', 'Fri', 6),
(230, 2, '2016-05-16', 'Mon', 2),
(231, 2, '2016-05-17', 'Tue', 3),

-- only Mon, Wed, Fri are included across two weeks plus partial third week
(310, 3, '2016-05-02', 'Mon', 2),
(311, 3, '2016-05-04', 'Wed', 4),
(314, 3, '2016-05-06', 'Fri', 6),
(315, 3, '2016-05-09', 'Mon', 2),
(317, 3, '2016-05-11', 'Wed', 4),
(319, 3, '2016-05-13', 'Fri', 6),
(330, 3, '2016-05-16', 'Mon', 2),

-- a whole week (without weekend), in the second week Mon is not included
(410, 4, '2016-05-02', 'Mon', 2),
(411, 4, '2016-05-03', 'Tue', 3),
(412, 4, '2016-05-04', 'Wed', 4),
(413, 4, '2016-05-05', 'Thu', 5),
(414, 4, '2016-05-06', 'Fri', 6),
(416, 4, '2016-05-10', 'Tue', 3),
(417, 4, '2016-05-11', 'Wed', 4),
(418, 4, '2016-05-12', 'Thu', 5),
(419, 4, '2016-05-13', 'Fri', 6),

-- three weeks, but without Mon in the second week (no weekends)
(510, 5, '2016-05-02', 'Mon', 2),
(511, 5, '2016-05-03', 'Tue', 3),
(512, 5, '2016-05-04', 'Wed', 4),
(513, 5, '2016-05-05', 'Thu', 5),
(514, 5, '2016-05-06', 'Fri', 6),
(516, 5, '2016-05-10', 'Tue', 3),
(517, 5, '2016-05-11', 'Wed', 4),
(518, 5, '2016-05-12', 'Thu', 5),
(519, 5, '2016-05-13', 'Fri', 6),
(520, 5, '2016-05-16', 'Mon', 2),
(521, 5, '2016-05-17', 'Tue', 3),
(522, 5, '2016-05-18', 'Wed', 4),
(523, 5, '2016-05-19', 'Thu', 5),
(524, 5, '2016-05-20', 'Fri', 6),

-- long gap between two intervals
(623, 6, '2016-05-05', 'Thu', 5),
(624, 6, '2016-05-06', 'Fri', 6),
(625, 6, '2016-05-09', 'Mon', 2),
(626, 6, '2016-05-10', 'Tue', 3),
(627, 6, '2016-05-11', 'Wed', 4),
(628, 6, '2016-05-12', 'Thu', 5),
(629, 6, '2016-05-13', 'Fri', 6),
(630, 6, '2016-05-16', 'Mon', 2),
(631, 6, '2016-05-17', 'Tue', 3),
(645, 6, '2016-06-06', 'Mon', 2),
(646, 6, '2016-06-07', 'Tue', 3),
(647, 6, '2016-06-08', 'Wed', 4),
(648, 6, '2016-06-09', 'Thu', 5),
(649, 6, '2016-06-10', 'Fri', 6),
(655, 6, '2016-06-13', 'Mon', 2),
(656, 6, '2016-06-14', 'Tue', 3),
(657, 6, '2016-06-15', 'Wed', 4),
(658, 6, '2016-06-16', 'Thu', 5),
(659, 6, '2016-06-17', 'Fri', 6),

-- two weeks, no gaps between days at all, even weekends are included
(710, 7, '2016-05-02', 'Mon', 2),
(711, 7, '2016-05-03', 'Tue', 3),
(712, 7, '2016-05-04', 'Wed', 4),
(713, 7, '2016-05-05', 'Thu', 5),
(714, 7, '2016-05-06', 'Fri', 6),
(715, 7, '2016-05-07', 'Sat', 7),
(716, 7, '2016-05-08', 'Sun', 1),
(725, 7, '2016-05-09', 'Mon', 2),
(726, 7, '2016-05-10', 'Tue', 3),
(727, 7, '2016-05-11', 'Wed', 4),
(728, 7, '2016-05-12', 'Thu', 5),
(729, 7, '2016-05-13', 'Fri', 6),

-- no gaps between days at all, even weekends are included, with partial weeks
(805, 8, '2016-04-30', 'Sat', 7),
(806, 8, '2016-05-01', 'Sun', 1),
(810, 8, '2016-05-02', 'Mon', 2),
(811, 8, '2016-05-03', 'Tue', 3),
(812, 8, '2016-05-04', 'Wed', 4),
(813, 8, '2016-05-05', 'Thu', 5),
(814, 8, '2016-05-06', 'Fri', 6),
(815, 8, '2016-05-07', 'Sat', 7),
(816, 8, '2016-05-08', 'Sun', 1),
(825, 8, '2016-05-09', 'Mon', 2),
(826, 8, '2016-05-10', 'Tue', 3),
(827, 8, '2016-05-11', 'Wed', 4),
(828, 8, '2016-05-12', 'Thu', 5),
(829, 8, '2016-05-13', 'Fri', 6),
(830, 8, '2016-05-14', 'Sat', 7),

-- only Mon-Wed included, two weeks plus partial third week
(910, 9, '2016-05-02', 'Mon', 2),
(911, 9, '2016-05-03', 'Tue', 3),
(912, 9, '2016-05-04', 'Wed', 4),
(915, 9, '2016-05-09', 'Mon', 2),
(916, 9, '2016-05-10', 'Tue', 3),
(917, 9, '2016-05-11', 'Wed', 4),
(930, 9, '2016-05-16', 'Mon', 2),
(931, 9, '2016-05-17', 'Tue', 3),

-- only Thu-Sun included, three weeks
(1013,10,'2016-05-05', 'Thu', 5),
(1014,10,'2016-05-06', 'Fri', 6),
(1015,10,'2016-05-07', 'Sat', 7),
(1016,10,'2016-05-08', 'Sun', 1),
(1018,10,'2016-05-12', 'Thu', 5),
(1019,10,'2016-05-13', 'Fri', 6),
(1020,10,'2016-05-14', 'Sat', 7),
(1021,10,'2016-05-15', 'Sun', 1),
(1023,10,'2016-05-19', 'Thu', 5),
(1024,10,'2016-05-20', 'Fri', 6),
(1025,10,'2016-05-21', 'Sat', 7),
(1026,10,'2016-05-22', 'Sun', 1),

-- only Tue for first three weeks, then only Thu for the next three weeks
(1111,11,'2016-05-03', 'Tue', 3),
(1116,11,'2016-05-10', 'Tue', 3),
(1131,11,'2016-05-17', 'Tue', 3),
(1123,11,'2016-05-19', 'Thu', 5),
(1124,11,'2016-05-26', 'Thu', 5),
(1125,11,'2016-06-02', 'Thu', 5),

-- one week, then one week gap, then one week
(1210,12,'2016-05-02', 'Mon', 2),
(1211,12,'2016-05-03', 'Tue', 3),
(1212,12,'2016-05-04', 'Wed', 4),
(1213,12,'2016-05-05', 'Thu', 5),
(1214,12,'2016-05-06', 'Fri', 6),
(1215,12,'2016-05-16', 'Mon', 2),
(1216,12,'2016-05-17', 'Tue', 3),
(1217,12,'2016-05-18', 'Wed', 4),
(1218,12,'2016-05-19', 'Thu', 5),
(1219,12,'2016-05-20', 'Fri', 6);

SELECT ID, ContractID, dt, dowChar, dowInt
FROM @Src
ORDER BY ContractID, dt;


DECLARE @Dst TABLE (ContractID int, StartDT date, EndDT date, DayCount int, WeekDays varchar(255));
INSERT INTO @Dst (ContractID, StartDT, EndDT, DayCount, WeekDays) VALUES
(1, '2016-05-02', '2016-05-13', 10, 'Mon,Tue,Wed,Thu,Fri,'),
(2, '2016-05-05', '2016-05-17',  9, 'Mon,Tue,Wed,Thu,Fri,'),
(3, '2016-05-02', '2016-05-16',  7, 'Mon,Wed,Fri,'),
(4, '2016-05-02', '2016-05-06',  5, 'Mon,Tue,Wed,Thu,Fri,'),
(4, '2016-05-10', '2016-05-13',  4, 'Tue,Wed,Thu,Fri,'),
(5, '2016-05-02', '2016-05-06',  5, 'Mon,Tue,Wed,Thu,Fri,'),
(5, '2016-05-10', '2016-05-20',  9, 'Mon,Tue,Wed,Thu,Fri,'),
(6, '2016-05-05', '2016-05-17',  9, 'Mon,Tue,Wed,Thu,Fri,'),
(6, '2016-06-06', '2016-06-17', 10, 'Mon,Tue,Wed,Thu,Fri,'),
(7, '2016-05-02', '2016-05-13', 12, 'Sun,Mon,Tue,Wed,Thu,Fri,Sat,'),
(8, '2016-04-30', '2016-05-14', 15, 'Sun,Mon,Tue,Wed,Thu,Fri,Sat,'),
(9, '2016-05-02', '2016-05-17',  8, 'Mon,Tue,Wed,'),
(10,'2016-05-05', '2016-05-22', 12, 'Sun,Thu,Fri,Sat,'),
(11,'2016-05-03', '2016-05-17',  3, 'Tue,'),
(11,'2016-05-19', '2016-06-02',  3, 'Thu,'),
(12,'2016-05-02', '2016-05-06',  5, 'Mon,Tue,Wed,Thu,Fri,'),
(12,'2016-05-16', '2016-05-20',  5, 'Mon,Tue,Wed,Thu,Fri,');

SELECT ContractID, StartDT, EndDT, DayCount, WeekDays
FROM @Dst
ORDER BY ContractID, StartDT;

Comparison of answers

The real table @Src has 403,555 rows with 15,857 distinct ContractIDs.
All answers produce correct results (at least for my data) and all of them are reasonably fast, but they differ in optimality. The less intervals generated, the better. I included run times just for curiosity. The main focus is the correct and optimal result, not the speed (unless it takes too long – I stopped the non-recursive query by Ziggy Crueltyfree Zeitgeister after 10 minutes).

+--------------------------------------------------------+-----------+---------+
|                         Answer                         | Intervals | Seconds |
+--------------------------------------------------------+-----------+---------+
| Ziggy Crueltyfree Zeitgeister                          |     25751 |    7.88 |
| While loop                                             |           |         |
|                                                        |           |         |
| Ziggy Crueltyfree Zeitgeister                          |     25751 |    8.27 |
| Recursive                                              |           |         |
|                                                        |           |         |
| Michael Green                                          |     25751 |   22.63 |
| Recursive                                              |           |         |
|                                                        |           |         |
| Geoff Patterson                                        |     26670 |    4.79 |
| Weekly gaps-and-islands with merging of partial weeks  |           |         |
|                                                        |           |         |
| Vladimir Baranov                                       |     34560 |    4.03 |
| Daily, then weekly gaps-and-islands                    |           |         |
|                                                        |           |         |
| Mikael Eriksson                                        |     35840 |    0.65 |
| Weekly gaps-and-islands                                |           |         |
+--------------------------------------------------------+-----------+---------+
| Vladimir Baranov                                       |     25751 |  121.51 |
| Cursor                                                 |           |         |
+--------------------------------------------------------+-----------+---------+

Best Answer

This one uses a recursive CTE. Its result is identical to the example in the question. It was a nightmare to come up with... The code includes comments to ease through its convoluted logic.

SET DATEFIRST 1 -- Make Monday weekday=1

DECLARE @Ranked TABLE (RowID int NOT NULL IDENTITY PRIMARY KEY,                   -- Incremental uninterrupted sequence in the right order
                       ID int NOT NULL UNIQUE, ContractID int NOT NULL, dt date,  -- Original relevant values (ID is not really necessary)
                       WeekNo int NOT NULL, dowBit int NOT NULL);                 -- Useful to find gaps in days or weeks
INSERT INTO @Ranked
SELECT ID, ContractID, dt,
       DATEDIFF(WEEK, '1900-01-01', DATEADD(DAY, 1-DATEPART(dw, dt), dt)) AS WeekNo,
       POWER(2, DATEPART(dw, dt)-1) AS dowBit
FROM @Src
ORDER BY ContractID, WeekNo, dowBit

/*
Each evaluated date makes part of the carried sequence if:
  - this is not a new contract, and
    - sequence started this week, or
    - same day last week was part of the sequence, or
    - sequence started last week and today is a lower day than the accumulated weekdays list
  - and there are no sequence gaps since previous day
(otherwise it does not make part of the old sequence, so it starts a new one) */

DECLARE @RankedRanges TABLE (RowID int NOT NULL PRIMARY KEY, WeekDays int NOT NULL, StartRowID int NULL);

WITH WeeksCTE AS -- Needed for building the sequence gradually, and comparing the carried sequence (and previous day) with a current evaluated day
( 
    SELECT RowID, ContractID, dowBit, WeekNo, RowID AS StartRowID, WeekNo AS StartWN, dowBit AS WeekDays, dowBit AS StartWeekDays
    FROM @Ranked
    WHERE RowID = 1 
    UNION ALL
    SELECT RowID, ContractID, dowBit, WeekNo, StartRowID,
           CASE WHEN StartRowID IS NULL THEN StartWN ELSE WeekNo END AS WeekNo,
           CASE WHEN StartRowID IS NULL THEN WeekDays | dowBit ELSE dowBit END AS WeekDays,
           CASE WHEN StartRowID IS NOT NULL THEN dowBit WHEN WeekNo = StartWN THEN StartWeekDays | dowBit ELSE StartWeekDays END AS StartWeekDays
    FROM (
        SELECT w.*, pre.StartWN, pre.WeekDays, pre.StartWeekDays,
               CASE WHEN w.ContractID <> pre.ContractID OR     -- New contract always break the sequence
                         NOT (w.WeekNo = pre.StartWN OR        -- Same week as a new sequence always keeps the sequence
                              w.dowBit & pre.WeekDays > 0 OR   -- Days in the sequence keep the sequence (provided there are no gaps, checked later)
                              (w.WeekNo = pre.StartWN+1 AND (w.dowBit-1) & pre.StartWeekDays = 0)) OR -- Days in the second week when less than a week passed since the sequence started remain in sequence
                         (w.WeekNo > pre.StartWN AND -- look for gap after initial week
                          w.WeekNo > pre.WeekNo+1 OR -- look for full-week gaps
                          (w.WeekNo = pre.WeekNo AND                            -- when same week as previous day,
                           ((w.dowBit-1) ^ (pre.dowBit*2-1)) & pre.WeekDays > 0 -- days between this and previous weekdays, compared to current series
                          ) OR
                          (w.WeekNo > pre.WeekNo AND                                   -- when following week of previous day,
                           ((-1 ^ (pre.dowBit*2-1)) | (w.dowBit-1)) & pre.WeekDays > 0 -- days between this and previous weekdays, compared to current series
                          )) THEN w.RowID END AS StartRowID
        FROM WeeksCTE pre
        JOIN @Ranked w ON (w.RowID = pre.RowID + 1)
        ) w
) 
INSERT INTO @RankedRanges -- days sequence and starting point of each sequence
SELECT RowID, WeekDays, StartRowID
--SELECT *
FROM WeeksCTE
OPTION (MAXRECURSION 0)

--SELECT * FROM @RankedRanges

DECLARE @Ranges TABLE (RowNo int NOT NULL IDENTITY PRIMARY KEY, RowID int NOT NULL);

INSERT INTO @Ranges       -- @RankedRanges filtered only by start of each range, with numbered rows to easily find the end of each range
SELECT StartRowID
FROM @RankedRanges
WHERE StartRowID IS NOT NULL
ORDER BY 1

-- Final result putting everything together
SELECT rs.ContractID, rs.dt AS StartDT, re.dt AS EndDT, re.RowID-rs.RowID+1 AS DayCount,
       CASE WHEN rr.WeekDays & 64 > 0 THEN 'Sun,' ELSE '' END +
       CASE WHEN rr.WeekDays & 1 > 0 THEN 'Mon,' ELSE '' END +
       CASE WHEN rr.WeekDays & 2 > 0 THEN 'Tue,' ELSE '' END +
       CASE WHEN rr.WeekDays & 4 > 0 THEN 'Wed,' ELSE '' END +
       CASE WHEN rr.WeekDays & 8 > 0 THEN 'Thu,' ELSE '' END +
       CASE WHEN rr.WeekDays & 16 > 0 THEN 'Fri,' ELSE '' END +
       CASE WHEN rr.WeekDays & 32 > 0 THEN 'Sat,' ELSE '' END AS WeekDays
FROM (
    SELECT r.RowID AS StartRowID, COALESCE(pos.RowID-1, (SELECT MAX(RowID) FROM @Ranked)) AS EndRowID
    FROM @Ranges r
    LEFT JOIN @Ranges pos ON (pos.RowNo = r.RowNo + 1)
    ) g
JOIN @Ranked rs ON (rs.RowID = g.StartRowID)
JOIN @Ranked re ON (re.RowID = g.EndRowID)
JOIN @RankedRanges rr ON (rr.RowID = re.RowID)

Another strategy

This one should be significantly faster than the previous one because it doesn't rely on the slow limited recursive CTE in SQL Server 2008, although it implements more or less the same strategy.

There is a WHILE loop (I couldn't devise a way to avoid it), but goes for a reduced number of iterations (the highest number of sequences (minus one) on any given contract).

It's a simple strategy, and could be used for sequences either shorter or longer than a week (replacing any occurrence of the constant 7 for any other number, and the dowBit calculated from MODULUS x of DayNo rather than DATEPART(wk)) and up to 32.

SET DATEFIRST 1 -- Make Monday weekday=1

-- Get the minimum information needed to calculate sequences
DECLARE @Days TABLE (ContractID int NOT NULL, dt date, DayNo int NOT NULL, dowBit int NOT NULL, PRIMARY KEY (ContractID, DayNo));
INSERT INTO @Days
SELECT ContractID, dt, CAST(CAST(dt AS datetime) AS int) AS DayNo, POWER(2, DATEPART(dw, dt)-1) AS dowBit
FROM @Src

DECLARE @RangeStartFirstPass TABLE (ContractID int NOT NULL, DayNo int NOT NULL, PRIMARY KEY (ContractID, DayNo))

-- Calculate, from the above list, which days are not present in the previous 7
INSERT INTO @RangeStartFirstPass
SELECT r.ContractID, r.DayNo
FROM @Days r
LEFT JOIN @Days pr ON (pr.ContractID = r.ContractID AND pr.DayNo BETWEEN r.DayNo-7 AND r.DayNo-1) -- Last 7 days
GROUP BY r.ContractID, r.DayNo, r.dowBit
HAVING r.dowBit & COALESCE(SUM(pr.dowBit), 0) = 0

-- Update the previous list with all days that occur right after a missing day
INSERT INTO @RangeStartFirstPass
SELECT *
FROM (
    SELECT DISTINCT ContractID, (SELECT MIN(DayNo) FROM @Days WHERE ContractID = d.ContractID AND DayNo > d.DayNo + 7) AS DayNo
    FROM @Days d
    WHERE NOT EXISTS (SELECT 1 FROM @Days WHERE ContractID = d.ContractID AND DayNo = d.DayNo + 7)
    ) d
WHERE DayNo IS NOT NULL AND
      NOT EXISTS (SELECT 1 FROM @RangeStartFirstPass WHERE ContractID = d.ContractID AND DayNo = d.DayNo)

DECLARE @RangeStart TABLE (ContractID int NOT NULL, DayNo int NOT NULL, PRIMARY KEY (ContractID, DayNo));

-- Fetch the first sequence for each contract
INSERT INTO @RangeStart
SELECT ContractID, MIN(DayNo)
FROM @RangeStartFirstPass
GROUP BY ContractID

-- Add to the list above the next sequence for each contract, until all are added
-- (ensure no sequence is added with less than 7 days)
WHILE @@ROWCOUNT > 0
  INSERT INTO @RangeStart
  SELECT f.ContractID, MIN(f.DayNo)
  FROM (SELECT ContractID, MAX(DayNo) AS DayNo FROM @RangeStart GROUP BY ContractID) s
  JOIN @RangeStartFirstPass f ON (f.ContractID = s.ContractID AND f.DayNo > s.DayNo + 7)
  GROUP BY f.ContractID

-- Summarise results
SELECT ContractID, StartDT, EndDT, DayCount,
       CASE WHEN WeekDays & 64 > 0 THEN 'Sun,' ELSE '' END +
       CASE WHEN WeekDays & 1 > 0 THEN 'Mon,' ELSE '' END +
       CASE WHEN WeekDays & 2 > 0 THEN 'Tue,' ELSE '' END +
       CASE WHEN WeekDays & 4 > 0 THEN 'Wed,' ELSE '' END +
       CASE WHEN WeekDays & 8 > 0 THEN 'Thu,' ELSE '' END +
       CASE WHEN WeekDays & 16 > 0 THEN 'Fri,' ELSE '' END +
       CASE WHEN WeekDays & 32 > 0 THEN 'Sat,' ELSE '' END AS WeekDays
FROM (
    SELECT r.ContractID,
           MIN(d.dt) AS StartDT,
           MAX(d.dt) AS EndDT,
           COUNT(*) AS DayCount,
           SUM(DISTINCT d.dowBit) AS WeekDays
    FROM (SELECT *, COALESCE((SELECT MIN(DayNo) FROM @RangeStart WHERE ContractID = rs.ContractID AND DayNo > rs.DayNo), 999999) AS DayEnd FROM @RangeStart rs) r
    JOIN @Days d ON (d.ContractID = r.ContractID AND d.DayNo BETWEEN r.DayNo AND r.DayEnd-1)
    GROUP BY r.ContractID, r.DayNo
    ) d
ORDER BY ContractID, StartDT
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