## TSQL Challenge 12: Completing sequence by inserting missing rows

TSQL Challenge 12 was a relatively easier one. The participants were given month-wise score values and were asked to complete the sequence by creating entries for missing month.

Here’s the sample input:

```YearMonth   Score
----------- -----------
200903      100
200803      95
200802      99
200801      100
200711      100
```

And here’s the desired output. Notice that the score of last month is replicated in each of the missing rows:

```YearMonth   Score
----------- -----------
200908      100
200907      100
200906      100
200905      100
200904      100
200903      100
200902      95
200901      95
200812      95
200811      95
200810      95
200809      95
200808      95
200807      95
200806      95
200805      95
200804      95
200803      95
200802      99
200801      100
200712      100
200711      100
```

The script to generate sample data is provided below:

```DECLARE @Scores TABLE
(
YearMonth	INT,
Score		INT
)

INSERT @Scores VALUES(200903, 100)
INSERT @Scores VALUES(200803, 95)
INSERT @Scores VALUES(200802, 99)
INSERT @Scores VALUES(200801 ,100)
INSERT @Scores VALUES(200711, 100)
```

Solution

I once blogged about creating a sequence of numbers/dates using a recursive CTE in this post. The same technique can be used here. However, since the `YearMonth` column in the sample data is integer, we have two choices:

1. Convert it to DateTime and apply T-SQL DateTime functions
2. Leave it as Integer and apply some intelligent arithmetic

I am providing both the solutions here. Note that the first solution will be slower due to overhead of casting and applying T-SQL scalar functions.

The first solution: Converting to DateTime

```;with cte as
(
select score, Cast(Cast(YearMonth as varchar)+'01' as datetime) as dateVal
from @scores
union all
from cte
where not exists
--the resultant YearMonth value should not lie in the original table
( select 1 from @scores s where s.YearMonth = cast( left(convert(varchar, dateadd(month, 1, cte.dateval), 112), 6) as int) )
--stop at current month
and dateadd(month, 1, cte.dateval) < getdate()
)

select left(convert(varchar, dateval, 112), 6) as yearmonth, score
from cte
order by dateval desc
```

Explanation:
Here I am simply converting the integer `YearMonth` column to a datetime `dateval` column by appending 01 to the end (so a `200901` becomes `20090101` that can easily be cast to a dateTime) and then finding subsequent dates by adding one month in each CTE iteration.

The second solution: Integer Arithmetic

```;with cte as
(
select YearMonth, Score
from @Scores
union all
select YearMonth + YearMonth % 100 / 12 * 88 + 1 as YearMonth, Score
from cte
where not exists
--the resultant YearMonth value should not lie in the original table
( select s.YearMonth from @Scores s where s.YearMonth = (cte.YearMonth + cte.YearMonth % 100 / 12 * 88 + 1) )
--stop at current month
and cte.YearMonth < month(getdate()) + year(getdate())*100
)

select *
from cte
order by YearMonth desc
```

Explanation:
The important point is to increment the value of `YearMonth` correctly. So `200811` should get incremented to `200812` but `200812` should get incremented to `200901`. This isn’t difficult if we introduce a case statement like this:

`YearMonth + (Case When YearMonth%100 < 12 Then 1 Else 89 End)`

But I wanted to do this purely using arithmetic with no `Case` statements, so I came up with this formula:

`(YearMonth % 100 / 12 * 88) + 1`

Note that the factor `(YearMonth % 100 / 12 * 88)` will reduce to zero for all values from January to November, i.e. from `200801` to `200811`.

I hope you enjoyed the solution.

Update:
It was pointed out in one of the comments by Rakesh that the solution could reach the default limit of recursion which is 100. In order to avoid this, we need to add `option (maxrecursion 12,000)` in the final select statement. Then, we can have 10,000 years missing between two adjacent entries. Thanks, Rakesh.

```...
select *
from cte
order by YearMonth desc
option (maxrecursion 12,000)
```