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If you're running the code to test it, remember to turn on the Discard Results After Execution option in SSMS; otherwise, you will get an output with a million rows.
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You have to use a hint that removes the default recursion limit of 100. This solution runs for about 20 seconds. You can optimize the solution significantly by using a CTE (call it Base) that generates as many rows as the square root of the target number of rows. Take the cross join of two instances of Base to get the target number of rows, and finally, generate row numbers for the result to serve as the sequence of numbers. Here's the code that implements this approach: DECLARE @n AS BIGINT; SET @n = 1000000; WITH Base AS ( SELECT 1 AS n UNION ALL SELECT n + 1 FROM Base WHERE n < CEILING(SQRT(@n)) ), Expand AS ( SELECT 1 AS c FROM Base AS B1, Base AS B2 ), Nums AS ( SELECT ROW_NUMBER() OVER(ORDER BY c) AS n FROM Expand ) SELECT n FROM Nums WHERE n <= @n OPTION(MAXRECURSION 0);
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This solution runs for only 0.8 seconds (results discarded).
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Next, I'll describe the third approach to generate Nums. You start with a CTE that has only two rows, and multiply the number of rows with each following CTE by cross-joining two instances of the previous CTE. With n levels of CTEs (0-based), you reach 2 2n rows. For example, with 5 levels, you get 4,294,967,296 rows. Another CTE generates row numbers, and finally the outer query filters the desired number of values (where row number column <= input). Remember that when you filter a row number <= some value, SQL Server doesn't bother to generate row numbers beyond that point. So you shouldn't be concerned about performance. It's not the case that your code will really generate more than four billion rows every time and then filter. Here's the code that implements this approach: DECLARE @n AS BIGINT; SET @n = 1000000; WITH L0 AS(SELECT 1 AS c UNION ALL SELECT L1 AS(SELECT 1 AS c FROM L0 AS A, L0 L2 AS(SELECT 1 AS c FROM L1 AS A, L1 L3 AS(SELECT 1 AS c FROM L2 AS A, L2 L4 AS(SELECT 1 AS c FROM L3 AS A, L3 L5 AS(SELECT 1 AS c FROM L4 AS A, L4 Nums AS(SELECT ROW_NUMBER() OVER(ORDER SELECT n FROM Nums WHERE n <= @n;
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1), AS B), AS B), AS B), AS B), AS B), BY c) AS n FROM L5)
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It runs for about 0.9 seconds to generate a sequence of 1,000,000 numbers. As I mentioned earlier, you can wrap the logic in a UDF. The value of this solution is that it will never near the MAXRECURSION limit, and that limit cannot be modified in a UDF definition. The code in Listing 4-9 encapsulates the last solution's logic in a UDF.
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Listing 4-9. UDF returning an auxiliary table of numbers
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CREATE FUNCTION dbo.fn_nums(@n AS BIGINT) RETURNS TABLE AS RETURN WITH L0 AS(SELECT 1 AS c UNION ALL SELECT 1), L1 AS(SELECT 1 AS c FROM L0 AS A, L0 AS B), L2 AS(SELECT 1 AS c FROM L1 AS A, L1 AS B), L3 AS(SELECT 1 AS c FROM L2 AS A, L2 AS B), L4 AS(SELECT 1 AS c FROM L3 AS A, L3 AS B), L5 AS(SELECT 1 AS c FROM L4 AS A, L4 AS B), Nums AS(SELECT ROW_NUMBER() OVER(ORDER BY c) AS n FROM L5) SELECT n FROM Nums WHERE n <= @n; GO
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To test the function, run the following code, which returns an auxiliary table with 10 numbers: SELECT * FROM dbo.fn_nums(10) AS F;
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Existing and Missing Ranges (Also Known as Islands and Gaps)
To put your knowledge of subqueries, table expressions, and ranking calculations into action, I'll provide a couple of problems that have many applications in production environments. I'll present a generic form of the problem, though, so you can focus on the techniques and not the data. Create and populate a table named T1 by running the code in Listing 4-10.
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