Pascals Triangle in SQL

Looking around online, I could not find a great example of how to draw Pascal’s Triangle in SQL. The solution is quite cool in SQL, because management studio prints out a nice grid for you. Here are three examples. The first one is simple and well documented, the second one is a little more squished, and the third one is a complete dumpster fire that I got too by looking up how to code golf in SQL.

CREATE PROCEDURE PascalsTriangle
    @Levels INT
AS
BEGIN
    SET NOCOUNT ON

    -- Declare variables
    DECLARE @counter        INT = 2
    DECLARE @innerCount     INT
    DECLARE @tmp            DECIMAL(38,0)
    DECLARE @tmp2           DECIMAL(38,0)
    DECLARE @dquery         NVARCHAR(2048)

    -- Create the results table with its one column
    CREATE TABLE #result
    (
        [1] DECIMAL(38,0)
    )
    INSERT INTO #result VALUES (1)

    -- For every level beyond 1
    WHILE(@counter <= @Levels)
    BEGIN
        
        -- Add another column to to the table
        EXEC('ALTER TABLE #result ADD [' + @counter + '] DECIMAL(38,0)')

        -- Select the previous row into a temp table
        SELECT *
        INTO #row
        FROM #result
        ORDER BY 1
        OFFSET (@counter - 2) ROWS
        FETCH NEXT 1 ROWS ONLY

        -- Re-initialize the temp variables, and loop counter
        SET @tmp = 1
        SET @tmp2 = 1
        SET @innerCount = 2

        -- For every column beyond 1
        WHILE(@innerCount <= @counter)
        BEGIN

            -- Create a query which selects the current value of the cell to back it up.
            SET @dquery = 'SELECT @t = [' + CAST(@innerCount AS NVARCHAR(10)) + '] FROM #row'
            EXEC sp_executesql @dquery, N'@t DECIMAL(38,0) OUTPUT', @t = @tmp2 OUTPUT

            -- Set the value of this cell in this row to that + @tmp
            EXEC('UPDATE #row SET [' + @innerCount + '] = ISNULL([' + @innerCount + '], 0) + ' + @tmp)

            -- Reset the temp variable
            SET @tmp = @tmp2

            -- Increment the count
            SET @innerCount += 1

        END

        -- Insert the row into result
        INSERT INTO #result
        SELECT * FROM #row

        -- Increment the counter
        SET @counter += 1

        -- Drop the row temp table
        DROP TABLE #row
    END

    -- Output the result
    SELECT * FROM #result
    DROP TABLE #result
END

There is another post in PowerShell which does a much better job actually explaining details about how this triangle works. But long story short, every item is the sum of the two above it added together. So now let’s make the script a little smaller.

CREATE PROCEDURE PascalsTriangle2
	@Levels INT
AS
BEGIN
	SET NOCOUNT ON
	DECLARE @o INT=2
	DECLARE @ INT
	DECLARE @1 DECIMAL(38,0)
	DECLARE @2 DECIMAL(38,0)
	DECLARE @q NVARCHAR(2048)
	CREATE TABLE #o([1] DECIMAL(38,0))
	INSERT #o VALUES(1)
	o:
 		EXEC('ALTER TABLE #o ADD['+@o+']DECIMAL(38,0)')
 		SELECT *INTO #r FROM #o ORDER BY 1 OFFSET(@o-2)ROWS	FETCH NEXT 1 ROWS ONLY
 		SET @1 = 1
 		SET @2 = 1
 		SET @ = 2
 		i:
			SET @q = CONCAT('DECLARE @ TABLE (val DECIMAL(38,0));UPDATE #r SET [',@,']=ISNULL([',@,'], 0)+',@1,'OUTPUT deleted.[',@,']INTO @;SET @t=(SELECT *FROM @)')
			EXEC sp_executesql @q,N'@t DECIMAL(38,0) OUTPUT',@t=@2 OUTPUT  			
  			SET @1 = @2
  			SET @ += 1
 		IF @ <= @o GOTO i
 		INSERT #o
 		SELECT * FROM #r
 		SET @o += 1
 		DROP TABLE #r
	IF @o <= @Levels GOTO o
	SELECT * FROM #o
	DROP TABLE #o
END

As you can see, I removed all the pesky comments which were just getting in the way of looking small. Also, the while loops were all turned into GOTO loops to take up a little less space. The variable names were shortened a little as well.

DECLARE @s NVARCHAR(MAX)='CREATE PROCEDURE PascalsTriangle3
@Levels INT
AS
BEGIN
	SET NOCOUNT ON
	~o |=2~ |~1 &~2 &~q NVARCHAR(2048)CREATE TABLE #o([1] &)INSERT #o VALUES(1)
	o:EXEC(''ALTER TABLE #o ADD[''+@o+'']&'')$|O #r ^#o ORDER BY 1 OFFSET(@o-2)ROWS	FETCH NEXT 1 ROWS ONLY!1 = 1!2 = 1! = 2
 		i:!q = CONCAT(''~ TABLE (val &amp;);UPDATE #r SET ['',@,'']=ISNULL(['',@,''], 0)+'',@1,''OUTPUT deleted.['',@,'']|O @;!t=($^@)'')EXEC sp_executesql @q,N''@t &amp; OUTPUT'',@t=@2 OUTPUT!1 = @2!+=1IF @ <= @o GOTO i
 		INSERT #o$ ^#r!o += 1%#r IF @o <= @Levels goto o$ ^#o%#o
END'
SELECT @s=REPLACE(@s,LEFT(i,1),SUBSTRING(i,2,20))
FROM(VALUES('~ DECLARE @'),('! SET @'),('&amp; DECIMAL(38,0)'),('% DROP TABLE '),('$ SELECT *'),('^ FROM '),('| INT'))a(i)
EXEC(@s)

Now there’s the real beast. It does a bunch of replacements on a string, to make some longer valid SQL, then executes the SQL dynamically to produce the stored procedure. That’s some production quality code.