问题
Learning a little about T-SQL, and thought an interesting exercise would be to generate a Mandelbrot set with it.
Turns out someone already has (and recently, it appears). I'll let someone else post it as an answer, but I'm curious what optimizations can be made.
Alternately, what would you do to make the code more readable?
I'll select the most readable (yet reasonably compact) version as the accepted answer (too bad we don't have rep bounties yet!) unless someone really comes along with a great optimization.
Bonus points to those answers that teach me a little something about T-SQL.
-Adam
回答1:
Create PROCEDURE dbo.mandlebrot
@left float,
@right float,
@Top float,
@Bottom float,
@Res float,
@MaxIterations Integer = 500
As
Set NoCount On
Declare @Grid Table (
X float Not Null,
Y float Not Null,
InSet Bit
Primary Key (X, Y))
Declare @Xo float, @Yo float, @Abs float
Declare @PtX Float, @PtY Float
Declare @Iteration Integer Set @Iteration = 0
Select @Xo = @Left, @Yo = @Bottom
While @Yo <= @Top Begin
While @Xo <= @Right Begin
Select @PtX = @Xo, @PtY = @Yo
While @Iteration < @MaxIterations
And (Square(@PtX) + Square(@PtY)) < 4.0 Begin
Select @PtX = Square(@PtX) - Square(@PtY) + @Xo,
@PtY = 2* @PtX * @PtY + @Yo
Select @Iteration, @PtX, @PtY
Set @Iteration = @Iteration + 1
End
Insert @Grid(X, Y, InSet)
Values(@Xo, @Yo, Case
When @Iteration < @MaxIterations
Then 1 Else 0 End)
Set @Xo = @Xo + @res
Set @Iteration = 0
End
Select @Xo = @Left,
@Yo = @Yo + @Res
End
Select * From @Grid
回答2:
From thedailywtf.com
-- AUTHOR: GRAEME JOB
-- CREATED: 12-OCT-2008
-- BECAUSE: SINGLE SQL COMMAND < 50 LINES. JUST BECAUSE.
WITH
XGEN(X, IX) AS ( -- X DIM GENERATOR
SELECT CAST(-2.2 AS FLOAT) AS X, 0 AS IX UNION ALL
SELECT CAST(X + 0.031 AS FLOAT) AS X, IX + 1 AS IX
FROM XGEN
WHERE IX < 100
),
YGEN(Y, IY) AS ( -- Y DIM GENERATOR
SELECT CAST(-1.5 AS FLOAT) AS Y, 0 AS IY UNION ALL
SELECT CAST(Y + 0.031 AS FLOAT) AS Y, IY + 1 AS IY
FROM YGEN
WHERE IY < 100
),
Z(IX, IY, CX, CY, X, Y, I) AS ( -- Z POINT ITERATOR
SELECT IX, IY, X, Y, X, Y, 0
FROM XGEN, YGEN
UNION ALL
SELECT IX, IY, CX, CY, X * X - Y * Y + CX AS X, Y * X * 2 + CY, I + 1
FROM Z
WHERE X * X + Y * Y < 16
AND I < 100
)
SELECT REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(
REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(
REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(REPLACE(
(X0+X1+X2+X3+X4+X5+X6+X7+X8+X9+X10+X11+X12+X13+X14+X15+X16+X17+X18+X19+
X20+X21+X22+X23+X24+X25+X26+X27+X28+X29+X30+X31+X32+X33+X34+X35+X36+X37+X38+X39+
X40+X41+X42+X43+X44+X45+X46+X47+X48+X49+X50+X51+X52+X53+X54+X55+X56+X57+X58+X59+
X60+X61+X62+X63+X64+X65+X66+X67+X68+X69+X70+X71+X72+X73+X74+X75+X76+X77+X78+X79+
X80+X81+X82+X83+X84+X85+X86+X87+X88+X89+X90+X91+X92+X93+X94+X95+X96+X97+X98+X99),
'A',' '), 'B','.'), 'C',','), 'D',','), 'E',','), 'F','-'), 'G','-'),
'H','-'), 'I','-'), 'J','-'), 'K','+'), 'L','+'), 'M','+'), 'N','+'),
'O','%'), 'P','%'), 'Q','%'), 'R','%'), 'S','@'), 'T','@'), 'U','@'),
'V','@'), 'W','#'), 'X','#'), 'Y','#'), 'Z',' ')
FROM (
SELECT 'X' + CAST(IX AS VARCHAR) AS IX,
IY, SUBSTRING('ABCDEFGHIJKLMNOPQRSTUVWXYZ', ISNULL(NULLIF(I, 0), 1), 1) AS I
FROM Z) ZT
PIVOT (
MAX(I) FOR IX IN (
X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,
X20,X21,X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37,X38,X39,
X40,X41,X42,X43,X44,X45,X46,X47,X48,X49,X50,X51,X52,X53,X54,X55,X56,X57,X58,X59,
X60,X61,X62,X63,X64,X65,X66,X67,X68,X69,X70,X71,X72,X73,X74,X75,X76,X77,X78,X79,
X80,X81,X82,X83,X84,X85,X86,X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98,X99)
) AS PZT
(source: thedailywtf.com)
回答3:
Hopefully, this teaches a bit about T-SQL as well, It does everything in a set based approach which is TSQL's strength (i.e. no while loops) or variables:
SET NOCOUNT ON;
--populate
;WITH Numbers ([row]) AS
(
SELECT TOP 100 CAST(ROW_NUMBER() OVER (ORDER BY NEWID()) AS FLOAT) [row]
FROM sys.columns
)
SELECT A.row AS x,
B.row AS y,
0 AS iter,
A.row AS iterx,
B.row AS itery,
'.' AS symbol
INTO #GRID
FROM Numbers A, Numbers B
WHERE B.[row] <= 24
GO
-- scale
UPDATE #GRID
SET x = x * 3.0 / 100.0 - 2,
y = y * 2.0 / 24.0 - 1,
iterx = x * 3.0 / 100.0 - 2,
itery = y * 2.0 / 24.0 - 1
GO
--iterate
UPDATE #GRID
SET iterx = iterx*iterx - itery*itery + x,
itery = 2*iterx*itery + y,
iter = iter+1
WHERE iterx*iterx+itery*itery <= 2*2
GO 257
UPDATE #GRID SET symbol = CHAR(64+(iter%26)) WHERE NOT iter = 257
GO
--print
WITH concatenated (y, c) AS
(
SELECT G2.y,
(SELECT SUBSTRING(G.symbol, 1, 1) AS [data()] FROM #GRID G WHERE G.y = G2.y FOR XML PATH('')) c
FROM (SELECT DISTINCT y FROM #GRID) AS G2
)
SELECT REPLACE(c, ' ', '') FROM concatenated ORDER BY y
GO
DROP TABLE #GRID
回答4:
with points (x1,y1,x2,y2,depth) as
(
select convert(float,-2.40), convert(float,-2.40), convert(float,2.40), convert(float,2.40), 8
union all select x1,y1,(x1+x2)/2,(y1+y2)/2,depth-1 from points where depth>0
union all select (x1+x2)/2,y1,x2,(y1+y2)/2,depth-1 from points where depth>0
union all select x1,(y1+y2)/2,(x1+x2)/2,y2,depth-1 from points where depth>0
union all select (x1+x2)/2,(y1+y2)/2,x2,y2,depth-1 from points where depth>0
),
mandelbrot(x1,y1,x2,y2,x,y,depth) as
(
select x1,y1,x2,y2,convert(float,0),convert(float,0),20 from points where depth=0
union all
select x1,y1,x2,y2, x*x-y*y+x1, 2*x*y+y1,depth-1 from mandelbrot where depth > 0 and (x*x+y*y<4)
)
select geometry::STGeomFromText('POLYGON((' +
convert(varchar,x1) + ' ' + convert(varchar,y1) + ',' +
convert(varchar,x1) + ' ' + convert(varchar,y2) + ',' +
convert(varchar,x2) + ' ' + convert(varchar,y2) + ',' +
convert(varchar,x2) + ' ' + convert(varchar,y1) + ',' +
convert(varchar,x1) + ' ' + convert(varchar,y1) + '))',0)
from mandelbrot where depth = 0
来源：https://stackoverflow.com/questions/314864/how-to-generate-a-mandelbrot-with-t-sql