【发布时间】：2010-09-23 19:30:14
【问题描述】：
了解一点 T-SQL，并认为一个有趣的练习是用它生成一个 Mandelbrot 集。
原来有人已经拥有（最近，它出现了）。我会让其他人将其发布为答案，但我很好奇可以进行哪些优化。
或者，您会如何使代码更具可读性？
我会选择最易读（但相当紧凑）的版本作为接受的答案（可惜我们还没有代表赏金！）除非有人真的提出了很好的优化。
奖励点指向那些教会我一些关于 T-SQL 的答案。
-亚当
【问题讨论】：
【发布时间】：2010-09-23 19:30:14
【问题描述】：
-- 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
（来源：thedailywtf.com）
【讨论】：
-
抱歉，我的意思是包含它的样子。
-
让我想起了 1987-1992 年的时间，当时有人用 PostScript 编写了一个 Mandelbrot 生成器，而一些白痴一直将它发送给我们公司，只有一个 LaserWriter。
-
@paul - 搞笑！我工作场所的激光打印机故障仅限于更改 HP 打印机上的状态消息。
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
【讨论】：
希望这也能教授一些关于 T-SQL 的知识，它以基于集合的方法完成所有操作，这是 TSQL 的强项（即没有 while 循环）或变量：
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
【讨论】：
-
哈哈，不错的技巧“没有循环或变量”，除了“GO 257”，它本质上是一个循环。不过还是很酷。
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
【讨论】：