quote:

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Originally posted by robvolk
BTW, you cannot solve the equations containing <= as an operator, the number of solutions is infinite.

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-- Need a table of Numbers
IF OBJECT_ID('dbo.F_TABLE_NUMBER_RANGE') IS NOT NULL DROP FUNCTION dbo.F_TABLE_NUMBER_RANGE

GO
CREATE FUNCTION dbo.F_TABLE_NUMBER_RANGE
(
	@startNumber INT
	, @endNumber INT
)
RETURNS TABLE AS RETURN
(
WITH powers AS (
	SELECT
		[N01], [N02], [N03]
	FROM
		(
			SELECT [N01] =  0 UNION SELECT    1 UNION SELECT    2 UNION SELECT    3
			UNION SELECT    4 UNION SELECT    5 UNION SELECT    6 UNION SELECT    7
			UNION SELECT    8 UNION SELECT    9 UNION SELECT   10 UNION SELECT   11
			UNION SELECT   12 UNION SELECT   13 UNION SELECT   14 UNION SELECT   15
		) NO1

		CROSS JOIN (
			SELECT [N02] =  0 UNION SELECT   16 UNION SELECT   32 UNION SELECT   48
			UNION SELECT   64 UNION SELECT   80 UNION SELECT   96 UNION SELECT  112
			UNION SELECT  128 UNION SELECT  144 UNION SELECT  160 UNION SELECT  176
			UNION SELECT  192 UNION SELECT  208 UNION SELECT  224 UNION SELECT  240
		) NO2

		CROSS JOIN (
			SELECT [N03] =  0 UNION SELECT  256 UNION SELECT  512 UNION SELECT  768
			UNION SELECT 1024 UNION SELECT 1280 UNION SELECT 1536 UNION SELECT 1792
			UNION SELECT 2048 UNION SELECT 2304 UNION SELECT 2560 UNION SELECT 2816
			UNION SELECT 3072 UNION SELECT 3328 UNION SELECT 3584 UNION SELECT 3840
		) N03
	)
SELECT TOP 100 PERCENT
	[number] = ( a.[number] + b.[number] ) + CASE WHEN @startNumber <= @endNumber THEN @startNumber ELSE @endNumber END
FROM
	(
		SELECT TOP 100 PERCENT
			[number] = CAST([N01] + [N02] + [N03] AS INT)
		FROM
			powers
		WHERE
			[N01] + [N02] + [N03] < CAST(CEILING(SQRT(ABS(@startNumber - @endNumber) + 1 )) AS INT)
		ORDER BY
			1
	) a
	CROSS JOIN (
		SELECT TOP 100 PERCENT
			[number] =  CAST(([N01] + [N02] + [N03]) * CAST(CEILING(SQRT(ABS(@startNumber - @endNumber) + 1 )) AS INT) AS INT)
		FROM 
			powers
		WHERE
			[N01] + [N02] + [N03] < CAST(CEILING(SQRT(ABS(@startNumber - @endNumber) + 1 )) AS INT)
		ORDER BY
			1
	) b
WHERE
	a.[number] + b.[number] < ABS(@startNumber - @endNumber) + 1
	AND (16777216 - ABS( @startNumber - @endNumber ) - 1 ) > 0
ORDER BY
	1
)
GO


/*
Yes i need to solve X and Y
5x+4y<=10
3x-y<=15

For example i took above equation

5x+4y<=10
3x-y<=15
s1+s2-s3=0

for above problem we need to find X & Y
Edited by - WoodHouse on 09/01/2009 05:44:15
*/


IF OBJECT_ID('tempdb..#matrixX') IS NOT NULL DROP TABLE #matrixX
IF OBJECT_ID('tempdb..#matrixY') IS NOT NULL DROP TABLE #matrixY

CREATE TABLE #matrixX ([x] INT PRIMARY KEY)
CREATE TABLE #matrixY ([y] INT PRIMARY KEY)

-- populate matrices
INSERT #matrixX
SELECT
	[number]
FROM
	dbo.F_TABLE_NUMBER_RANGE (0, 1000)

INSERT #matrixY SELECT [x] FROM #matrixX


-- Calculations
DECLARE @limit INT
DECLARE @floor INT


-- 5x + 4Y <= 10
SET @limit = 10
SET @floor = 0
SELECT
	mx.[x]
	, my.[y]
FROM
	#matrixX mx
	CROSS JOIN #matrixY my 
WHERE
	5 * mx.[x] + 4 * my.[y] BETWEEN @floor AND @limit

-- 3x-y<=15
SET @limit = 15
SET @floor = 0
SELECT
	mx.[x]
	, my.[y]
FROM
	#matrixX mx
	CROSS JOIN #matrixY my 
WHERE
	3 * mx.[x] - my.[y] BETWEEN @floor AND @limit

quote:

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Linear programming is a method of finding optimal solutions using graphs of areas under a curve. It does include the use of inequalities.
http://en.wikipedia.org/wiki/Linear_programming

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