https://blogs.lotterypost.com/jadelottery/2010/9/combinatorial-index.htm JADELottery's Blog: Combinatorial Index en-us Lottery Post RSS Generator https://blogs.lotterypost.com/jadelottery/2010/9/combinatorial-index.htm https://blogs.lotterypost.com/jadelottery/2010/9/combinatorial-index.htm Sun, 05 Sep 2010 02:39:20 GMT JADELottery We posted this in the topic Excel help need Combination FROM Lexicographix number in the Mathematics Forum.

Adjust the Data Types on different programming platforms.

The functions may error out on very large Combinatorial Sets.

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Ok, Here It Is.

You can download the Excel file at ftp://www.jadexcode.com/excel

The file name is CombinatorialIndex.xls

The VB Macro Source Code is shown below

Function Fact(N As Integer) As Double

If (N 1) Then

Fact = 1

Else

Fact = N * Fact(N - 1)

End If

End Function

Function Perm(N As Integer, R As Integer) As Double

If (N R) Then

Perm = 0

Else

Perm = Fact(N) / Fact(N - R)

End If

End Function

Function Comb(N As Integer, R As Integer) As Long

If (N R) Then

Comb = 0

Else

Comb = Perm(N, R) / Fact(R)

End If

End Function

Function Cdist(N As Integer, R As Integer, C As Integer, Z As Integer) As Long

If (Z C) Or (Z (N - R + C)) Or (Z N) Or (C R) Or (N 1) Or (R 1) Or (C 1) Or (Z 1) Then

Cdist = 0

Else

Cdist = Comb(Z - 1, C - 1) * Comb(N - Z, R - C)

End If

End Function

Function fColumnSum(N As Integer, R As Integer, Z As Integer) As Long

Dim a As Integer

If Z 1 Then

fColumnSum = 0

ElseIf (Z = 1) And (Z N - R + 1) Then

col_sum = 0

For a = 1 To Z

col_sum = col_sum + Cdist(N, R, 1, a)

Next a

fColumnSum = col_sum

ElseIf Z = N - R + 1 Then

fColumnSum = Comb(N, R)

End If

End Function

Function Index2Combin(N As Integer, R As Integer, I As Double) As String

Dim Combination(), Z As Integer

ReDim Combination(R)

Dim tmpString As String

Dim NumberFound As Boolean

tmpString =

I = I - 1

Z = 0

For a = 1 To R

If I = Comb(N, R) Then

If a = 1 Then

Combination(a) = 1

Else

Combination(a) = Combination(a - 1) + 1

End If

NumberFound = False

Do

Select Case (I - fColumnSum(N - Z, R - (a - 1), Combination(a) - Z - 1))

Case Is 0

Combination(a) = Combination(a) - 1

NumberFound = True

Case Is = 0

NumberFound = True

Case Is 0

Combination(a) = Combination(a) + 1

End Select

Loop Until NumberFound

I = I - fColumnSum(N - Z, R - (a - 1), Combination(a) - Z - 1)

Z = Combination(a)

Else

Combination(a) = 0

End If

tmpString = tmpString Format(Combination(a), 00 )

If a R Then tmpString = tmpString

Next a

Index2Combin = tmpString

End Function

Function Combin2Index(N As Integer, R As Integer, theRange As Range) As Long

Dim a As Integer

Dim fSum As Double

Dim NotInAscendingOrder, NotInPool As Boolean

NotInAscendingOrder = False

NotInPool = False

If (theRange.Rows.Count 1) Or (theRange.Columns.Count R) Then

Combin2Index = -1

Exit Function

End If

For a = 1 To R

If a R Then

If theRange.Cells(1, a) = theRange.Cells(1, a + 1) Then

NotInAscendingOrder = True

End If

End If

If (theRange.Cells(1, a) 1) Or (theRange.Cells(1, a) N) Then

NotInPool = True

End If

Next a

If NotInAscendingOrder Or NotInPool Then

Combin2Index = -1

Exit Function

End If

fSum = fColumnSum(N, R, theRange.Cells(1, 1) - 1) + 1

For a = 2 To R

fSum = fSum + fColumnSum(N - theRange.Cells(1, a - 1), R - a + 1, theRange.Cells(1, a) - theRange.Cells(1, a - 1) - 1)

Next a

Combin2Index = fSum

End Function

... [ More ]

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