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  1. #1
    VBAX Expert TrippyTom's Avatar
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    find all combinations (no repeats)

    I'm trying to figure out a way to list all possible combinations (no repeats) of any list of items (I'm using numbers for now to make it simpler). Anything beyond 16 items would be too many rows for Excel to display. 16 items = (2^16)-1 = 65535 possible combinations (rows)

    By no repeats, i mean: 1,2,3 and 2,3,1 would be the same item combination (not 2 different ones).

    Anyway, I've attached the file as it is so far, but I'm missing the part where it actually outputs the subsets, like sets of 2, sets of 3, etc. I would like the output to start in F1 and go down.

    I have searched this site and google all day with very little promising results. There's a ton of samples, but none of them showed a general formula or code that would handle this type of thing.

    Can anyone walk me through this? This is not homework. I'm doing this as a curious experiment because I had the need to show all possible combinations (by using different colored dots on a map) at work and had to do it in my head. I knew there had to be an easier way.

    If there's a solution via formulas instead of VBA I would like to see how that would work too. Also, my mapping program allows me to query things with SQL. If any SQL expert out there knows of a way to do this automatically via SQL, that'd be awesome too.

    Thanks,
    Tom
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    goal: to learn the most efficient way

  2. #2
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    Anything beyond 16 items would be too many rows for Excel to display. 16 items = (2^16)-1 = 65535 possible combinations (rows)
    The number of combanations of 18 items, taken 9 at a time

    C(18,9) = 48,620

    C(19,9) = 92,378

    so you could get a few more and not exceed the 2003 row limit

    But I'm not sure what you want running down the rows?

    For ex for C(4,2) = 6, were you looking for something like

    1,2
    1,3
    1,4
    2,3
    2,4
    3,4

    Paul

  3. #3
    VBAX Expert TrippyTom's Avatar
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    Yes, but i want to do that for all sets, not just combinations of 9 at a time.

    For instance, say I have a set of 3 numbers: (1,2,3)
    Sets of 1 number each = 3 possibles
    Sets of 2 numbers each = 3 possibles
    Sets of 3 numbers each = 1 possible

    Added up that would be 7 possibles but i want to show them all, either with commas like you have above, or each number in its own cell, going down however many rows it would take (in this case 7 rows). I hope that makes sense?
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  4. #4
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    Good day Sir,

    Really hoping you could see this soon because this thread is pretty old but this particular response exactly describes what I am trying achieve. I am very new to VBA and have been literally surfing all day on how to achieve generating results of a number of combinations from a list of N items, taking R at a time. Too many confusing codes.

    I have got a list of 15 alphabets (A - O) in a column and want to be able to combine 4 at a time.
    The number of combinations for this is C(15,4) = 1365

    I want the results displayed down the rows just like in your comment. Something like;

    A,B,C,D
    A,B,J,K
    L,M,N,O
    C,E,F,H

    etc

    Already getting a headache from attempting. Can you please be of help?

  5. #5
    VBAX Wizard
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    Yes, but i want to do that for all sets, not just combinations of 9 at a time.
    Yes, I meant that it seems like you can do up to 18 and not 16 before you run out of rows

    I did a prelim last night very small amount of data with max = 4

    So I came up with 4 columns the way I was playing around (for N = 4)

    C(4,1)__C(4,2)___C(4,3)___C(4,4)
    1______1,2_______1,2,3___1,2,3,4
    2______1,3_______1,2,4
    3 _____1,4_______1,3,4
    4 _____2,3_______2,3,4
    _______2,4
    _______3,4

    I set it up so that I could just input N and it will (eventually) generate the N columns and the 'whole bunch of' rows (that's a technical Excel term )

    It's an interesting problem

    Paul

  6. #6
    VBAX Expert TrippyTom's Avatar
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    Oh! I was putting them all in 1 column. I didn't think to put the sets in different columns like you did. I guess that's why I came up with the limit at 16.

    I'd appreciate if you could walk me through how you did it, or show the code. Thanks!
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    goal: to learn the most efficient way

  7. #7
    VBAX Expert TrippyTom's Avatar
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    sorry, image didn't come through. here it is.
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    goal: to learn the most efficient way

  8. #8
    Knowledge Base Approver VBAX Guru GTO's Avatar
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    Hi Tom,

    Have you looked at Tushar Mehta's work?

    http://www.tushar-mehta.com/excel/tips/powerset.html

    Very quickly put together, and early bound, but using several of his functions from the above link... Does this help at all?

    Option Explicit
        
    Sub exa()
    Dim FSO As FileSystemObject
    Dim FIL As TextStream
        
    Dim a, b
    Dim i As Long, n As Long
        
        Set FSO = New FileSystemObject
        Set FIL = FSO.CreateTextFile(ThisWorkbook.Path & "\Test.txt")
        
        a = Array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
        
        For i = LBound(a) To UBound(a)
            b = createCombinations(a, i + 1, ",")
            For n = LBound(b) To UBound(b)
                FIL.WriteLine b(n)
            Next
        Next
        FIL.Close
    End Sub
        
    Public Function createCombinations(Arr, NbrItems As Integer, Delim As String)
        createCombinations = createSubset(Arr, NbrItems, Delim)
    End Function
        
    Public Function createSubset(Arr, NbrItems As Integer, Delim As String)
    Dim Rslt
    ReDim Rslt(0)
        
        aSubset Arr, LBound(Arr), NbrItems, Delim, "", Rslt
        ReDim Preserve Rslt(UBound(Rslt) - 1)
        'Debug.Assert NbrElements(Rslt) = _
            Application.WorksheetFunction.Combin(NbrElements(Arr), NbrItems)
        createSubset = Rslt
    End Function
        
    Private Sub aSubset(Arr, CurrIdx, NbrItems, ByVal Delim As String, _
            ByVal PreString As String, ByRef Rslt)
        Dim i As Integer
        If NbrItems = 0 Then
            If PreString = "" Then Rslt(UBound(Rslt)) = PreString _
            Else Rslt(UBound(Rslt)) = Left(PreString, Len(PreString) - Len(Delim))
            ReDim Preserve Rslt(UBound(Rslt) + 1)
        Else
            For i = CurrIdx To NbrElements(Arr) - NbrItems + LBound(Arr)
                aSubset Arr, i + 1, NbrItems - 1, Delim, _
                    PreString & Arr(i) & Delim, Rslt
                Next i
            End If
    End Sub
        
    Private Function NbrElements(Arr) As Integer
       On Error Resume Next
       NbrElements = UBound(Arr) - LBound(Arr) + 1
    End Function
    Mark

  9. #9
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    My effort

    [vba]
    Option Explicit
    Option Base 1
    Sub Test1()
    Dim iNumber As Long
    Dim iCol As Long, iRow As Long
    Dim s As String
    Dim i As Long, j As Long
    Dim aIndex() As Long
    Dim aData() As Variant
    Dim bDone As Boolean


    iNumber = InputBox("How Many?, 0 to exit")
    If iNumber < 1 Then Exit Sub
    If iNumber > 16 Then Exit Sub


    'this just uses intgers for demo, but
    'aData could = Array("CA", "NY", "PA", "NJ", ....)
    ReDim aData(1 To iNumber)
    For i = 1 To iNumber
    aData(i) = i
    Next i



    'clear working area
    ActiveSheet.Cells(1, 1).CurrentRegion.ClearContents

    'columns = C(iNumber, iCol)
    For iCol = 1 To iNumber

    'start in first row of iCol
    iRow = 1

    'add C(N, iCol) as header
    ActiveSheet.Cells(iRow, iCol).Value = "C(" & iNumber & "," & iCol & ")"


    Select Case iCol
    Case 1
    For i = 1 To iNumber
    ActiveSheet.Cells(i + 1, iCol).Value = "{" & aData(i) & "}"
    Next i

    Case iNumber
    s = vbNullString
    For i = 1 To iNumber - 1
    s = aData(i) & ","
    Next i
    ActiveSheet.Cells(2, iCol).Value = "{" & s & aData(iNumber) & "}"

    Case Else
    'init the index array to hold starting positions (1) and the max positon (2)
    'N = 12, T = 4
    'ABCDEFGHIJKL
    ' ^^^^ so N-T+1 = 9,10,11,12 or I,J,K,L
    ReDim aIndex(1 To iCol, 1 To 2)
    For i = 1 To iCol
    aIndex(i, 1) = i
    aIndex(i, 2) = iNumber - iCol + i
    Next i

    bDone = False

    While Not bDone

    'do first one
    s = aData(aIndex(1, 1))

    For i = 2 To iCol
    s = s & "," & aData(aIndex(i, 1))
    Next i

    iRow = iRow + 1
    ActiveSheet.Cells(iRow, iCol).Value = "{" & s & "}"


    If aIndex(iCol, 1) <> aIndex(iCol, 2) Then
    aIndex(iCol, 1) = aIndex(iCol, 1) + 1
    Else
    j = iCol
    While aIndex(j, 1) = aIndex(j, 2) And j > 0
    j = j - 1
    If j = 1 Then GoTo NextCol
    Wend

    'bump the highest order, not-maxed out index
    aIndex(j, 1) = aIndex(j, 1) + 1


    For i = j + 1 To iCol
    aIndex(i, 1) = aIndex(i - 1, 1) + 1
    Next i
    End If



    'when the first index exceeds the last possible starting position, we're done
    If aIndex(1, 1) > aIndex(1, 2) Then bDone = True
    Wend

    End Select

    NextCol:
    Next iCol

    End Sub
    [/vba]

    There's a little more brute force ('inelagance') than I'd like, so maybe some others can offer clean up suggestions


    Paul
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  10. #10
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    Issue with VBA

    Hi Paul,
    I've tried use the below but for "aData(i) = Array("5L", "5R", "4L", "4R", "3L", "3R", "B2", "B3", "B4")" as this is exactly what I need to find however it's not seems to be working. VBA is new to me so going through trial and error here. Would you be able to point what I'm doing wrong please?

    Quote Originally Posted by Paul_Hossler View Post
    My effort

    [vba]
    Option Explicit
    Option Base 1
    Sub Test1()
    Dim iNumber As Long
    Dim iCol As Long, iRow As Long
    Dim s As String
    Dim i As Long, j As Long
    Dim aIndex() As Long
    Dim aData() As Variant
    Dim bDone As Boolean


    iNumber = InputBox("How Many?, 0 to exit")
    If iNumber < 1 Then Exit Sub
    If iNumber > 16 Then Exit Sub


    'this just uses intgers for demo, but
    'aData could = Array("CA", "NY", "PA", "NJ", ....)
    ReDim aData(1 To iNumber)
    For i = 1 To iNumber
    aData(i) = i
    Next i



    'clear working area
    ActiveSheet.Cells(1, 1).CurrentRegion.ClearContents

    'columns = C(iNumber, iCol)
    For iCol = 1 To iNumber

    'start in first row of iCol
    iRow = 1

    'add C(N, iCol) as header
    ActiveSheet.Cells(iRow, iCol).Value = "C(" & iNumber & "," & iCol & ")"


    Select Case iCol
    Case 1
    For i = 1 To iNumber
    ActiveSheet.Cells(i + 1, iCol).Value = "{" & aData(i) & "}"
    Next i

    Case iNumber
    s = vbNullString
    For i = 1 To iNumber - 1
    s = aData(i) & ","
    Next i
    ActiveSheet.Cells(2, iCol).Value = "{" & s & aData(iNumber) & "}"

    Case Else
    'init the index array to hold starting positions (1) and the max positon (2)
    'N = 12, T = 4
    'ABCDEFGHIJKL
    ' ^^^^ so N-T+1 = 9,10,11,12 or I,J,K,L
    ReDim aIndex(1 To iCol, 1 To 2)
    For i = 1 To iCol
    aIndex(i, 1) = i
    aIndex(i, 2) = iNumber - iCol + i
    Next i

    bDone = False

    While Not bDone

    'do first one
    s = aData(aIndex(1, 1))

    For i = 2 To iCol
    s = s & "," & aData(aIndex(i, 1))
    Next i

    iRow = iRow + 1
    ActiveSheet.Cells(iRow, iCol).Value = "{" & s & "}"


    If aIndex(iCol, 1) <> aIndex(iCol, 2) Then
    aIndex(iCol, 1) = aIndex(iCol, 1) + 1
    Else
    j = iCol
    While aIndex(j, 1) = aIndex(j, 2) And j > 0
    j = j - 1
    If j = 1 Then GoTo NextCol
    Wend

    'bump the highest order, not-maxed out index
    aIndex(j, 1) = aIndex(j, 1) + 1


    For i = j + 1 To iCol
    aIndex(i, 1) = aIndex(i - 1, 1) + 1
    Next i
    End If



    'when the first index exceeds the last possible starting position, we're done
    If aIndex(1, 1) > aIndex(1, 2) Then bDone = True
    Wend

    End Select

    NextCol:
    Next iCol

    End Sub
    [/vba]

    There's a little more brute force ('inelagance') than I'd like, so maybe some others can offer clean up suggestions


    Paul

  11. #11
    VBAX Wizard
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    I think I must have posted an imternediate version

    That does NOT do what I had it doing before

    I'll have to track down my working version

    That one doesn't finish all the combinations

    Really sorry about that

    Paul

  12. #12
    VBAX Wizard
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    Dumb mistake - I was working in 2010 and made changes to my 2010 .xlsm after I back-saved in it 2003 .xls format

    Only difference was changing the test in the j loop

    [vba]
    Option Explicit
    Option Base 1
    Sub Test1()
    Dim iNumber As Long
    Dim iCol As Long, iRow As Long
    Dim s As String
    Dim i As Long, j As Long
    Dim aIndex() As Long
    Dim aData() As Variant
    Dim bDone As Boolean


    iNumber = InputBox("How Many?, 0 to exit")
    If iNumber < 1 Then Exit Sub
    If iNumber > 16 Then Exit Sub


    'this just uses intgers for demo, but
    'aData could = Array("CA", "NY", "PA", "NJ", ....)
    ReDim aData(1 To iNumber)
    For i = 1 To iNumber
    aData(i) = i
    Next i



    'clear working area
    ActiveSheet.Cells(1, 1).CurrentRegion.ClearContents

    'columns = C(iNumber, iCol)
    For iCol = 1 To iNumber

    'start in first row of iCol
    iRow = 1

    'add C(N, iCol) as header
    ActiveSheet.Cells(iRow, iCol).Value = "C(" & iNumber & "," & iCol & ")"


    Select Case iCol
    Case 1
    For i = 1 To iNumber
    ActiveSheet.Cells(i + 1, iCol).Value = "{" & aData(i) & "}"
    Next i

    Case iNumber
    s = vbNullString
    For i = 1 To iNumber - 1
    s = aData(i) & ","
    Next i
    ActiveSheet.Cells(2, iCol).Value = "{" & s & aData(iNumber) & "}"

    Case Else
    'init the index array to hold starting positions (1) and the max positon (2)
    'N = 12, T = 4
    'ABCDEFGHIJKL
    ' ^^^^ so N-T+1 = 9,10,11,12 or I,J,K,L
    ReDim aIndex(1 To iCol, 1 To 2)
    For i = 1 To iCol
    aIndex(i, 1) = i
    aIndex(i, 2) = iNumber - iCol + i
    Next i

    bDone = False

    While Not bDone

    'do first one
    s = aData(aIndex(1, 1))

    For i = 2 To iCol
    s = s & "," & aData(aIndex(i, 1))
    Next i

    iRow = iRow + 1
    ActiveSheet.Cells(iRow, iCol).Value = "{" & s & "}"


    If aIndex(iCol, 1) <> aIndex(iCol, 2) Then
    aIndex(iCol, 1) = aIndex(iCol, 1) + 1
    Else
    j = iCol
    While aIndex(j, 1) = aIndex(j, 2) And j > 0
    j = j - 1
    If j = 0 Then GoTo NextCol ' <<<<<<<<<
    Wend

    'bump the highest order, not-maxed out index
    aIndex(j, 1) = aIndex(j, 1) + 1


    For i = j + 1 To iCol
    aIndex(i, 1) = aIndex(i - 1, 1) + 1
    Next i
    End If



    'when the first index exceeds the last possible starting position, we're done
    If aIndex(1, 1) > aIndex(1, 2) Then bDone = True
    Wend

    End Select

    NextCol:
    Next iCol

    End Sub
    [/vba]

    Paul
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  13. #13
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    I was also looking for a answer to this question. Thanks.

    Quote Originally Posted by Paul_Hossler View Post
    Dumb mistake - I was working in 2010 and made changes to my 2010 .xlsm after I back-saved in it 2003 .xls format

    Only difference was changing the test in the j loop

    [vba]
    Option Explicit
    Option Base 1
    Sub Test1()
    Dim iNumber As Long
    Dim iCol As Long, iRow As Long
    Dim s As String
    Dim i As Long, j As Long
    Dim aIndex() As Long
    Dim aData() As Variant
    Dim bDone As Boolean


    iNumber = InputBox("How Many?, 0 to exit")
    If iNumber < 1 Then Exit Sub
    If iNumber > 16 Then Exit Sub


    'this just uses intgers for demo, but
    'aData could = Array("CA", "NY", "PA", "NJ", ....)
    ReDim aData(1 To iNumber)
    For i = 1 To iNumber
    aData(i) = i
    Next i



    'clear working area
    ActiveSheet.Cells(1, 1).CurrentRegion.ClearContents

    'columns = C(iNumber, iCol)
    For iCol = 1 To iNumber

    'start in first row of iCol
    iRow = 1

    'add C(N, iCol) as header
    ActiveSheet.Cells(iRow, iCol).Value = "C(" & iNumber & "," & iCol & ")"


    Select Case iCol
    Case 1
    For i = 1 To iNumber
    ActiveSheet.Cells(i + 1, iCol).Value = "{" & aData(i) & "}"
    Next i

    Case iNumber
    s = vbNullString
    For i = 1 To iNumber - 1
    s = aData(i) & ","
    Next i
    ActiveSheet.Cells(2, iCol).Value = "{" & s & aData(iNumber) & "}"

    Case Else
    'init the index array to hold starting positions (1) and the max positon (2)
    'N = 12, T = 4
    'ABCDEFGHIJKL
    ' ^^^^ so N-T+1 = 9,10,11,12 or I,J,K,L
    ReDim aIndex(1 To iCol, 1 To 2)
    For i = 1 To iCol
    aIndex(i, 1) = i
    aIndex(i, 2) = iNumber - iCol + i
    Next i

    bDone = False

    While Not bDone

    'do first one
    s = aData(aIndex(1, 1))

    For i = 2 To iCol
    s = s & "," & aData(aIndex(i, 1))
    Next i

    iRow = iRow + 1
    ActiveSheet.Cells(iRow, iCol).Value = "{" & s & "}"


    If aIndex(iCol, 1) <> aIndex(iCol, 2) Then
    aIndex(iCol, 1) = aIndex(iCol, 1) + 1
    Else
    j = iCol
    While aIndex(j, 1) = aIndex(j, 2) And j > 0
    j = j - 1
    If j = 0 Then GoTo NextCol ' <<<<<<<<<
    Wend

    'bump the highest order, not-maxed out index
    aIndex(j, 1) = aIndex(j, 1) + 1


    For i = j + 1 To iCol
    aIndex(i, 1) = aIndex(i - 1, 1) + 1
    Next i
    End If



    'when the first index exceeds the last possible starting position, we're done
    If aIndex(1, 1) > aIndex(1, 2) Then bDone = True
    Wend

    End Select

    NextCol:
    Next iCol

    End Sub
    [/vba]

    Paul

  14. #14
    VBAX Wizard
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    I thought that there was an other problem that I had found/fixed

    I figure it'd be easier to just make the VBA change if you're interested

    [VBA]
    Case iNumber
    s = vbNullString
    For i = 1 To iNumber - 1
    s = s & aData(i) & "," ' <<<<<<<<<
    Next i
    ActiveSheet.Cells(2, iCol).Value = "{" & s & aData(iNumber) & "}"
    [/VBA]

    Paul

  15. #15
    VBAX Tutor PAB's Avatar
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    Good afternoon Paul,

    I know this is an old tread, 02-20-2011, 02:41 PM, but I came across it while searching Google.

    I have been trying to adapt the code to put the total number of combinations produced for each distribution directly after the last entry for each distribution. I just can't seem to get it quite right though.

    This is what I am using for Case 1...

    ActiveSheet.Cells(i + 2, iCol).Value = Application.Count(aData(i))
    ...and this is what I am using for Case iNumber...

    ActiveSheet.Cells(3, iCol).Value = Application.CountA(aData(iNumber))
    ...any help will be appreciated.

    Thanks in advance.
    -----------------------------------------∏-

    12:45, restate my assumptions.
    Mathematics is the language of nature.
    Everything around us can be represented and understood through numbers.
    If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature.

    -----------------------------------------∏-

  16. #16
    VBAX Wizard
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    If I'm understanding, adding these 3 lines towards the end


    NextCol:
            
            With ActiveSheet.Cells(1, iCol).End(xlDown).Offset(1, 0)
                .Value = (.Row - 2) & " Comb"
            End With
        
        Next iCol
    End Sub
    Attached Files Attached Files
    Paul

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  17. #17
    VBAX Tutor PAB's Avatar
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    Spot on Paul, thanks very much.
    -----------------------------------------∏-

    12:45, restate my assumptions.
    Mathematics is the language of nature.
    Everything around us can be represented and understood through numbers.
    If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature.

    -----------------------------------------∏-

  18. #18

    Hi, I need help regarding listing of all possible combinations without repetitions.

    Quote Originally Posted by TrippyTom View Post
    I'm trying to figure out a way to list all possible combinations (no repeats) of any list of items (I'm using numbers for now to make it simpler). Anything beyond 16 items would be too many rows for Excel to display. 16 items = (2^16)-1 = 65535 possible combinations (rows)

    By no repeats, i mean: 1,2,3 and 2,3,1 would be the same item combination (not 2 different ones).

    Anyway, I've attached the file as it is so far, but I'm missing the part where it actually outputs the subsets, like sets of 2, sets of 3, etc. I would like the output to start in F1 and go down.

    I have searched this site and google all day with very little promising results. There's a ton of samples, but none of them showed a general formula or code that would handle this type of thing.

    Can anyone walk me through this? This is not homework. I'm doing this as a curious experiment because I had the need to show all possible combinations (by using different colored dots on a map) at work and had to do it in my head. I knew there had to be an easier way.

    If there's a solution via formulas instead of VBA I would like to see how that would work too. Also, my mapping program allows me to query things with SQL. If any SQL expert out there knows of a way to do this automatically via SQL, that'd be awesome too.

    Thanks,
    Tom

  19. #19

    Hi, I need help regarding listing of all possible combinations without repetitions.

    I have ten columns, each column has five rows in them. Each row has one word, I need to list out combinations without repetition using these ten column and 5 rows in each column. One element to be taken from one column at a time. Each combination will have five elements, one from each column. Please help me how to do this.
    Last edited by sanchit22; 07-27-2016 at 01:57 AM.

  20. #20
    VBAX Wizard
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    I didn't go through the macro, but try changing this line


    aData = Array("5L", "5R", "4L", "4R", "3L", "3R", "B2", "B3", "B4")
    
    aData(I) = … refers to just one element
    Paul

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