How to fill in a dynamic combination of numbers into an array - arrays

Question

In my Excel worksheet users can enter 1 to 5 rows of data in the form of minimum, maximum and step size values. I want to create an multidimensional array that has all the combinations of the data.
Is there a way to code this in VBA to dynamically size the array and loop through the cell values without knowing how many data items beforehand?
Example data of 3 rows of inputs (can be more or less)
Min, Max, Step
Data 1: 1, 10, 1
Data 2: 10, 50, 10
Data 3: 5, 25, 5
Total combinations is 250 (10 x 5 x 5)
Combo 1: 1, 10, 5
Combo 2: 1, 10, 10
Combo 3: 1, 10, 15
...
Thanks!

Answer 1

I found your question a little unclear but I believe the macro below does what you want.
If you have a variant Result, you can set Result to an array. You can then, in turn, set Result(1), Result(1)(1), Result(1)(1)(1) and so on to nested arrays. With suitable recursive routines I believe you could create the sort of array you seek of any size within the limits Excel. However, I think this approach would be very difficult to understand.
I do not believe there is a simpler way of creating an array with a variable number of dimensions. Changing the size of the dimensions is, however, not a problem.
Since you have a maximum of five dimensions, I have decided to go for a fixed number of dimensions with trailing, unused dimensions having a width of one. With your example (1 to 10 step 1, 10 to 50 step 10, 5 to 25 step 5), this would require:
Dim Result(1 To 10, 1 To 5, 1 To 5, 1 To 1, 1 To 1)
The first three dimensions have 10, 5 and 5 elements, ready to hold a range of values. The final two dimensions are just place holders.
You are getting your users to enter dimension details. I have loaded details from worksheet "Dyn Dims". For the test that matches your example, I set this worksheet to:
Min Max Step
1 10 1
10 50 10
5 25 5
I load this information to long array Requirements(1 To 3, 1 To 5). The columns are minimum, maximum and step. The rows allow for a maximum of five dimensions. If column 3 (step) is zero, the dimension is not used. I do not allow for negative step values but indicate where changes would be required if this was necessary.
You will need to initialise this array from the data entered by your users.
From array Requirements, the macro calculates the number of elements in each dimension. I have tested this calculation with values, such as 1 step 2 to 10, where there is no value for N such that Min + N * Step = Max.
The macro then dimensions array Result as necessary.
You do not say what values you want within the array so I have set them to values of the form "N:N:N" where the Ns are the values from the Min-To-Max-Step calculation. I have explained this in the macro and will not repeat myself here.
Finally, I output the contents of the array to a file named for the date and time. With your example the output is:
Dimensions
1 2 3 Value
1 1 1 1:10:5
2 1 1 2:10:5
3 1 1 3:10:5
4 1 1 4:10:5
5 1 1 5:10:5
6 1 1 6:10:5
7 1 1 7:10:5
8 1 1 8:10:5
9 1 1 9:10:5
10 1 1 10:10:5
1 2 1 1:20:5
: : : :
5 5 5 5:50:25
6 5 5 6:50:25
7 5 5 7:50:25
8 5 5 8:50:25
9 5 5 9:50:25
10 5 5 10:50:25
I believe I have included enough comments to explain the macro but come back with questions if necessary.
Option Explicit
Sub DD()
Const ColReqMin As Long = 1
Const ColReqMax As Long = 2
Const ColReqStep As Long = 3
Dim DimCrnt As Long
Dim Entry(1 To 5) As Long
Dim EntryStepped As Boolean
Dim FileOutNum As Long
Dim Index(1 To 5) As Long
Dim IndexStepped As Boolean
Dim NumEntries(1 To 5) As Long
Dim Requirements(1 To 3, 1 To 5) As Long
Dim Result() As String
Dim RowDDCrnt As Long
Dim Stg As String
Dim Value As String
' Load Requirements with the required ranges
With Worksheets("Dyn Dims")
RowDDCrnt = 2 ' First data row of worksheet Dyn Dims
' Note this macro does not check for blank lines in the middle
' of the table.
For DimCrnt = 1 To 5
If IsEmpty(.Cells(RowDDCrnt, ColReqStep)) Then
' No step value so this dimension not required for this run
Requirements(ColReqStep, DimCrnt) = 0
Else
Requirements(ColReqMin, DimCrnt) = .Cells(RowDDCrnt, ColReqMin)
Requirements(ColReqMax, DimCrnt) = .Cells(RowDDCrnt, ColReqMax)
Requirements(ColReqStep, DimCrnt) = .Cells(RowDDCrnt, ColReqStep)
End If
RowDDCrnt = RowDDCrnt + 1
Next
End With
' Calculate number of entries for each dimension
For DimCrnt = 1 To 5
If Requirements(ColReqStep, DimCrnt) = 0 Then
' Dummy dimension
NumEntries(DimCrnt) = 1
Else
NumEntries(DimCrnt) = (Requirements(ColReqMax, DimCrnt) - _
Requirements(ColReqMin, DimCrnt) + _
Requirements(ColReqStep, DimCrnt)) \ _
Requirements(ColReqStep, DimCrnt)
End If
Next
' Size array
ReDim Result(1 To NumEntries(1), _
1 To NumEntries(2), _
1 To NumEntries(3), _
1 To NumEntries(4), _
1 To NumEntries(5))
' Initialise entry for each dimension to minimum value, if any,
' and index for each dimension to 1
For DimCrnt = 1 To 5
Index(DimCrnt) = 1
If Requirements(ColReqStep, DimCrnt) <> 0 Then
Entry(DimCrnt) = Requirements(ColReqMin, DimCrnt)
End If
Next
' Starting with Entry(1), this loop steps the entry if the dimension is used.
' If the stepped entry is not greater than the maximum, then this repeat of
' the loop has finished. If the stepped entry is greater than the maximum,
' it is reset to its minimum and the next entry stepped and checked in the
' same way. If no entry is found that can be stepped, the loop is finished.
' If the dimensions after all 1 to 3 step 1, the values created by this loop
' are:
' 1 1 1 1 1
' 2 1 1 1 1
' 3 1 1 1 1
' 1 2 1 1 1
' 2 2 1 1 1
' 3 2 1 1 1
' 1 3 1 1 1
' 2 3 1 1 1
' 3 3 1 1 1
' 1 1 2 1 1
' 2 1 2 1 1
' 3 1 2 1 1
' : : : : :
' 3 3 3 3 3
Do While True
' Concatenate entries to create value for initial element
' or for element identified by last loop
Value = Entry(1)
For DimCrnt = 2 To 5
If Requirements(ColReqStep, DimCrnt) = 0 Then
Exit For
End If
Value = Value & ":" & Entry(DimCrnt)
Next
Result(Index(1), Index(2), Index(3), Index(4), Index(5)) = Value
' Find an entry to step
EntryStepped = False
For DimCrnt = 1 To 5
If Requirements(ColReqStep, DimCrnt) = 0 Then
Exit For
End If
Index(DimCrnt) = Index(DimCrnt) + 1
Entry(DimCrnt) = Entry(DimCrnt) + _
Requirements(ColReqStep, DimCrnt)
' ### Changes required her if a negative step value is allow
If Entry(DimCrnt) <= Requirements(ColReqMax, DimCrnt) Then
' This stepped entry is within permitted range
EntryStepped = True
Exit For
End If
' This entry past its maximum so reset to minimum
' and let for loop step entry for next dimension
Index(DimCrnt) = 1
Entry(DimCrnt) = Requirements(ColReqMin, DimCrnt)
Next
If Not EntryStepped Then
' All elements of Result initialised
Exit Do
End If
Loop
' All elements of Result initialised
' Output values as test.
FileOutNum = FreeFile
Open ActiveWorkbook.Path & "\" & Format(Now(), "yymmdd hhmmss") & ".txt" _
For Output As #FileOutNum
' Initialise Index
For DimCrnt = 1 To 5
Index(DimCrnt) = 1
Next
' Create header line for table
Print #FileOutNum, "Dimensions"
Stg = ""
For DimCrnt = 1 To 5
If Requirements(ColReqStep, DimCrnt) = 0 Then
Exit For
End If
Stg = Stg & Right(" " & DimCrnt, 4)
Next
Stg = Stg & " Value"
Print #FileOutNum, Stg
' Similar logic to loop that intialised Result but using Index and UBound.
Do While True
' Output initial element or element identified by previous loop
Stg = ""
For DimCrnt = 1 To 5
If Requirements(ColReqStep, DimCrnt) = 0 Then
Exit For
End If
Stg = Stg & Right(" " & Index(DimCrnt), 4)
Next
Stg = Stg & " " & Result(Index(1), Index(2), Index(3), Index(4), Index(5))
Print #FileOutNum, Stg
' Identify next element, if any
IndexStepped = False
For DimCrnt = 1 To 5
If Requirements(ColReqStep, DimCrnt) = 0 Then
Exit For
End If
Index(DimCrnt) = Index(DimCrnt) + 1
If Index(DimCrnt) <= UBound(Result, DimCrnt) Then
IndexStepped = True
Exit For
Else
Index(DimCrnt) = 1
End If
Next
If Not IndexStepped Then
' All entries output
Exit Do
End If
Loop
Close #FileOutNum
End Sub