Generate List of All 2^n subsets - vba

Question

I'm looking for code in VBA to generate all subsets of the items in a passed array.
Below is simple code to select all N choose 2 subsets of array size N.
Looking to augment this for N choose (N-1)... all the way down to N choose 1.
Option Base 1
Sub nchoose2()
iarray = Array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
n = UBound(iarray)
x = 1
t = 0
r = 0
Do While (n - x) >= 1
For i = 1 To (n - x)
Cells((i + t), 1) = iarray(x)
Cells((i + t), 2) = iarray(i + x)
Next i
x = x + 1
t = t + (n - (1 + r))
r = r + 1
Loop
End Sub

Answer 1

In addition to the Gray-code algorithm, you can also exploit the correspondence between subsets of an n-element set and binary vectors of length n. The following code illustrates this approach:
Sub AddOne(binaryVector As Variant)
'adds one to an array consisting of 0s and 1s
'thought of as a binary number in little-endian
'the vector is modified in place
'all 1's wraps around to all 0's
Dim bit As Long, carry As Long, i As Long, n As Long
carry = 1
n = UBound(binaryVector)
i = LBound(binaryVector)
Do While carry = 1 And i <= n
bit = (binaryVector(i) + carry) Mod 2
binaryVector(i) = bit
i = i + 1
carry = IIf(bit = 0, 1, 0)
Loop
End Sub
Function listSubsets(items As Variant) As Variant
'returns a variant array of collections
Dim lb As Long, ub As Long, i As Long, j As Long, numSets As Long
Dim vect As Variant 'binary vector
Dim subsets As Variant
lb = LBound(items)
ub = UBound(items)
ReDim vect(lb To ub)
numSets = 2 ^ (1 + ub - lb)
ReDim subsets(1 To numSets)
For i = 1 To numSets
Set subsets(i) = New Collection
For j = lb To ub
If vect(j) = 1 Then subsets(i).Add items(j)
Next j
AddOne vect
Next i
listSubsets = subsets
End Function
Function showCollection(c As Variant) As String
Dim v As Variant
Dim i As Long, n As Long
n = c.Count
If n = 0 Then
showCollection = "{}"
Exit Function
End If
ReDim v(1 To n)
For i = 1 To n
v(i) = c(i)
Next i
showCollection = "{" & Join(v, ", ") & "}"
End Function
Sub test()
Dim stooges As Variant
Dim stoogeSets As Variant
Dim i As Long
stooges = Array("Larry", "Curly", "Moe")
stoogeSets = listSubsets(stooges)
For i = LBound(stoogeSets) To UBound(stoogeSets)
Debug.Print showCollection(stoogeSets(i))
Next i
End Sub
Running the code results in the following output:
{}
{Larry}
{Curly}
{Larry, Curly}
{Moe}
{Larry, Moe}
{Curly, Moe}
{Larry, Curly, Moe}

Answer 2

I asked a similar question a while back (2005) and received this excellent code from John Coleman:
Sub MAIN()
Dim i As Long, st As String
Dim a(1 To 12) As Integer
Dim ary
For i = 1 To 12
a(i) = i
Next i
st = ListSubsets(a)
ary = Split(st, vbCrLf)
For i = LBound(ary) To UBound(ary)
Cells(i + 1, 1) = ary(i)
Next i
End Sub
Function ListSubsets(Items As Variant) As String
Dim CodeVector() As Integer
Dim i As Integer
Dim lower As Integer, upper As Integer
Dim SubList As String
Dim NewSub As String
Dim done As Boolean
Dim OddStep As Boolean
OddStep = True
lower = LBound(Items)
upper = UBound(Items)
ReDim CodeVector(lower To upper) 'it starts all 0
Do Until done
'Add a new subset according to current contents
'of CodeVector
NewSub = ""
For i = lower To upper
If CodeVector(i) = 1 Then
If NewSub = "" Then
NewSub = Items(i)
Else
NewSub = NewSub & ", " & Items(i)
End If
End If
Next i
If NewSub = "" Then NewSub = "{}" 'empty set
SubList = SubList & vbCrLf & NewSub
'now update code vector
If OddStep Then
'just flip first bit
CodeVector(lower) = 1 - CodeVector(lower)
Else
'first locate first 1
i = lower
Do While CodeVector(i) <> 1
i = i + 1
Loop
'done if i = upper:
If i = upper Then
done = True
Else
'if not done then flip the *next* bit:
i = i + 1
CodeVector(i) = 1 - CodeVector(i)
End If
End If
OddStep = Not OddStep 'toggles between even and odd steps
Loop
ListSubsets = SubList
End Function
The original question and answer:
John Coleman