Step through a single permutation order based on a number provided - vba

Question

I have 5 items that can be placed in any unique order, I want to store the values (numbers) of a single unique order to a variable, one by one. For example:
User input: 7
Then i_Int = 7
should give me
v_Var = 1
wait 1 sec
v_Var = 3
wait 1 sec
v_Var = 2
wait 1 sec
v_Var = 4
wait 1 sec
v_Var = 5
The data below list all possible permutations of 5 items, where the first row lists the permutation #, I will not have this data to make things easy.
1 1 2 3 4 5
2 1 2 3 5 4
3 1 2 4 3 5
4 1 2 4 5 3
5 1 2 5 3 4
6 1 2 5 4 3
7 1 3 2 4 5
8 1 3 2 5 4
9 1 3 4 2 5
10 1 3 4 5 2
...
111 5 3 2 1 4
112 5 3 2 4 1
113 5 3 4 1 2
114 5 3 4 2 1
115 5 4 1 2 3
116 5 4 1 3 2
117 5 4 2 1 3
118 5 4 2 3 1
119 5 4 3 1 2
120 5 4 3 2 1

Answer 1

Here is a function that returns the permutation of 1,...,n of rank i:
Function Unrank(ByVal n As Long, ByVal rank As Long, Optional lb As Long = 1) As Variant
Dim Permutation As Variant
Dim Items As Variant
ReDim Permutation(lb To lb + n - 1)
ReDim Items(0 To n - 1)
Dim i As Long, j As Long, k As Long, q As Long
Dim fact As Long
For i = 0 To n - 1
Items(i) = i + 1
Next i
rank = rank - 1
j = lb
For i = n - 1 To 1 Step -1
fact = Application.WorksheetFunction.fact(i)
q = Int(rank / fact)
Permutation(j) = Items(q)
'slide items above q 1 unit to left
For k = q + 1 To i
Items(k - 1) = Items(k)
Next k
j = j + 1
rank = rank Mod fact
Next i
'place last item:
Permutation(lb + n - 1) = Items(0)
Unrank = Permutation
End Function
As a default, it returns the result as a 1-based array. To make it 0-based, use a call like Unrank(5,7,0). As a test:
Sub test()
'fills A1:A120 with the permutations of 1,2,3,4,5
Dim i As Long
For i = 1 To 120
Cells(i, 1).Value = Join(Unrank(5, i), " ")
Next i
End Sub
13! is too large to hold in a Long variable, so the code throws an untrapped error when n=14. The algorithm that I use depends on the ability to do modular arithmetic with the relevant factorials, so there is no easy fix in VBA. Note that you could easily tweak the code so that you pass it an array of items to permute rather than always permuting 1-n. The algorithm destroys the array Items, so such a tweak would involve creating a 0-based (so that the modular arithmetic works out) copy of the passed array.