VBA loop where order doesn't matter - excel

Question

I'm trying to run a loop on 3 variables, where order doesn't matter.
The code I've tried first is the following, where nx runs through the rows, and limit is the last row of my database:
Do While n3 <= limit
Do While n2 <= limit
Do While n1 <= limit
Call Output
n1 = n1 + 1
Loop
Call Output
n2 = n2 + 1
n1 = n0
Loop
Call Output
n3 = n3 + 1
n2 = n0
n1 = n0
Loop
This allows me to test every possibility, but it does also repeat the same combination several times, which increases the runtime. This will make the code unusable if I plan on testing, let's say, 20 variables.
Any tips on how to optimize this loop?
Thank you.

Answer 1

Based on your comment that you do not want permutations of a given combination. Lets say we are mixing paint. We have five different colors:
white
black
yellow
blue
green
We want to mix all possible combinations of three cans, but once we have mixed
white,blue,green
we don't need any of these:
white,green,bluegreen,white,bluegreen,blue,whiteblue,green,whiteblue,white,green
because they all result in the same light teal.
First we run the loops in this staggered fashion:
Sub MixPaint()
Dim arr(1 To 5) As String
Dim i As Long, j As Long, k As Long, LL As Long
arr(1) = "white"
arr(2) = "black"
arr(3) = "blue"
arr(4) = "green"
arr(5) = "yellow"
LL = 1
For i = 1 To 3
For j = i + 1 To 4
For k = j + 1 To 5
Cells(LL, 1) = arr(i) & ":" & arr(j) & ":" & arr(k)
LL = LL + 1
Next k
Next j
Next i
End Sub
This gets us:
This removes the permuted duplicates, but it also removes combinations like:
blue,blue,white
To get these back we adjust the loops slightly:
Sub MixPaint2()
Dim arr(1 To 5) As String
Dim i As Long, j As Long, k As Long, LL As Long
arr(1) = "white"
arr(2) = "black"
arr(3) = "blue"
arr(4) = "green"
arr(5) = "yellow"
LL = 1
For i = 1 To 5
For j = i To 5
For k = j To 5
Cells(LL, 5) = arr(i) & ":" & arr(j) & ":" & arr(k)
LL = LL + 1
Next k
Next j
Next i
End Sub
Now we have:
Which may be what you are after.

Answer 2

If you need to loop through a table I would loop throw the rows and columns of the table, with a double for o double while, through all the cells, to avoid repeating combinations. According to your while approach this would be:
Do While row <= rowLimit
Do While col <= colLimit
'with if conditions you can make your operations
col = col +1
Loop
row = row + 1
Loop
If you need to loop through the rows independently, you dont need to the whiles to be nested, and each while can loop its row independently. If n1, n2, and n3 have dependencies with each other, you would need to explain those, so that their relation can be taken into account to exclude determined combinations from the nested loop.
However, if the order of the combination matters as far as I checked there are no combinations repeated in your loop.
This is the log of your loop for example for n1=n2=n3 and limit =2
1 0 0
0 1 0
0 0 0
1 0 0
2 0 0
3 0 0
0 1 0
1 1 0
2 1 0
3 1 0
0 2 0
1 2 0
2 2 0
3 2 0
0 3 0
0 0 1
1 0 1
2 0 1
3 0 1
0 1 1
1 1 1
2 1 1
3 1 1
0 2 1
1 2 1
2 2 1
3 2 1
0 3 1
0 0 2
1 0 2
2 0 2
3 0 2
0 1 2
1 1 2
2 1 2
3 1 2
0 2 2
1 2 2
2 2 2
3 2 2
0 3 2
But if the order does not matter and you need to loop through every n, up to the row limit, with no n value reptition, then the while loop can be independent so do not need to be nested.
So I am not sure if I have answered your question or I am missing something.
Hope that helps anyhow