Vba subset summation algorithm

I am trying to write an algorithm to solve the subset sum problem.

I believe I have the beginning of an algorithm, but I want to write something that will start with 1 set of N sets depending on the length of the array. Ideally this will spill out the first result that matches.

I believe it could be better written as it follows the pattern.

Any input is greatly appreciated.

Thank!

Antonio

Function SubnetSum()

Dim num() As Variant
Dim goal As Double
Dim result As Double

Num() = array (1,2,3,4,5,6,7,8,9,10)

goal = 45

For i = LBound(num) To UBound(num)
    If num(i) = goal Then
        MsgBox num(i) & " " & goal & " 1 Set"
        Exit Function
    End If
Next

For i = LBound(num) To UBound(num)
    For j = i + 1 To UBound(num)
        If num(i) + num(j) = goal Then
            result = num(i) + num(j)
            MsgBox result & " " & goal & " 2 Sets"
            Exit Function
        End If
    Next
Next

For i = LBound(num) To UBound(num)
    For j = i + 1 To UBound(num)
        For k = j + 1 To UBound(num)
            If num(i) + num(j) + num(k) = goal Then
                result = num(i) + num(j) + num(k)
                MsgBox result & " " & goal & " 3 Sets"
                Exit Function
            End If
        Next
    Next
Next

For i = LBound(num) To UBound(num)
    For j = i + 1 To UBound(num)
        For k = j + 1 To UBound(num)
            For l = k + 1 To UBound(num)
                If num(i) + num(j) + num(k) + num(l) = goal Then
                    result = num(i) + num(j) + num(k) + num(l)
                    MsgBox result & " " & goal & " 4 Sets"
                    Exit Function
                End If
            Next
        Next
    Next
Next

For i = LBound(num) To UBound(num)
    For j = i + 1 To UBound(num)
        For k = j + 1 To UBound(num)
            For l = k + 1 To UBound(num)
                For m = l + 1 To UBound(num)
                    If num(i) + num(j) + num(k) + num(l) + num(m) = goal Then
                        result = num(i) + num(j) + num(k) + num(l) + num(m)
                        MsgBox result & " " & goal & " 5 Sets"
                        Exit Function
                    End If
                Next
            Next
        Next
    Next
Next

MsgBox "Nothing found"

End Function

      

        
        
        
      

    

Edit

@Enderland Thanks for the article, I found it quite amusing and sorry as this is my first post on this site.

What I am trying to do is solve the subset sum problem, that is, I have a goal of 9 and using a set of numbers [1,2,3,4,5], I want to find the most optimal way to go to 5 using the combination numbers in the array.

Possible solutions are [5], [5.4], [5,3,1], [4,3,2]. However, I want to get the most optimal solution, which is [5].

Also, if my goal is to get 14 from [1,2,3,4,5], it will loop through all possible combinations of additions in the array of numbers and splash out the most optimal solution, which in this case [5,4,3, 2].

What my code does is that it pushes the array numbers down to 5 values ​​until it gets the most optimal solution.

What I want to do is write a recursive loop so that it is not hardcoded for only 5 possible values. Instead, I want to be able to loop through a combination of numbers with N possible values ​​based on the size of the array.

However, I cannot think of a loop that would support this feature. I'm sure this is possible with a little recursion.

I guess my question would be ... Is there a way to solidify the code I have above into one complex recursive function?

Thank!