Some 4 years ago I wrote an article for calculating magic square with python. What the article did was actually checking whether the square is magic, and not calculating a new one. This one is going to show how these squares are built.
Wikipedia says that magic square is a square grid, filled with distinct positive integers in range 1,2, 3... n^2, such that each cell contains a different integer and the sum of the integers per column, row and diagonals is equal. In the general case, building a magic square in VBA requires a few more checks, but as I have recently got a bit deeper into Python, I have noticed that Python has its own way of mathematics, when it comes to negative numbers. (Modulo Operation on Negative Numbers). Long story short, Python claims that:
while in the VBA (and all the C languages), -1 mod 3 and 1 mod 3 would return -1 or 1 . Nothing to do with 2. Which mathematics is “better” is another story, the thing is that the “Python way of doing maths” allows us to write a magic square in quite quick way. If we want to represent the Python mod function in VBA, this is it:
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Public Function PythonMod(a, b) As Long PythonMod = (((a Mod b) + b) Mod b) End Function |
With this function in hand, building a Magic Square in VBA becomes “a piece of cake”:
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While n <= size * size magicArray(i, j) = n n = n + 1 ii = PythonModule((i - 1), size) jj = PythonModule((j + 1), size) If magicArray(ii, jj) Then i = i + 1 Else i = ii j = jj End If Wend |
With a size big enough to see what is going on, one may notice the logic – build always up and to the left except for the case when the Array((i-1) mod size, (j+1) mod size) is taken:
This is the whole code, allowing you to impress someone. Start with the Main() function and feel free to change the size:
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Sub CreateMagicSquare(size As Long) Dim ws As Worksheet Set ws = Worksheets(1) ws.Cells.Delete Dim magicRange As Range Dim magicArray() As Long ReDim magicArray(size - 1, size - 1) With ws Set magicRange = .Range(.Cells(1, 1), .Cells(size, size)) End With SetColumnWidth ws, 1, size, 2.8 Dim i As Long: i = 0 Dim j As Long: j = size \ 2 Dim n As Long: n = 1 Dim ii As Long Dim jj As Long While n <= size * size magicArray(i, j) = n magicRange(i + 1, j + 1) = n n = n + 1 ii = PythonModule((i - 1), size) jj = PythonModule((j + 1), size) If magicArray(ii, jj) Then i = i + 1 Else i = ii j = jj End If Wend End Sub Public Function PythonModule(a, b) As Long PythonModule = (((a Mod b) + b) Mod b) End Function Sub SetColumnWidth(ws As Worksheet, fromColumn As Long, toColumn As Long, size As Double) Dim i As Long For i = fromColumn To toColumn ws.Columns(i).ColumnWidth = size Next i End Sub Sub Main() CreateMagicSquare 9 End Sub |
The same code in Python, without the “fancy” excel visualisation looks like this:
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import numpy as np N = 7 magic_square = np.zeros((N,N),dtype=int) n = 1 i = 0 j = N//2 while n <= N * N: magic_square[i,j] = n n += 1 ii = (i-1) % N jj = (j+1) % N if magic_square[ii, jj]: i += 1 else: i, j = ii, jj print(magic_square) print("\n") #fancy formatting here: nice_list = [["%3s" % str(str(j)+"|") for j in i] for i in magic_square] for line in nice_list: print(" ".join(map(str,line))) |
Still, the formatting is not that bad:
Cheers!