How to Create Magic Matrix ?

This one does (http://www.codeproject.com/KB/recipes/Magic_Square.aspx ) if that's what the OP means by a "magic matrix".

For a bit of fun, I've translated the C++ code into C# - took me about 10 minutes as, apart from the vector stuff, it's virtually the same! Surprisingly, it seems to work:

using System;

using System.Collections.Generic;

class Program

{

static int Main()

{

int n;

Console.Write("Enter order of square: ");

int.TryParse(Console.ReadLine(), out n);

if (n < 3)

{

Console.WriteLine("\nError: n must be greater than 2\n");

return -1;

}

List> matrix = new List>();

for (int i = 0; i < n; i++)

{

List temp = new List();

for (int j = 0; j < n; j++)

{

temp.Add(0);

}

matrix.Add(temp);

}

MagicSquare(matrix, n);

//Print results

PrintMagicSquare(matrix, n);

Console.ReadKey();

return 0;

}

static void MagicSquare(List> matrix, int n)

{

if (n % 2 == 1) // n is Odd

{

OddMagicSquare(matrix, n);

}

else if (n % 4 == 0) // doubly even order

{

DoublyEvenMagicSquare(matrix, n);

}

else // singly even order

{

SinglyEvenMagicSquare(matrix, n);

}

static void OddMagicSquare(List> matrix, int n)

{

int nsqr = n * n;

int i = 0, j = n / 2; // start position

for (int k = 1; k <= nsqr; ++k)

{

matrix[i][j] = k;

i--;

j++;

if (k % n == 0)

{

i += 2;

j--;

}

else if (j == n)

{

j -= n;

}

else if (i < 0)

{

i += n;

}

static void DoublyEvenMagicSquare(List> matrix, int n)

{

List> I = new List>();

for (int k = 0; k < n; k++)

{

List temp = new List();

for (int l = 0; l < n; l++)

{

temp.Add(0);

}

I.Add(temp);

}

List> J = new List>();

for (int k = 0; k < n; k++)

{

List temp = new List();

for (int l = 0; l < n; l++)

{

temp.Add(0);

}

J.Add(temp);

}

int i, j;

//prepare I, J

int index = 1;

for (i = 0; i < n; i++)

{

for (j = 0; j < n; j++)

{

I[i][j] = ((i + 1) % 4) / 2;

J[j][i] = ((i + 1) % 4) / 2;

matrix[i][j] = index;

index++;

}

for (i = 0; i < n; i++)

{

for (j = 0; j < n; j++)

{

if (I[i][j] == J[i][j])

matrix[i][j] = n * n + 1 - matrix[i][j];

}

static void SinglyEvenMagicSquare(List> matrix, int n)

{

int p = n / 2;

List> M = new List>();

for (int m = 0; m < p; m++)

{

List list = new List();

for (int q = 0; q < p; q++)

{

list.Add(0);

}

M.Add(list);

}

MagicSquare(M, p);

int i, j, k;

for (i = 0; i < p; i++)

{

for (j = 0; j < p; j++)

{

matrix[i][j] = M[i][j];

matrix[i + p][j] = M[i][j] + 3 * p * p;

matrix[i][j + p] = M[i][j] + 2 * p * p;

matrix[i + p][j + p] = M[i][j] + p * p;

}

if (n == 2) return;

List I = new List();

for (int m = 0; m < p; m++)

{

I.Add(0);

}

List J = new List();

for (i = 0; i < p; i++)

{

I[i] = i + 1;

}

k = (n - 2) / 4;

for (i = 1; i <= k; i++)

{

J.Add(i);

}

for (i = n - k + 2; i <= n; i++)

{

J.Add(i);

}

int temp;

for (i = 1; i <= p; i++)

{

for (j = 1; j <= J.Count; j++)

{

temp = matrix[i - 1][J[j - 1] - 1];

matrix[i - 1][J[j - 1] - 1] = matrix[i + p - 1][J[j - 1] - 1];

matrix[i + p - 1][J[j - 1] - 1] = temp;

}

//j=1, i

//i=k+1, k+1+p

}

i = k;

j = 0;

temp = matrix[i][j]; matrix[i][j] = matrix[i + p][j]; matrix[i + p][j] = temp;

j = i;

temp = matrix[i + p][j]; matrix[i + p][j] = matrix[i][j]; matrix[i][j] = temp;

}

static void PrintMagicSquare(List> matrix, int n)

{

Console.WriteLine();

for (int i = 0; i < n; i++)

{

for (int j = 0; j < n; j++)

{

Console.Write(" {0, 3}", matrix[i][j]);

}

Console.WriteLine();

}

Console.WriteLine();

}

2 Replies

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Vulpes15y ago
This one does (http://www.codeproject.com/KB/recipes/Magic_Square.aspx ) if that's what the OP means by a "magic matrix".

For a bit of fun, I've translated the C++ code into C# - took me about 10 minutes as, apart from the vector stuff, it's virtually the same! Surprisingly, it seems to work:

using System;
using System.Collections.Generic;

class Program
{
   static int Main()
   {
   int n;
   Console.Write("Enter order of square: ");
   int.TryParse(Console.ReadLine(), out n);

   if (n < 3)
   {
   Console.WriteLine("\nError: n must be greater than 2\n");
   return -1;
   }

   List> matrix = new List>();

   for (int i = 0; i < n; i++)
   {
   List temp = new List();
   for (int j = 0; j < n; j++)
   {
   temp.Add(0);
   }
   matrix.Add(temp);
   }

   MagicSquare(matrix, n);

   //Print results

   PrintMagicSquare(matrix, n);

   Console.ReadKey();

   return 0;
   }

   static void MagicSquare(List> matrix, int n)
   {
   if (n % 2 == 1) // n is Odd
   {
   OddMagicSquare(matrix, n);
   }
   else if (n % 4 == 0) // doubly even order
   {
   DoublyEvenMagicSquare(matrix, n);
   }
   else // singly even order
   {
   SinglyEvenMagicSquare(matrix, n);
   }
   }

   static void OddMagicSquare(List> matrix, int n)
   {
   int nsqr = n * n;
   int i = 0, j = n / 2; // start position

   for (int k = 1; k <= nsqr; ++k)
   {
   matrix[i][j] = k;
   i--;
   j++;

   if (k % n == 0)
   {
   i += 2;
   j--;
   }
   else if (j == n)
   {
   j -= n;
   }
   else if (i < 0)
   {
   i += n;
   }
   }
   }

   static void DoublyEvenMagicSquare(List> matrix, int n)
   {
   List> I = new List>();

   for (int k = 0; k < n; k++)
   {
   List temp = new List();
   for (int l = 0; l < n; l++)
   {
   temp.Add(0);
   }
   I.Add(temp);
   }

   List> J = new List>();

   for (int k = 0; k < n; k++)
   {
   List temp = new List();
   for (int l = 0; l < n; l++)
   {
   temp.Add(0);
   }
   J.Add(temp);
   }

   int i, j;

   //prepare I, J

   int index = 1;
   for (i = 0; i < n; i++)
   {
   for (j = 0; j < n; j++)
   {
   I[i][j] = ((i + 1) % 4) / 2;
   J[j][i] = ((i + 1) % 4) / 2;
   matrix[i][j] = index;
   index++;
   }
   }

   for (i = 0; i < n; i++)
   {
   for (j = 0; j < n; j++)
   {
   if (I[i][j] == J[i][j])
   matrix[i][j] = n * n + 1 - matrix[i][j];
   }
   }
   }

   static void SinglyEvenMagicSquare(List> matrix, int n)
   {
   int p = n / 2;

   List> M = new List>();

   for (int m = 0; m < p; m++)
   {
   List list = new List();
   for (int q = 0; q < p; q++)
   {
   list.Add(0);
   }
   M.Add(list);
   }

   MagicSquare(M, p);

   int i, j, k;

   for (i = 0; i < p; i++)
   {
   for (j = 0; j < p; j++)
   {
   matrix[i][j] = M[i][j];
   matrix[i + p][j] = M[i][j] + 3 * p * p;
   matrix[i][j + p] = M[i][j] + 2 * p * p;
   matrix[i + p][j + p] = M[i][j] + p * p;
   }
   }
   if (n == 2) return;

   List I = new List();
   for (int m = 0; m < p; m++)
   {
   I.Add(0);
   }

   List J = new List();

   for (i = 0; i < p; i++)
   {
   I[i] = i + 1;
   }

   k = (n - 2) / 4;

   for (i = 1; i <= k; i++)
   {
   J.Add(i);
   }

   for (i = n - k + 2; i <= n; i++)
   {
   J.Add(i);
   }

   int temp;

   for (i = 1; i <= p; i++)
   {
   for (j = 1; j <= J.Count; j++)
   {
   temp = matrix[i - 1][J[j - 1] - 1];
   matrix[i - 1][J[j - 1] - 1] = matrix[i + p - 1][J[j - 1] - 1];
   matrix[i + p - 1][J[j - 1] - 1] = temp;
   }

   //j=1, i

   //i=k+1, k+1+p
   }

   i = k;
   j = 0;
   temp = matrix[i][j]; matrix[i][j] = matrix[i + p][j]; matrix[i + p][j] = temp;

   j = i;
   temp = matrix[i + p][j]; matrix[i + p][j] = matrix[i][j]; matrix[i][j] = temp;
   }

   static void PrintMagicSquare(List> matrix, int n)
   {
   Console.WriteLine();

   for (int i = 0; i < n; i++)
   {
   for (int j = 0; j < n; j++)
   {
   Console.Write(" {0, 3}", matrix[i][j]);
   }

   Console.WriteLine();
   }

   Console.WriteLine();
   }

}
Sam Hobbs15y ago
Magicians don't tell the secrets of how it is done.