How to Create Magic Matrix ?

Question

Hi I want to a magic matrix .

Vulpes · Answer

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 { Console.WriteLine("
Error: n must be greater than 2
"); return -1; } List > matrix = new List >(); for (int i = 0; i { List temp = new List (); for (int j = 0; 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 { matrix[i][j] = k; i--; j++; if (k % n == 0) { i += 2; j--; } else if (j == n) { j -= n; } else if (i { i += n; } } } static void DoublyEvenMagicSquare(List > matrix, int n) { List > I = new List >(); for (int k = 0; k { List temp = new List (); for (int l = 0; l { temp.Add(0); } I.Add(temp); } List > J = new List >(); for (int k = 0; k { List temp = new List (); for (int l = 0; l { temp.Add(0); } J.Add(temp); } int i, j; //prepare I, J int index = 1; for (i = 0; i { for (j = 0; j { I[i][j] = ((i + 1) % 4) / 2; J[j][i] = ((i + 1) % 4) / 2; matrix[i][j] = index; index++; } } for (i = 0; i { for (j = 0; 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 { List list = new List (); for (int q = 0; q { list.Add(0); } M.Add(list); } MagicSquare(M, p); int i, j, k; for (i = 0; i { for (j = 0; 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 { I.Add(0); } List J = new List (); for (i = 0; i { I[i] = i + 1; } k = (n - 2) / 4; for (i = 1; i { J.Add(i); } for (i = n - k + 2; i { J.Add(i); } int temp; for (i = 1; i { for (j = 1; 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 { for (int j = 0; j { Console.Write(" {0, 3}", matrix[i][j]); } Console.WriteLine(); } Console.WriteLine(); } }

Sam Hobbs · Answer

Magicians don't tell the secrets of how it is done.