Generates a magic square of order N. A magic squares is an N-by-N
* matrix of the integers 1 to N^2, such that all row, column, and
* diagonal sums are equal.
*
* One way to generate a magic square when N is odd is to assign
* the integers 1 to N^2 in ascending order, starting at the
* bottom, middle cell. Repeatedly assign the next integer to the
* cell adjacent diagonally to the right and down. If this cell
* has already been assigned another integer, instead use the
* cell adjacently above. Use wrap-around to handle border cases.
*must be an odd

public class MagicSquare {

    public static void main(String[] args) { 
        int N = Integer.parseInt(args[0]);
        if (N % 2 == 0) throw new RuntimeException("N must be odd");

        int[][] magic = new int[N][N];

        int row = N-1;
        int col = N/2;
        magic[row][col] = 1;

        for (int i = 2; i <= N*N; i++) {
            if (magic[(row + 1) % N][(col + 1) % N] == 0) {
                row = (row + 1) % N;
                col = (col + 1) % N;
            }
            else {
                row = (row - 1 + N) % N;
                // don't change col
            }
            magic[row][col] = i;
        }

        // print results
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                if (magic[i][j] < 10)  System.out.print(" ");  // for alignment
                if (magic[i][j] < 100) System.out.print(" ");  // for alignment
                System.out.print(magic[i][j] + " ");
            }
            System.out.println();
        }

    }
}

Edited 3 Years Ago by Nick Evan: Fixed formatting

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