How do I generate a magic square using only a 1 dimensional array?

Question

I am assigned to prompt a user to give the order of a magic square (a magic square of order 3 would be a 3x3 matrix) and then generate a magic square of that order without using a 2 dimensional array.

Here's what I know and understand:

• The Array will have order squared elements.
• When you print out the table, the location of number in the array is [order × row + col]
• The index of the array's location on the table is (index/order, index % order)

Here's what I am given but don't understand how to implement properly:

1. row = order − 1, col = order/2 and i = 1

2. Repeat the following until i = order^2 + 1:

   (a) magic[index] = i

   (b) increment row and col by 1. that is, row = (row + 1) mod order and col = (col + 1) % order

   (c) If magic[index] != 0

      i. row = (row + order − 2) % order
   
      ii. col = (col + order − 1) % order
   

   (d) increment i by 1

This is my code so far:

package magicsquarecreator;

import java.io.IOException;
import java.util.Scanner;


public class MagicSquareDemo
{
   public static void main(String[] args) 
   {
      Scanner keyIn = new Scanner(System.in); 
      String option; 
      do
      {
         System.out.println();        
         System.out.println("             MAGIC SQUARE APPLICATION             ");
         System.out.println("==================================================");
         System.out.println("Generate a Magic Square........................[1]");
         System.out.println("Test for a Magic Square........................[2]");
         System.out.println("Quit the Program...............................[0]");
         System.out.println();
         System.out.print("Select an option -> ");
         option = keyIn.next(); 
         System.out.println(); 

         switch(option)
         {
            case "1": 
               try
               {
                    System.out.println("Enter the dimension of the magic square -> ");
                    int order = keyIn.nextInt();
                    if (order < 1)
                    {
                        System.out.println("The order must be positive and odd");
                    }
                    else if (order % 2 == 0)
                    {
                        System.out.println("The program can only generate a magic square"
                                + "\nwhose dimension is positive odd number.");
                    }
                    else if (order % 2 != 0)
                    {
                        int i=1, j=1;
                        int row = order - 1;
                        int col = order/2;
                        int[] magic = new int[order*order];
                        for (i=1; i<=order; i++)
                        {
                            magic[i] = i;
                            row = (row + 1) % order;
                            col = (col + 1) % order;
                            if (magic[i] != 0)
                            {
                              row = (row + order − 2) % order;
                              col = (col + order − 1) % order;
                            }
                        }
                    }
               }
               catch(IOException e)
               {
                  System.out.println(e);
               }
               break;                    
            case "2": 
               try
               {


               }
               catch(IOException e)
               {
                  System.out.println(e);
               }
               break;    
            case "0": 
               break;    
            default: System.out.println("Invalid choice...please select a valid menu option.");
         }
      } 
      while (option.compareTo("0") != 0); 
   } 
}

Right now I am just worried about getting and understanding case 1. The Try Catch statements for file output, but I can do that on my own time. The biggest problem currently is understanding how to create this loop.

Answer 1

to be honest, i also didnt really understand the taks, as it was written from u. if i do it as i understand it there, it does not work. but i looked ub how it should work and finally i got it. here is the part for the else if (order % 2 != 0) condition as a methode (i tested it, it is working right now):

public static void magicSqare(int order){
    System.out.println(order);
    int row = order - 1;
    int col = order /2;
    int [] magic = new int [order*order];
    int index;

    index = (row)*order + col;
    magic[index]= 1;

    for (int i = 2; i <= order*order; i++) {
        if (magic[((row +1) % order)*order + ((col +1) % order)] == 0) {
        row = (row +1) % order;
        col = (col +1) % order;
        }

        else {
            row = (row + order -1) % order;
            //col = (col + order -1) % order;
        }
        index = (row)*order + col;
        magic[index]= i;
    }

    //System.out.println(Arrays.toString(magic));
}