Java Magic Square 2d Array

Java Magic Square 2d Array | A magic square is a matrix that has a different integer, the sum of a number in every row, column, and diagonally is the same. This sum value is called a magic constant.

The formula to find the magic constant is M = n[(n^2+1) / 2]
Where, n = is the order of the matrix.

Observe the below examples of Java magic square 2d array:-

2 7 6
9 5 1
4 3 8
The above matrix is of 3X3 hence applying the above formula, magic constant M => 3[(3^2+1) / 2] = 15. The sum of each row and column is 15. Similarly, the sum of each diagonal is also 15 hence the given matrix is a magic square.

Let us see another example in a different order.
9 3 22 16 15
2 21 20 14 8
25 19 13 7 1
18 12 6 5 24
11 10 4 23 17
This is a 5X5 matrix hence the magic constant will be 5(52+1)/2 = 65.

Java Magic Square 2d Array Code

Now let us see a Java program to generate a magic square of the given order.

public class Main {

   public static void magicSquare(int n) {
      int[][] magic = new int[n][n];

      int i = n / 2;
      int j = n - 1;

      for (int num = 1; num <= n * n;) {
         if (i == -1 && j == n) {
            j = n - 2;
            i = 0;
         } else {
            if (j == n) {
               j = 0;
            }
            if (i < 0) {
               i = n - 1;
            }
         }

         if (magic[i][j] != 0) {
            j -= 2;
            i++;
            continue;
         } else {
            magic[i][j] = num++;
         }

         j++;
         i--;
      }

      System.out.println("The Magic Square for order " + n + ",");
      System.out.println("Magic constant: " + n * (n * n + 1) / 2);
      System.out.println("Matrix: ");
      for (i = 0; i < n; i++) {
         for (j = 0; j < n; j++) {
            System.out.print(magic[i][j] + " ");
         }
         System.out.println();
      }
   }

   public static void main(String[] args) {
      int order = 3;
      magicSquare(order);
   }
}

Output:-

The Magic Square for order 3,
Magic constant: 15
Matrix:
2 7 6
9 5 1
4 3 8

Test-case:- Demonstrating Java magic square 2d array code of order 5×5

public class Main {

   public static void magicSquare(int n) {
      int[][] magic = new int[n][n];

      int i = n / 2;
      int j = n - 1;

      for (int num = 1; num <= n * n;) {
         if (i == -1 && j == n) {
            j = n - 2;
            i = 0;
         } else {
            if (j == n) {
               j = 0;
            }
            if (i < 0) {
               i = n - 1;
            }
         }

         if (magic[i][j] != 0) {
            j -= 2;
            i++;
            continue;
         } else {
            magic[i][j] = num++;
         }

         j++;
         i--;
      }

      System.out.println("The Magic Square for order " + n + ",");
      System.out.println("Magic constant: " + n * (n * n + 1) / 2);
      System.out.println("Matrix: ");
      for (i = 0; i < n; i++) {
         for (j = 0; j < n; j++) {
            System.out.print(magic[i][j] + " ");
         }
         System.out.println();
      }
   }

   public static void main(String[] args) {
      int order = 3;
      magicSquare(order);
   }
}

Output:-

The Magic Square for order 5,
Magic constant: 65
Matrix:
9 3 22 16 15
2 21 20 14 8
25 19 13 7 1
18 12 6 5 24
11 10 4 23 17

Also see:- Java Count Occurrences in 2D Array

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