Step by Step solution about How to resolve the algorithm Magic squares of odd order step by step in the Java programming language

The provided Java code defines a class MagicSquare that generates a magic square of odd order. A magic square is an arrangement of numbers, usually integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.

Implementation Details:

• magicSquareOdd Method:

  • This method takes an int parameter base which represents the order of the magic square (it has to be an odd number greater than 2).
  • It initializes a 2D array grid to represent the magic square, with a size of base x base.
  • The method uses two variables r and c to keep track of the current row and column, and a variable number to keep track of the number being placed in the square.
  • It enters a while loop that runs base * base times to fill the grid with numbers.
  • Inside the loop:
    • It places the current number in the grid at the current r and c position.
    • It adjusts r and c based on specific rules to determine the next position to place a number:
      • If it's on the first row, it either moves down or wraps around to the last row.
      • If it's on the last column, it either moves left or wraps around to the first column.
      • Otherwise, it moves diagonally down and right, or up if the space is already occupied.
  • After filling the grid, it returns the grid as a 2D array.

• main Method:

  • Creates a magic square of order 5 using the magicSquareOdd method and prints it to the console.
  • It also calculates and prints the magic constant, which is a constant sum for all rows, columns, and diagonals of a valid magic square.

Example Output:

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

public class MagicSquare {

    public static void main(String[] args) {
        int n = 5;
        for (int[] row : magicSquareOdd(n)) {
            for (int x : row)
                System.out.format("%2s ", x);
            System.out.println();
        }
        System.out.printf("\nMagic constant: %d ", (n * n + 1) * n / 2);
    }

    public static int[][] magicSquareOdd(final int base) {
        if (base % 2 == 0 || base < 3)
            throw new IllegalArgumentException("base must be odd and > 2");

        int[][] grid = new int[base][base];
        int r = 0, number = 0;
        int size = base * base;

        int c = base / 2;
        while (number++ < size) {
            grid[r][c] = number;
            if (r == 0) {
                if (c == base - 1) {
                    r++;
                } else {
                    r = base - 1;
                    c++;
                }
            } else {
                if (c == base - 1) {
                    r--;
                    c = 0;
                } else {
                    if (grid[r - 1][c + 1] == 0) {
                        r--;
                        c++;
                    } else {
                        r++;
                    }
                }
            }
        }
        return grid;
    }
}