Magic squares. An n × n matrix that is filled with the numbers 1, 2, 3, . . ., n

Question

Magic squares. An n × n matrix that is filled with the numbers
1, 2, 3, . . ., n2 is a magic square if the sum of the elements in each row,
in each column, and in the two diagonals is the same value.
Write a program that reads in 16 values from the keyboard and tests
whether they form a magic square when put into a 4 × 4 array.
4 15 14 1
9 6 7 12
5 10 11 8
16 3 2 13
You need to test two features:
1. Does each of the numbers 1, 2, ..., 16 occur in the user input?
2. When the numbers are put into a square, are the sums of the rows, columns,
and diagonals equal to each other?

Explanation / Answer

import java.util.Scanner;

public class MagicSqure {

   public static void main(String[] args) {

       int[][] a = new int[4][4];
       Scanner scanner = new Scanner(System.in);

       for (int i = 0; i < 4; i++) {
           for (int j = 0; j < 4; j++) {
               System.out
                       .print("Enter the value for a[" + i + "][" + j + "]:");
               a[i][j] = scanner.nextInt();
           }

       }

       System.out.println("User Matrix:");

       for (int i = 0; i < 4; i++) {
           for (int j = 0; j < 4; j++)
               System.out.print(a[i][j] + " ");
           System.out.println();
       }

       if (matchNumbers(a)) {

           if (isMagicSquare(a)) {

               System.out.println("Magic Square");
           } else {
               System.out.println("Not Magic Square");
           }
       } else {

           System.out.println("Invalid Square");
       }
       // System.out.println(isMagicSquare(a));
   }

   /**
   * method to check each of the numbers 1, 2, ..., 16 occur in the user input
   *
   * @param a
   * @return
   */
   public static boolean matchNumbers(int a[][]) {
       int matches = 0;

       int[][] square = new int[4][4];
       int count = 1;
       for (int i = 0; i < 4; i++)
           for (int j = 0; j < 4; j++)
               square[i][j] = count++;

       for (int m = 0; m < 4; m++) {
           for (int n = 0; n < 4; n++) {
               int value = a[m][n];

               for (int i = 0; i < 4; i++) {
                   for (int j = 0; j < 4; j++) {
                       if (square[i][j] == value) {
                           matches++;
                           square[i][j] = 0;

                       }

                   }
               }
           }
       }
       if (matches == 16) {
           return true;

       } else {

           return false;
       }
   }

   /**
   * method to check are the sums of the rows, columns,and diagonals equal to
   * each other(magic square or not
   *
   * @param arr
   * @return
   */
   public static boolean isMagicSquare(int[][] arr) {
       final int n = arr.length;
       final int nSquare = n * n;
       final int M = (n * n * (n * n + 1) / 2) / n;
       int sumOfRow = 0, sumOfColoumns = 0, sumOfPrimaryDiagonal = 0, sumOfSecondaryDiagonal = 0;
       boolean[] flag = new boolean[n * n];
       for (int row = 0; row < n; row++) {
           sumOfRow = 0;
           sumOfColoumns = 0;
           for (int col = 0; col < n; col++) {
               if (arr[row][col] < 1 || arr[row][col] > nSquare)
                   return false;
               if (flag[arr[row][col] - 1] == true)
                   return false;
               flag[arr[row][col] - 1] = true;
               sumOfRow += arr[row][col];
               sumOfColoumns += arr[col][row];
           }

           sumOfPrimaryDiagonal += arr[row][row];
           sumOfSecondaryDiagonal += arr[row][n - row - 1];
           if (sumOfRow != M || sumOfColoumns != M)
               return false;
           // System.out.println(M);
       }
       if (sumOfPrimaryDiagonal != M || sumOfSecondaryDiagonal != M)
           return false;
       return true;
   }
}

OUTPUT1:
Enter the value for a[0][0]:1
Enter the value for a[0][1]:2
Enter the value for a[0][2]:3
Enter the value for a[0][3]:4
Enter the value for a[1][0]:5
Enter the value for a[1][1]:6
Enter the value for a[1][2]:7
Enter the value for a[1][3]:8
Enter the value for a[2][0]:9
Enter the value for a[2][1]:10
Enter the value for a[2][2]:11
Enter the value for a[2][3]:12
Enter the value for a[3][0]:13
Enter the value for a[3][1]:14
Enter the value for a[3][2]:15
Enter the value for a[3][3]:16

User Matrix:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Not Magic Square

OUTPUT2:
Enter the value for a[0][0]:4
Enter the value for a[0][1]:15
Enter the value for a[0][2]:14
Enter the value for a[0][3]:1
Enter the value for a[1][0]:9
Enter the value for a[1][1]:6
Enter the value for a[1][2]:7
Enter the value for a[1][3]:12
Enter the value for a[2][0]:5
Enter the value for a[2][1]:10
Enter the value for a[2][2]:11
Enter the value for a[2][3]:8
Enter the value for a[3][0]:16
Enter the value for a[3][1]:3
Enter the value for a[3][2]:2
Enter the value for a[3][3]:13
User Matrix:
4 15 14 1
9 6 7 12
5 10 11 8
16 3 2 13
Magic Square

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