JAVA!!!- Activity 3. Magic Squares. In this activity, you will be given a 2D arr

Question

JAVA!!!- Activity 3. Magic Squares. In this activity, you will be given a 2D array of integers (acquired within the main: code is provided to you), and you have to check if this 2D array (table or matrix as you prefer) is a magic square.

What is a magic square?

A magic square is a square 2D array or table or matrix, which has the following properties: the numbers in each row, column, and diagonal (main and secondary) add up to the same value.

So for instance, the following table is a magic square:

Method MagicSquare

Parameter: a 2D array of integers

Return type: Boolean

This method returns true if the parameter is a magic square, false otherwise.

Requirement: The implementation of this method requires the implementation of four auxiliary methods: sumRow, sumColumn, sumDiagonal1, and sumDiagonal2.

Method sumRow

Parameters:

·         A 2D array of integers; and

·         An integer i

Return type: integer

This method returns the sum of the numbers in the ith row of the 2D array.

Requirement: You are expected to use a for loop to implement this method.

Method sumColumn

Parameters:

·         A 2D array of integers; and

·         An integer i

Return type: integer

This method returns the sum of the numbers in the ith column of the 2D array.

Requirement: You are expected to use a for loop to implement this method.

Method sumDiagonal1

Parameters: a 2D array of integers

Return type: integer

This method returns the sum of the numbers in the main diagonal of the 2D array.

Requirement: You are expected to use a for loop to implement this method.

Method sumDiagonal2

Parameters: a 2D array of integers

Return type: integer

This method returns the sum of the numbers in the secondary diagonal of the 2D array.

Requirement: You are expected to use a for loop to implement

Given:

public static boolean MagicSquare(int[][] table) {
       
        // your code goes here
       
        return true;
    }
   
    // this method computes the sum of row number "row" of a given 2D array of integers
    public static int sumRow(int[][] table, int row) {
        int sum = 0;
        // your code goes here
        return sum;
    }   
   
    // this method computes the sum of column number "column" of a given 2D array of integers
    // we will assume the table is not ragged
    public static int sumColumn(int[][] table, int column) {
        int sum = 0;
        // your code goes here
        return sum;
    }

    // this method computes the sum of numbers in the main diagonal of a given 2D array of integers
    public static int sumDiagonal1(int[][] table) {
        int sum = 0;
        // your code goes here
        return sum;
    }   
   
    // this method computes the sum of numbers in the secondary diagonal of a given 2D array of integers
    public static int sumDiagonal2(int[][] table) {
        int sum = 0;
        // your code goes here
        return sum;
    }  

Method MagicSquare

Parameter: a 2D array of integers

Return type: Boolean

Explanation / Answer

/**
* @author Srinivas Palli
*
*/
public class MagicSquare {
   // method returns true if the parameter is a magic square, false otherwise.
   public static boolean MagicSquare(int[][] table) {

       // your code goes here
       final int n = table.length;

       final int M = (n * n * (n * n + 1) / 2) / n;

       for (int j = 0; j < table.length; j++) {

           if (sumRow(table, j) != M || sumColumn(table, j) != M)
               return false;
       }

       if (sumDiagonal1(table) != M || sumDiagonal2(table) != M)
           return false;

       return true;
   }

   // this method computes the sum of row number "row" of a given 2D array of
   // integers
   public static int sumRow(int[][] table, int row) {
       int sum = 0;
       // your code goes here
       for (int j = 0; j < table.length; j++) {
           sum += table[row][j];

       }
       return sum;
   }

   // this method computes the sum of column number "column" of a given 2D
   // array of integers
   // we will assume the table is not ragged
   public static int sumColumn(int[][] table, int column) {
       int sum = 0;
       // your code goes here
       for (int i = 0; i < table.length; i++) {
           sum += table[i][column];

       }
       return sum;
   }

   // this method computes the sum of numbers in the main diagonal of a given
   // 2D array of integers
   public static int sumDiagonal1(int[][] table) {
       int sum = 0;
       // your code goes here
       for (int i = 0; i < table.length; i++) {
           sum += table[i][i];

       }

       return sum;
   }

   // this method computes the sum of numbers in the secondary diagonal of a
   // given 2D array of integers
   public static int sumDiagonal2(int[][] table) {
       int sum = 0;
       for (int i = 0; i < table.length; i++) {
           sum += table[i][table.length - i - 1];

       }

       return sum;
   }

   public static void main(String[] args) {
       int[][] table = { { 2, 7, 6 }, { 9, 5, 1 }, { 4, 3, 8 } };
       if (MagicSquare(table))
           System.out.println("Magic Square");
       else
           System.out.println("Not a Magic Square");
   }
}

OUTPUT:

Magic Square

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