How to Check if the Matrix is a Magic Square in Java?

Matrices are nothing but a collection of data elements arranged in a rectangular layout that is two-dimensional. In Java, an array with two dimensions can be considered as a matrix.

As per the problem statement the task is to check if the matrix is a magic square or not.

A matrix is said to be a magic square if the sum of elements of any row, column or diagonal is equal to a specific number.

Let’s deep dive into this article, to know how it can be done by using Java programming language.

To show you some instances

Instance-1

Suppose the original matrix is {
   { 13, 8, 15 },
   { 14, 12, 10 },
   { 9, 16, 11 }
}; 

Here the sum of any row or any column or diagonal is equal to 36.

After checking for magic matrix, the result index will be

Given matrix is a Magic Square

Instance-2

Suppose the original matrix is{
   { 8, 7, 6 },
   { 9, 5, 1 },
   { 5, 3, 8 }
}; 

Here the sum of any row or any column or diagonals are not equal.

After checking for magic matrix, the result index will be

Given matrix is a not a magic Square

Algorithm

Step 1 − Initialise and declare the matrix

Step 2 − Declare Boolean to check for magic square.

Step 3 − Find the sum of the two diagonals using a loop.

Step 4 − Find the sum of the rows and columns using a for loop.

Step 5 − Check for magic square.

Step 6 − Print the result.

Syntax

To get the length of an array (number of elements in that array), there is an inbuilt property of array i.e length

Below refers to the syntax of it-

array.length

where, ‘array’ refers to the array reference.

Multiple Approaches

We have provided the solution in different approaches.

• By Using Static Initialization of Matrix

• By Using User Defined Method

Let’s see the program along with its output one by one.

Approach-1: By Using Static Initialization of Matrix

In this approach, matrix elements will be initialized in the program. Then as per the algorithm check if the matrix is a magic square or not.

Example

public class Main {
   //main method
   public static void main(String[] args){
     
     //Initialising and declaring matrix
      int mat[][] = {{ 13, 8, 15 }, { 14, 12, 10 }, { 9, 16, 11 }};
      int M = 3;
      
      //declare boolean to check for magic square or not
      boolean flag = false;
      
      //Initialising and declaring the diagonal sum as 0
      int sum1 = 0,sum2=0;
      
      //finding the sum of the two diagonals i.e. sum1 and sum2
      for (int i = 0; i < M; i++){
         sum1 += mat[i][i];
         sum2 += mat[i][M-1-i];
      }
      
      //check if sum of diagonals are unequal then it is not a magic square
      if(sum1!=sum2)
      flag = true; 
      for (int i = 0; i < M; i++) {
         
         //Initialising and declaring the row sum and column sum as 0
         int rowSum = 0, colSum = 0;
         
         //finding the sum of the rows and columns i.e. row and column
         for (int j = 0; j < M; j++){
            rowSum += mat[i][j];
            colSum += mat[j][i];
         }
         
         //check if sum of rows, columns and diagonals are unequal then it is not a magic square
         if (rowSum != colSum || colSum != sum1)
            flag = true; 
      }
      
      //checking and printing magic square
      if (!flag)
         System.out.println("Given matrix is a Magic Square");
      else
         System.out.println("Given matrix is a not a magic" + " Square");
   }
} 

Output

Given matrix is a Magic Square

Approach-2: By Using User Defined Method

In this approach, matrix elements will be initialized in the program. Then call a user defined method by passing the matrix as parameter and inside the method as per the algorithm check if the matrix is a magic square or not.

Example

public class Main {
   //main method
   public static void main(String[] args){
      
      //Initialising and declaring matrix 
      int mat[][] = {{ 8, 7, 6 }, { 9, 5, 1 }, { 5, 3, 8 }};
      //calling user defined function			
      magicSquare(mat);
   }
   static int M = 3;
   
   //user defined method
   static void magicSquare(int mat[][]) {
      
      //declare boolean to check for magic square or not
      boolean flag = false;
      
      //Initialising and declaring the diagonal sum as 0
      int sum1 = 0,sum2=0;
      
      //finding the sum of the two diagonals i.e. sum1 and sum2
      for (int i = 0; i < M; i++)	{
         sum1 += mat[i][i];
         sum2 += mat[i][M-1-i];
      }
      
      //check if sum of diagonals are unequal then it is not a magic square
      if(sum1!=sum2)
      flag = true; 
      for (int i = 0; i < M; i++) {
         
         //Initialising and declaring the rows and columns sum as 0
         int rowSum = 0, colSum = 0;
         
         //finding the sum of the rows and columns i.e. row and column
         for (int j = 0; j < M; j++)	{
            rowSum += mat[i][j];
            colSum += mat[j][i];
         }
         
         //check if sum of rows, columns and diagonals are unequal then it is not a magic square
         if (rowSum != colSum || colSum != sum1)
         flag = true; 
      }
      
      //checking and printing magic square
       if (!flag)
         System.out.println("Given matrix is a Magic Square");
      else
         System.out.println("Given matrix is a not a magic" + " Square");
   }
}

Output

Given matrix is a not a magic Square

In this article, we explored different approaches to check if the matrix is a magic square or not by using Java programming language.