Question

THIS IS JAVA

Magic squares.

An n × n matrix that is filled with the numbers 1, 2, 3, . . ., n^2 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 randomly generates 16 numbers, and it assigns them to the array after testing that the number was not already assigned. The program should test whether they form a magic square when put into a 4 × 4 array.

You need to test two features:

1. Build the array so that each of the numbers 1, 2, ..., 16 is present?

2.When the numbers are put into a square, are the sums of the rows, columns, and diagonals equal to each other? If so, display an appropriate message.

Answer 1

package test;

import java.util.ArrayList;
import java.util.Random;

public class magicMatrix {
  
  
   // method to check if the matrix is magic
   public static boolean magicCheck(int[][] mat) {
       int sum = rowSum(mat,0);
       for(int i=0;i<4;i++) {
           // check if mismatch in sum occurs in rows
           if(sum != rowSum(mat,i)) {
               return false;
           }
       }
       for(int i=0;i<4;i++) {
           // check if mismatch in sum occurs in cols
           if(sum != colSum(mat,i)) {
               return false;
           }
       }
       // check if mismatch in sum occurs in diagonal in left direction
       if(sum!= diagLSum(mat))
           return false;
       // check if mismatch in sum occurs in diagonal in right direction
       if(sum!=diagRSum(mat))
           return false;
       return true;
      
   }
   //calculates row sum
   public static int rowSum(int[][] mat,int r) {
       int sum=0;
       for(int i=0;i<4;i++) {
           sum+=mat[r][i];
       }
       return sum;
   }
   //calculates column sum
   public static int colSum(int[][] mat,int c) {
       int sum=0;
       for(int i=0;i<4;i++) {
           sum+=mat[i][c];
       }
       return sum;
   }
   public static int diagLSum(int[][] mat) {
       int sum=0;
       for(int i=0;i<4;i++) {
           sum+=mat[i][i];
       }
       return sum;
      
   }
   //calculates diagonal sum in right diagonal
   public static int diagRSum(int[][] mat) {
       int sum=0;
       for(int i=0;i<4;i++) {
           sum+= mat[i][3-i];
       }
       return sum;
   }
  
   //prints the matrix
   public static void printMat(int[][] mat) {
       for(int i=0;i<4;i++) {
           for(int j=0;j<4;j++) {
               System.out.print(" "+mat[i][j]);
           }
           System.out.println("\n");
       }
   }
   static Random rand;

   public static void main(String[] args) {
       // TODO Auto-generated method stub
       rand = new Random();
       rand.setSeed(System.nanoTime());
       //creates an array of integers
       ArrayList<Integer> array = new ArrayList<Integer>();
       //adds the randomly generated numbers from 1 to 16 in the array
       for(int i=0;i<16;) {
           int y=rand.nextInt(16)+1;
           if(!array.contains(y)) {
               array.add(y);
               i++; // increments i if y is added to the array
           }
       }
       //declares the matrix
       int[][] matrix= new int[4][4];
      
       //adds integers from array into matrix
       for(int i=0;i<4;i++) {
           for(int j=0;j<4;j++) {
               matrix[i][j]=array.get(i*4+j);
           }
          
       }
       //prints the matrix
       System.out.println("The matrix generated is -> ");
       printMat(matrix);
      
       //checks if the matrix is magic or not and displays the appropriate message
       if(magicCheck(matrix)) {
           System.out.println("This matrix is a magic matrix");
       }else {
           System.out.println("This matrix is not a magic matrix");
       }

   }

}

==========================================================

above is result of one run..

Thanks

The matrix generated is -> 1 15 8 6 12 9 2 5 13 11 10 4 7 14 16 3 This matrix is not a magic matrix