One interesting application of two-dimensional arrays is magic squares. A magic square is a square matrix in which the sum of every row, every column, and both diagonals is the same. Magic squares have been studied for many years, and there are some particularly famous magic squares. Write a program to determine whether a series of square matrices are magic or not. The first line of input for each square specifies the size of the square (number of rows and columns). The square elements follow, one row per line. The end of the data is indicated by -1. Create a class called Square that has methods to construct a square of a specified size, to read in the elements of the square, to compute the sum of a row, to compute the sum of a column, to compute the sum of each diagonal, and to test to see if the square is magic. A driver should read in the dimension of each square, call the Square class to construct the square, print out the square and the various sums of rows, columns and diagonals; and prints out the result of the magic square test.

See explaination

Explanation:

import java.util.Scanner;

import java.io.*;

public class Square {

int[][] square;

//

//create new square of given size

//

public Square(int size) {

square = new int[size][size];

}

//

//return the sum of the values in the given row

//

public int sumRow(int row) {

// Add your code here

int sum = 0;

for (int i = 0; i < square.length; i++) {

sum = sum + square[row][i];

}

return sum;

}

//

//return the sum of the values in the given column

//

public int sumCol(int col) {

// Add your code here

int sum = 0;

for (int i = 0; i < square.length; i++) {

sum = sum + square[i][col];

}

return sum;

}

//

//return the sum of the values in the main diagonal

//

public int sumMainDiag() {

// Add your code here

int sum = 0;

for (int i = 0; i < square.length; i++) {

sum = sum + square[i][i];

}

return sum;

}

//

//return the sum of the values in the other ("reverse") diagonal

//

public int sumOtherDiag() {

// Add your code here

int sum = 0;

for (int i = 0; i < square.length; i++) {

sum = sum + square[square.length - i - 1][i];

}

return sum;

}

//

//return true if the square is magic (all rows, cols, and diags have

//same sum), false otherwise

//

public boolean magic() {

// Add your code here. Check if the sum of main diagonal equals the other diagonal,

// also if all rows and all columns sums equal to the diagonal as well. Any uneuqal will

// terminate the comparison.

int d1 = sumMainDiag();

int d2 = sumOtherDiag();

if (d1 != d2) {

return false;

}

for (int i = 0; i < square.length; i++) {

if (d1 != sumRow(i) || d1 != sumCol(i)) {

return false;

}

}

return true;

}

//

//read info into the square from the standard input.

//

public void readSquare(Scanner scan) {

for (int row = 0; row < square.length; row++) {

for (int col = 0; col < square.length; col++) {

square[row][col] = scan.nextInt();

}

}

}

//

//print the contents of the square, neatly formatted

//

public void printSquare() {

for (int row = 0; row < square.length; row++) {

for (int col = 0; col < square.length; col++) {

System.out.print(square[row][col] + "\t");

}

System.out.println();

}

}

}

//

// SquareTest.java

//

// Uses the Square class to read in square data and tell if

// each square is magic.

//

//

class SquareTest {

public static void main(String[] args) throws IOException {

File file = new File("magicData.txt");

Scanner scan = new Scanner(file);

int count = 1; //count which square we're on

int size = scan.nextInt(); //size of next square

//Expecting -1 at bottom of input file

while (size != -1) {

//create a new Square of the given size

Square magicSquare = new Square(size);

//call its read method to read the values of the square

magicSquare.readSquare(scan);

System.out.println("\n Square " + count + " ");

//print the square

magicSquare.printSquare();

//print the sums of its rows

for (int row = 0; row < size; row++) {

System.out.println("Sum of row " + row + ": "

+ magicSquare.sumRow(row));

}

//print the sums of its columns

for (int col = 0; col < size; col++) {

System.out.println("Sum of column " + col + ": "

+ magicSquare.sumCol(col));

}

//print the sum of the main diagonal

System.out.println("Sum of the main diagonal: "

+ magicSquare.sumMainDiag());

//print the sum of the other diagonal

System.out.println("Sum of the other diagonal: "

+ magicSquare.sumOtherDiag());

//determine and print whether it is a magic square

if (magicSquare.magic()) {

System.out.println("It's a magic square!");

} else {

System.out.println("It's not a magic square!");

}

System.out.println();

//get size of next square

size = scan.nextInt();

count++;

}

}

}