Question

The Lo Shu Magic Square is a grid with 3 rows and 3 columns shown in Figure 8-23. The Lo Shu Magic Square has the following properties:

l The grid contains the numbers 1 through 9 exactly.

l The sum of each row, each column, and each diagonal all add up to the same number. This is shown in Figure 8-24.

In a program, you can simulate a magic square using a two-dimensional array. Design a program that initializes a two-dimensional array with values entered by the user. The program should determine whether the array is a Lo Shu Magic Square.

Answer 1

Copyable Code:

MagicSquare.java:

public class MagicSquare

{

//function definition for check magic square

public static boolean checkMagicSquare(int[][] arr)

{

//declare the variable r for row, c for column

//declare the variable for sum

int sum=0,s, r, c,i;

for (c = 0; c<3; c++)

//assign the sum is 15 which is in two dimension array

sum += arr[0][c];

//check two rows

s = 0;

for (r = 1; r < 3; r++)

{

s = 0;

for (c = 0; c< 3; c++)

s += arr[r][c];

if (s != sum)

return false;

}

//validate columns

for (c = 0; c< 3; c++)

{

s = 0;

for (r = 0; r < 3; r++)

{

s += arr[r][c];

  

}

if (s != sum)

return false;

  

}

//validate diagonal 1

s =0;

for (r = 0; r < 3; r++)

{

s += arr[r][r];

}

if (s != sum)

return false;

//validate diagonal 2

s =0;

for (r = 0; r < 3; r++)

{

s += arr[r][2 - r];

  

}

if (s != sum)

return false;

//check that the numbers 1 to 9 existing

//assign the variable for selected

boolean[] selected = new boolean[9];

for (i=0; i < 9; i++)

{

selected[i] = false;

}

//check every number

for (c = 0; c< 3; c++)

{

for (r = 0; r < 3; r++)

{

int num = arr[r][c];

if (selected[num-1])

return false;

selected[num-1] = true;

  

}

}

//here check the every values in appears are true but

// since there are 9 positions in both selected and arr[][]

return true;

}

public static void main (String[] args)

{

int[][] sampleArray1 = {{4,9,2},{3,5,7},{8,1,6}};

System.out.println("Sample array 1 Lo Shu Magic Square: "+MagicSquare.checkMagicSquare(sampleArray1));

int[][] sampleArray2 = {{4,9,2},{3,1,5},{8,7,6}};

System.out.println("Sample array 2 Lo Shu Magic Square: "+MagicSquare.checkMagicSquare(sampleArray2));

}

}