Question

Java language only

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At the end of the code have the output in comment form

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public class MagicSquare {

static int[][] createMagicSquare(int square[][]) {

// Initialize position for 1

int i = 3/2;

int j = 3-1;

// One by one put all values in magic square

for (int num=1; num <= 9; )

{

if (i==-1 && j==3) //3rd condition

{

j = 3-2;

i = 0;

}

else

{

// 1st condition helper if next number

// goes to out of square's right side

if (j == 3)

j = 0;

// 1st condition helper if next number

// is goes to out of square's upper side

if (i < 0)

i=3-1;

}

if (square[i][j]!=0) //2nd condition

{

j -= 2;

i++;

continue;

}

else

square[i][j] = num++; //set number

j++; i--; //1st condition

}

return square;

}

static boolean checkSquare(int[][] square) {

// calculate the sum of

// the prime diagonal

int sum = 0;

for (int i = 0; i < 3; i++)

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

// For sums of Rows

for (int i = 0; i < 3; i++) {

int rowSum = 0;

for (int j = 0; j < 3; j++)

rowSum += square[i][j];

// check if every row sum is

// equal to prime diagonal sum

if (rowSum != sum)

return false;

}

// For sums of Columns

for (int i = 0; i < 3; i++) {

int colSum = 0;

for (int j = 0; j < 3; j++)

colSum += square[j][i];

// check if every column sum is

// equal to prime diagonal sum

if (sum != colSum)

return false;

}

return true;

}

public static void main(String args[]) {

int square[][]=new int[3][3];

//assigning all values in the array to 0

for(int i=0;i<3;i++) {

for(int j=0;j<3;j++) {

square[i][j]=0;

}

}

square=createMagicSquare(square);

// Print magic square

System.out.println("The magic square is:");

for (int i=0; i<3; i++)

{

for (int j=0; j<3; j++)

System.out.format("%3d ", square[i][j]);

System.out.println("");

}

if(checkSquare(square))

System.out.println("The given square is Lo Shu Magic Square...");

else

System.out.println("The given square is not a Lo Shu Magic Square...");

}

}

Answer 1

/**

* A magic square is an order of n^2 number in a matrix form the range of 1 to n^2, in which sum of element of all row, column and diagonal have same constant value.

The first number will be stored at position (n/2, n-1) i.e. (1,2). The next number will store at position (i-1, j+1) i.e. (0,0), we can consider each row & column as "circular array" [note this point] i.e. they wrap around.

1. position of next number is determine by decrementing row number of previous number by 1, and incrementing the column number of previous number by 1. At any time, if the determine row position becomes -1, it will wrap around to n-1.

Similarly, if the calculated column position becomes n, it will wrap around to 0.

2. If the magic square already contains a number at the calculated position, calculated column position will be decremented by 2, and calculated row position will be incremented by 1.

3. If the calculated row position is -1 & calculated column position is n, the new position would be: (0, n-2).

*

*/

public class MagicSquare {

static int[][] createMagicSquare(int square[][]) {

//This is the default position which we need to initialize i.e. (1,2)

// Initialize position for 1

int i = 3 / 2;

int j = 3 - 1;

//We have total 9 place (3*3) to fill the value in square matrix, so iterate 9 times only.

// One by one put all values in magic square

for (int num = 1; num <= 9;)

{

//This is condition when both row and column is out of bound i.e. new position will be (0, n-2) where n is 3 in this question

if (i == -1 && j == 3) // 3rd condition

{

j = 3 - 2;

i = 0;

}

else

{

//As I explained above that consider this as a circular and it is not the condition of (-1, n) where n=3, then once column reach to out of bound make it 0.  

// 1st condition helper if next number

// goes to out of square's right side

if (j == 3)

j = 0;

//As I explained above that consider this as a circular and it is not the condition of (-1, n) where n=3, then once row reach to out of bound make it n-1.

// 1st condition helper if next number

// is goes to out of square's upper side

if (i < 0)

i = 3 - 1;

}

//If the magic square already contains a number at the calculated position, calculated column position will be decremented by 2,

//and calculated row position will be incremented by 1.

if (square[i][j] != 0) // 2nd condition

{

j -= 2;

i++;

continue;

}

else

//if the magic square contains 0 then set the square equal to num and increment the num.

square[i][j] = num++; // set number

//The position of next number is determined by decrementing row number of previous number by 1, and incrementing the column number

//of previous number by 1. At any time, if the calculated row position becomes -1, it will wrap around to n-1. Similarly, if the

//calculated column position becomes n, it will wrap around to 0.

j++;

i--; // 1st condition

}

return square;

}

static boolean checkSquare(int[][] square) {

//Here we are adding the diagonal value and calculating the sum of diagonal which should be equal to sum of each row and each column

// calculate the sum of

// the prime diagonal

int sum = 0;

for (int i = 0; i < 3; i++)

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

//Here 2 loop require to check whether each row is equal to the diagonal sum or not, if not equal then its not magic square and return false

// For sums of Rows

for (int i = 0; i < 3; i++) {

int rowSum = 0;

for (int j = 0; j < 3; j++)

rowSum += square[i][j];

// check if every row sum is

// equal to prime diagonal sum

if (rowSum != sum)

return false;

}

//Here 2 loop require to check whether each column is equal to the diagonal sum or not, if not equal then its not magic square and return false

// For sums of Columns

for (int i = 0; i < 3; i++) {

int colSum = 0;

for (int j = 0; j < 3; j++)

colSum += square[j][i];

// check if every column sum is

// equal to prime diagonal sum

if (sum != colSum)

return false;

}

return true;

}

public static void main(String args[]) {

int square[][] = new int[3][3];

// assigning all values in the array to 0

for (int i = 0; i < 3; i++) {

for (int j = 0; j < 3; j++) {

square[i][j] = 0;

}

}

square = createMagicSquare(square);

// Print magic square

System.out.println("The magic square is:");

for (int i = 0; i < 3; i++)

{

for (int j = 0; j < 3; j++)

System.out.format("%3d ", square[i][j]);

System.out.println("");

}

if (checkSquare(square))

System.out.println("The given square is Lo Shu Magic Square...");

else

System.out.println("The given square is not a Lo Shu Magic Square...");

}

}

/**

* output of given problem:

*

* The magic square is:

2 7 6

9 5 1

4 3 8

The given square is Lo Shu Magic Square...

*/