# Java Magic Square 2d Array

Java Magic Square 2d Array | A magic square is a matrix that has a different integer, the sum of a number in every row, column, and diagonally is the same. This sum value is called a magic constant.

The formula to find the magic constant is M = n[(n^2+1) / 2]
Where, n = is the order of the matrix.

Observe the below examples of Java magic square 2d array:-

2 7 6
9 5 1
4 3 8
The above matrix is of 3X3 hence applying the above formula, magic constant M => 3[(3^2+1) / 2] = 15. The sum of each row and column is 15. Similarly, the sum of each diagonal is also 15 hence the given matrix is a magic square.

Let us see another example in a different order.
9 3 22 16 15
2 21 20 14 8
25 19 13 7 1
18 12 6 5 24
11 10 4 23 17
This is a 5X5 matrix hence the magic constant will be 5(52+1)/2 = 65.

## Java Magic Square 2d Array Code

Now let us see a Java program to generate a magic square of the given order.

``````public class Main {

public static void magicSquare(int n) {
int[][] magic = new int[n][n];

int i = n / 2;
int j = n - 1;

for (int num = 1; num <= n * n;) {
if (i == -1 && j == n) {
j = n - 2;
i = 0;
} else {
if (j == n) {
j = 0;
}
if (i < 0) {
i = n - 1;
}
}

if (magic[i][j] != 0) {
j -= 2;
i++;
continue;
} else {
magic[i][j] = num++;
}

j++;
i--;
}

System.out.println("The Magic Square for order " + n + ",");
System.out.println("Magic constant: " + n * (n * n + 1) / 2);
System.out.println("Matrix: ");
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
System.out.print(magic[i][j] + " ");
}
System.out.println();
}
}

public static void main(String[] args) {
int order = 3;
magicSquare(order);
}
}``````

Output:-

The Magic Square for order 3,
Magic constant: 15
Matrix:
2 7 6
9 5 1
4 3 8

Test-case:- Demonstrating Java magic square 2d array code of order 5×5

``````public class Main {

public static void magicSquare(int n) {
int[][] magic = new int[n][n];

int i = n / 2;
int j = n - 1;

for (int num = 1; num <= n * n;) {
if (i == -1 && j == n) {
j = n - 2;
i = 0;
} else {
if (j == n) {
j = 0;
}
if (i < 0) {
i = n - 1;
}
}

if (magic[i][j] != 0) {
j -= 2;
i++;
continue;
} else {
magic[i][j] = num++;
}

j++;
i--;
}

System.out.println("The Magic Square for order " + n + ",");
System.out.println("Magic constant: " + n * (n * n + 1) / 2);
System.out.println("Matrix: ");
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
System.out.print(magic[i][j] + " ");
}
System.out.println();
}
}

public static void main(String[] args) {
int order = 3;
magicSquare(order);
}
}``````

Output:-

The Magic Square for order 5,
Magic constant: 65
Matrix:
9 3 22 16 15
2 21 20 14 8
25 19 13 7 1
18 12 6 5 24
11 10 4 23 17

Also see:- Java Count Occurrences in 2D Array

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