Question

Magic squares. An n × n matrix that is filled with the numbers 1, 2, 3, ..., n2 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. For example,
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Write a program that reads in n2 values from the keyboard and tests whether they form a magic square
when arranged as a square matrix. You need to test three features:
• Did the user enter n2 numbers for some n?
• Do each of the numbers 1, 2, ..., n2 occur exactly once in the user input?
• When the numbers are put into a square, are the sums of the rows, columns, and diagonals equal to
each other?
If the size of the input is a square, test whether all numbers between 1 and n2 are present. Then compute
the row, columns, and diagonal sums. Implement a class Square with methods
public void add(int i)
public boolean isMagic()

Answer 1

/************************************************************************* * Compilation: javac MagicSquare.java * Execution: java MagicSquare N * *Generates a magic square of order N. A magic squares is an N-by-N * matrix of the integers 1 to N^2, such that all row, column, and * diagonal sums areequal. * * One way to generate a magic square when N is odd is to assign * the integers 1 to N^2 in ascending order, starting at the * bottom, middle cell.Repeatedly assign the next integer to the * cell adjacent diagonally to the right and down. If this cell * has already been assigned another integer,instead use the * cell adjacently above. Use wrap-around to handle border cases. * * * % java MagicSquare 3 * 4 9 2 * 3 5 7 * 8 1 6 * * % java MagicSquare5 * 11 18 25 2 9 * 10 12 19 21 3 * 4 6 13 20 22 * 23 5 7 14 16 * 17 24 1 8 15 * * Limitations * ----------- * - N must be odd **************************************************************************/ public class MagicSquare { public static void main(String[] args) { int N =Integer.parseInt(args[0]); if (N % 2 == 0) throw new RuntimeException("N must be odd"); int[][] magic = new int[N][N]; int row = N-1; int col = N/2;magic[row][col] = 1; for (int i = 2; i <= N*N; i++) { if (magic[(row + 1) % N][(col + 1) % N] == 0) { row = (row + 1) % N; col = (col + 1) % N; } else {row = (row - 1 + N) % N; // don't change col } magic[row][col] = i; } // print results for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { if(magic[i][j] < 10) System.out.print(" "); // for alignment if (magic[i][j] < 100) System.out.print(" "); // for alignmentSystem.out.print(magic[i][j] + " "); } System.out.println(); } }}