8.36 (Latin square) A Latin square is an n-by-n array filled with n different Latin letters, each occurring exactly once in each row and once in each column. Write a program that prompts the user to enter the number n and the array of characters, as shown in the sample output, and checks if the input array is a Latin square.
The characters are the first n characters starting from A .
Enter number n: 4
Enter 4 rows of letters separated by spaces:
A B C D
B A D C
C D B A
D C A B
The input array is a Latin square
Enter number n: 3
Enter 3 rows of letters separated by spaces:
A F D
Wrong input: the letters must be from A to C
The characters are the first n characters starting from A .
Enter number n: 4
Enter 4 rows of letters separated by spaces:
A B C D
B A D C
C D B A
D C A B
The input array is a Latin square
Enter number n: 3
Enter 3 rows of letters separated by spaces:
A F D
Wrong input: the letters must be from A to C
import java.util.Scanner; public class Exercise_36 { public static void main(String[] args) { Scanner input = new Scanner(System.in); System.out.print("Enter n number: "); int n = input.nextInt(); char[][] m = new char[n][n]; for (int i = 0; i < m.length; i++) { for (int j = 0; j < m[i].length; j++) { m[i][j] = input.next().charAt(0); } } System.out.println(checkLatinSquare(m)); } public static boolean checkLatinSquare(char[][] m) { // first check if grid has valid letters for (int i = 0; i < m.length; i++) { for (int j = 0; j < m[i].length; j++) { if (!isValidLetter(m[i][j], m.length)) { System.out.println("Invalid letters..."); System.out.println("n = " + m.length + " your letter range is " + 'A' + "-" +(char)('A' + m.length - 1)); return false; } } } // check if every row has unique letters for (int i = 0; i < m.length; i++) { if (!isRowValid(m, i)) return false; } // check if every column has unique letters for (int j = 0; j < m[0].length; j++) { if (!isColumnValid(m,j)) return false; } return true; } public static boolean isColumnValid(char[][] m, int column) { boolean[] hasBeenUsed = new boolean[m.length]; for (int i = 0; i < m.length; i++) { int index = m[i][column] - 'A'; if (hasBeenUsed[index]) { return false; } else { hasBeenUsed[index] = true; } } return true; } public static boolean isRowValid(char[][] m, int row) { boolean[] hasBeenUsed = new boolean[m.length]; for (int j = 0; j < m[row].length; j++) { int index = m[row][j] - 'A'; if (hasBeenUsed[index]) { return false; } else { hasBeenUsed[index] = true; } } return true; } public static void displayMatrix(char[][] m) { for (int i = 0; i < m.length; i++) { for (int j = 0; j < m[i].length; j++) { System.out.print(m[i][j] + " "); } System.out.println(""); } } public static boolean isValidLetter(char ch, int n) { // ch starts off from A, so subtract one from n n--; return (ch >= 'A' && ch <= 'A' + n); } }
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