MULTIDIMENSIONAL ARRAYS - Introduction to Java Programming: Comprehensive Version - page 315

*8.24

( Check Sudoku solution ) Listing 8.4 checks whether a solution is valid by check-
ing whether every number is valid in the board. Rewrite the program by checking
whether every row, every column, and every small box has the numbers 1 to 9.

*8.25

*

( Markov matrix ) An n n matrix is called a positive Markov matrix if each

element is positive and the sum of the elements in each column is 1. Write the
following method to check whether a matrix is a Markov matrix.

public static boolean isMarkovMatrix( double [][] m)

Write a test program that prompts the user to enter a 3 3 matrix of double

values and tests whether it is a Markov matrix. Here are sample runs:

*

Enter a 3-by-3 matrix row by row:
0.15 0.875 0.375
0.55 0.005 0.225
0.30 0.12 0.4
It is a Markov matrix

Enter a 3-by-3 matrix row by row:
0.95 -0.875 0.375
0.65 0.005 0.225
0.30 0.22 -0.4
It is not a Markov matrix

*8.26

( Row sorting ) Implement the following method to sort the rows in a two-
dimensional array. A new array is returned and the original array is intact.

public static double [][] sortRows( double [][] m)

Write a test program that prompts the user to enter a 3 3 matrix of double

values and displays a new row-sorted matrix. Here is a sample run:

*

Enter a 3-by-3 matrix row by row:
0.15 0.875 0.375
0.55 0.005 0.225
0.30 0.12 0.4

The row-sorted array is
0.15 0.375 0.875
0.005 0.225 0.55
0.12 0.30 0.4

*8.27

( Column sorting ) Implement the following method to sort the columns in a two-
dimensional array. A new array is returned and the original array is intact.

public static double [][] sortColumns( double [][] m)