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    kobe73er
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    *8.2 (Sum the major diagonal in a matrix) Write a method that sums all the numbers in the major diagonal in an n * n matrix of double values using the following header:

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

    Write a test program that reads a 4-by-4 matrix and displays the sum of all its elements on the major diagonal. Here is a sample run:

    Enter a 4-by-4 matrix row by row:
    1 2 3 4.0
    5 6.5 7 8
    9 10 11 12
    13 14 15 16
    Sum of the elements in the major diagonal is 34.5

    **8.4 (Compute the weekly hours for each employee) Suppose the weekly hours for all employees are stored in a two-dimensional array. Each row records an employee’s seven-day work hours with seven columns. For example, the following array stores the work hours for eight employees. Write a program that displays employees and their total hours in decreasing order of the total hours.

    **8.8 (All closest pairs of points) Revise FindNearestPoints.java, to display all closest pairs of points with the same minimum distance. Here is a sample run:

    Enter the number of points: 8
    Enter 8 points: 0 0 1 1 -1 -1 2 2 -2 -2 -3 -3 -4 -4 5 5
    The closest two points are (0.0, 0.0) and (1.0, 1.0)
    The closest two points are (0.0, 0.0) and (-1.0, -1.0)
    The closest two points are (1.0, 1.0) and (2.0, 2.0)
    The closest two points are (-1.0, -1.0) and (-2.0, -2.0)
    The closest two points are (-2.0, -2.0) and (-3.0, -3.0)
    The closest two points are (-3.0, -3.0) and (-4.0, -4.0)
    Their distance is 1.4142135623730951

    *8.10 (Largest row and column) Write a program that randomly fills in 0s and 1s into a 4-by-4 matrix, prints the matrix, and finds the first row and column with the most 1s. Here is a sample run of the program:

    0011
    
    0011
    
    1101
    
    1010
    
    The largest row index: 2
    
    The largest column index: 2

     

    **8.12 (Financial application: compute tax) Rewrite ComputeTax.java in chapter 3, using arrays. For each filing status, there are six tax rates. Each rate is applied to a certain amount of taxable income. For example, from the taxable income of $400,000 for a single filer, $8,350 is taxed at 10%, (33,950 – 8,350) at 15%,(82,250 –  33,950) at 25%, (171,550 –  82,550) at 28%, (372,550 –  82,250) at 33%, and (400,000 –  372,950) at 36%. The six rates are the same for all filing statuses, which can be represented in the following array:

    double[] rates = {0.10, 0.15, 0.25, 0.28, 0.33, 0.35};

    The brackets for each rate for all the filing statuses can be represented in a twodimensional array as follows:

    int[][] brackets = {
    {8350, 33950, 82250, 171550, 372950}, // Single filer
    {16700, 67900, 137050, 20885, 372950}, // Married jointly
    // -or qualifying widow(er)
    {8350, 33950, 68525, 104425, 186475}, // Married separately
    {11950, 45500, 117450, 190200, 372950} // Head of household
    };

    Suppose the taxable income is $400,000 for single filers. The tax can be computed as follows:

    tax = brackets[0][0] * rates[0] +
    
    (brackets[0][1] – brackets[0][0]) * rates[1] +
    
    (brackets[0][2] – brackets[0][1]) * rates[2] +
    
    (brackets[0][3] – brackets[0][2]) * rates[3] +
    
    (brackets[0][4] – brackets[0][3]) * rates[4] +
    
    (400000 – brackets[0][4]) * rates[5]

    **8.14 (Explore matrix) Write a program that prompts the user to enter the length of a square matrix, randomly fills in 0s and 1s into the matrix, prints the matrix, and finds the rows, columns, and diagonals with all 0s or 1s. Here is a sample run of the program:

    Enter the size for the matrix: 4
    0111
    0000
    0100
    1111
    All 0s on row 1
    All 1s on row 3
    No same numbers on a column
    No same numbers on the major diagonal
    No same numbers on the sub-diagonal

    *8.16 (Sort two-dimensional array) Write a method to sort a two-dimensional array using the following header:

    public static void sort(int m[][])

    The method performs a primary sort on rows and a secondary sort on columns.

    For example, the following array

    {{4, 2},{1, 7},{4, 5},{1, 2},{1, 1},{4, 1}}

    will be sorted to

    {{1, 1},{1, 2},{1, 7},{4, 1},{4, 2},{4, 5}}.

    *8.18 (Shuffle rows) Write a method that shuffles the rows in a two-dimensional int array using the following header:

    public static void shuffle(int[][] m)

    Write a test program that shuffles the following matrix:

    int[][] m = {{1, 2}, {3, 4}, {5, 6}, {7, 8}, {9, 10}};

    *8.22 (Even number of 1s) Write a program that generates a 6-by-6 two-dimensional matrix filled with 0s and 1s, displays the matrix, and checks if every row and every column have an even number of 1s.

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