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8.35
（最大塊）給定一個元素為0或者1的方陣，編寫一個程式，找到一個元素都為1的最大的子方陣。程式提示使用者輸入矩陣的行數。然後顯示最大的子方陣的第一個元素，以及該子方陣中的行數。

import java.util.Scanner;

public class MaximumSquare
{
    public static void main(String[] args)
    {
        int[][] matrix = creatMatrix();
        int[] result = findMax(matrix);
        System.out
 
.println("The maximun square submatrix is at(" +
            result[1] + ", " + result[2] + ") with size " + result[0]);
    }

    public static int[][] creatMatrix()
    {
        Scanner input = new Scanner(System.in);
        System.out.print("Enter the number of rows in the matrix: ");
        int
 
 number = input.nextInt();
        System.out.println("Enter the matrix row by row: ");
        int[][] matrix = new int[number][number];
        for (int row = 0; row < number; row++)
        {
            for (int column = 0; column < number; column++)
            {
                matrix[row][column] = input.nextInt();
            }
        }

        return
 
 matrix;
    }

    public static int[] findMax(int[][] matrix)
    {
        int[] result = new int[3];
        result[0] = 0;
        result[1] = 0;
        result[2] = 0;
        for (int row = 0; row < matrix.length - 1; row++)
        {
            for (int column = 0; column < matrix[0].length - 1; column++)
            {
                int record = findLength(matrix, row, column);
                if (record > result[0])
                {
                    result[0] = record;
                    result[1] = row;
                    result[2] = column;
                }
            }
        }

        return result;
    }

    public static int findLength(int[][] matrix, int row, int column)
    {
        //最重要的就是這句判斷，保證每一個元素都要在 matrix 中
        if ((matrix[row][column] == 0) || (matrix[row + 1][column + 1] == 0))
        {
            return 0;
        }

        int length = 0;
        boolean succ = false;
        while (!succ)
        {
            if ((row + length >= matrix.length) || (column + length >= matrix.length))
            {
                return length;
            }

            for (int r = row; r < row + length; r++)
            {
                //System.out.println(row + " " + column + " " + length);
                if (matrix[r][column + length] != 1)
                {
                    return length;
                }
            }

            for (int c = column; c < column + length; c++)
            {
                if (matrix[row + length][c] != 1)
                {
                    return length;
                }
            }

            length++;
        }
        System.out.println(length);
        return length;
    }
}
}

8.36
（拉丁正方形）拉丁正方形是一個n * n的陣列，有n個不同的拉丁字母填寫，每個拉丁字母恰好只在每行和每列中出現一次。程式設計一個程式，提示使用者輸入數字n以及字元陣列，檢查該輸出陣列是否是一個拉丁正方形。字元是從A開始的前面n個字元。

import java.util.Scanner;

public class MarkovMatrix
{
    public static void main(String[] args)
    {
        double[][] matrix = creatMatrix();
        isMarkovMatrix(matrix);
    }

    public static double[][] creatMatrix()
    {
        Scanner input = new Scanner(System.in);
        double[][] matrix = new double[6][6];
        System.out.println("Enter a 3-by-3 matrix: ");
        for (int row = 0; row < 3; row++)
        {
            for (int column = 0; column < 3; column++)
            {
                matrix[row][column] = input.nextDouble();
            }
        }

        return matrix;
    }

    public static void isMarkovMatrix(double[][] matrix)
    {
        boolean succ = false;
        for (int column = 0; column < 3; column++)
        {
            double sum = 0.0;
            for (int row = 0; row < 3; row++)
            {
                sum += matrix[row][column];
            }

            if (sum == 1.0)
            {
                succ = true;
                break;
            }
        }

        if (succ)
        {
            System.out.println("It is a markov matrix.");
        }
        else
            System.out.println("It is not a markov matrix.");
    }
}