如何在Matrix的二维中选择所有唯一的行和列

Question

我实现了一个简单的源代码来查找矩阵中所有可能的路径。然后选择唯一的行和列。但由于时间的复杂性，我们怎样才能直接获得独特的路径呢？ 这是我的源代码：

    import java.util.*;
public class MyAllPath {
    public static ArrayList<String> allPaths;
    public static void printpaths(double[][] matrix) {  
        String[] path = new String[matrix.length];

    for (int i = 0; i < matrix[0].length; i++)
    {
        printpaths(matrix, path, 0, 0, i);
    }
}

private static void printpaths(double[][] matrix, String[] path, int index, int row, int column)
{
    path[index++] = Integer.toString(column)+"|"+Double.toString(matrix[row][column])+"\t";
    row++;
    if (row == matrix.length)
        {
            print(path);
        }
    else if (row < matrix.length) 
    {
        int boundary = matrix[0].length-1;
        for (int i = column - boundary; i <= column + boundary; i++)
        {
            if (i > -1 && i < matrix[0].length)
            {
                printpaths(matrix, path, index, row, i);
            }
        }
    }
}

private static void print(String[] path) 
{
    String myPath="";
    for (int i = 0; i < path.length; i++)
    {
        myPath+=path[i]+" ";
        System.out.print(path[i] + " ");
    }
    System.out.println();
    allPaths.add(myPath);
}


public static void main(String args[]) 
{
    allPaths =new ArrayList<String>();
    double[][] matrix = {{1, 2, 3},
                        {4, 5, 6}, 
                        {7, 8, 9}};
    printpaths(matrix);
    System.out.println("-------------------------------------------------------");
    for(int i=0;i<allPaths.size();i++)
    {
        String[] path= allPaths.get(i).split(" ");
        TreeSet<Integer> duplicateColumn = new TreeSet<Integer>();
        for(int j= 0;j<path.length;j++)
        {
            String[] word=path[j].split("\\|");

            for(int k=0;k<word.length;k++)
            {
                duplicateColumn.add(Integer.parseInt(word[0]));
            }
        }
        if(duplicateColumn.size()==path.length)
            System.out.println(allPaths.get(i));

    }
}
}