Question

Hello

I am working on java and I have to generate all the possible patterns(combinations) of M-by-N matrices such that in the same row there should not be more than a single 1, Same column may contain more than a single 1, Taking an example of 3*3 matrix, matrices generated should look like:

1 0 0  
1 0 0  
1 0 0  

0 1 0  
1 0 0  
1 0 0  

0 0 1  
1 0 0  
1 0 0  

1 0 0  
0 1 0  
1 0 0  

1 0 0  
0 0 1  
1 0 0  

1 0 0  
1 0 0  
0 1 0  

1 0 0  
1 0 0  
0 0 1  

0 1 0  
0 1 0  
0 1 0  

1 0 0  
0 1 0  
0 1 0  

0 0 1  
0 1 0  
0 1 0  

0 1 0  
1 0 0  
0 1 0  

0 1 0  
0 0 1  
0 1 0  

….. and so on.

As I have already said that progrom should be flexible that can generate all such possible patterns for any value of M and N.

Please help me..

Thanks!

Answer 1

Here’s one solution. ideone.com demo.

I bet it can be done with half the number of rows though.

public static Set<int[][]> chooseFrom(List<int[]> choices, int choose) {
    Set<int[][]> results = new HashSet<int[][]>();
    if (choose == 1) {
        for (int[] choice : choices)
            results.add(new int[][] { choice });
    } else {
        for (int[] choice : choices) {
            for (int[][] submatrix : chooseFrom(choices, choose - 1)) {
                int[][] matrix = new int[choose][];
                matrix[0] = choice;
                for (int r = 1; r < choose; r++)
                    matrix[r] = submatrix[r-1];
                results.add(matrix);
            }
        }
    }

    return results;
}

public static Set<int[][]> matrices(int M, int N) {
    List<int[]> possibleRows = new ArrayList<int[]>();

    for (int i = 0; i < N; i++) {
        int[] row = new int[N];
        row[i] = 1;
        possibleRows.add(row);
    }

    return chooseFrom(possibleRows, M);
}

Output for the 2×3 case:

[ 0 0 1 ]
[ 0 1 0 ]

[ 1 0 0 ]
[ 0 0 1 ]

[ 0 0 1 ]
[ 0 0 1 ]

[ 0 0 1 ]
[ 1 0 0 ]

[ 0 1 0 ]
[ 1 0 0 ]

[ 0 1 0 ]
[ 0 1 0 ]

[ 1 0 0 ]
[ 1 0 0 ]

[ 0 1 0 ]
[ 0 0 1 ]

[ 1 0 0 ]
[ 0 1 0 ]