Matrix Circular Shift

Does anyone know an efficient way to right circular-shift a matrix? Btw, the matrix is binary but a method to solve a non-binary matrix is also fine.

Right now, I'm thinking of implementing a circular array for the rows of my matrix and updating each row whenever a shift operation is required.

Another method, I was considering was implementing a vector of pointers to columns (of the matrix) represented by vectors and swapping them around when a shift operation occurs.

E.g.

1 2 3
4 5 6
7 8 9

Right-shift

3 1 2
6 4 5
9 7 8

Another problem arises with all these solutions if I need to shift the matrix down as well. To implement both operations efficiently, is completely beyond me.

Down-shift

9 7 8
3 1 2
6 4 5

Solution

Something like this perhaps,

class matrix {
    std::vector<bool> elements;
    int rows, cols, row_ofs, col_ofs;

    std::size_t index(int r, int c) {
        r = (r + row_ofs) % rows;
        c = (c + col_ofs) % cols;
        return std::size_t(r)*cols + c; // row major layout
    }
public:
    matrix() : rows(0), cols(0) {}
    matrix(int r, int c)
    : elements(std::size_t(r)*c), rows(r), cols(c) {}

    int num_rows() const { return rows; }
    int num_cols() const { return cols; }

    std::vector<bool>::reference operator()(int r, int c) {
        return elements.at(index(r,c));
    }

    bool operator()(int r, int c) const {
        return elements.at(index(r,c));
    }

    void rotate_left()  { col_ofs = (col_ofs+1     ) % cols; }
    void rotate_right() { col_ofs = (col_ofs+cols-1) % cols; }
    void rotate_up()    { row_ofs = (row_ofs+1     ) % rows; }
    void rotate_down()  { row_ofs = (row_ofs+rows-1) % rows; }
};

(untested)

Edit: Here's an alternative: Use std::deque<std::deque<T> > internally. ;-) Yes, it does support random access. A deque is not a list. Plus, you don't need to bother anymore with the modulo arithmetic.