Number Of Paths In A Matrix

    static Integer number_of_paths(ArrayList<ArrayList<Integer>> matrix) {
        // We are going to use the Lazy manager approach to solve this problem.
        // We start at the top left corner. the formula that describe this problem
        // is given by the following :
        // NOW(r, c) = NOW(r, c-1) + NOW(r-1, c). OR NOW(r, c) = NOW(r, c+1) + NOW(r+1, c)

        int nr = matrix.size();
        int nc = matrix.get(0).size();
        int modulo = 1000000007;

        long[][] now = new long[nr][nc];
        now[0][0] = matrix.get(0).get(0);
        for (int r = 0; r < nr; r++) {
            for (int c = 0; c < nc; c++) {
                if (matrix.get(r).get(c) == 1 || (r == 0 && c == 0)) {
                    continue;
                }

                now[r][c] = (c >= 1 ? now[r][c - 1] : 0) % modulo +
                            (r >= 1 ? now[r - 1][c] : 0) % modulo;
            }
        }

        return (int)now[nr-1][nc-1] % modulo;
    }