List<Movie> movies = new ArrayList<>();
movies.add(new Movie(1, "Movie1"));
movies.add(new Movie(2, "Movie2"));
movies.add(new Movie(3, "Movie3"));
movies.add(new Movie(4, "Movie4"));

int[] sortIndex = [0, 3, 1, 2];
...Sorting Code...
for (Movie movie : movies) {
    Log.d(TAG, movie.getName());
}

Movie1
Movie4
Movie2
Movie3