Tips implementing permutation algorithm in Java

Question

As part of a school project, I need to write a function that will take an integer N and return a two-dimensional array of every permutation of the array {0, 1, ..., N-1}. The declaration would look like public static int[][] permutations(int N).

The algorithm described at http://www.usna.edu/Users/math/wdj/book/node156.html is how I've decided to implement this.

I wrestled for quite a while with arrays and arrays of ArrayLists and ArrayLists of ArrayLists, but so far I've been frustrated, especially trying to convert a 2d ArrayList to a 2d array.

So I wrote it in javascript. This works:

function allPermutations(N) {
    // base case
    if (N == 2) return [[0,1], [1,0]];
    else {
        // start with all permutations of previous degree
        var permutations = allPermutations(N-1);

        // copy each permutation N times
        for (var i = permutations.length*N-1; i >= 0; i--) {
            if (i % N == 0) continue;
            permutations.splice(Math.floor(i/N), 0, permutations[Math.floor(i/N)].slice(0));
        }

        // "weave" next number in
        for (var i = 0, j = N-1, d = -1; i < permutations.length; i++) {
            // insert number N-1 at index j
            permutations[i].splice(j, 0, N-1);

            // index j is  N-1, N-2, N-3, ... , 1, 0; then 0, 1, 2, ... N-1; then N-1, N-2, etc.
            j += d;
            // at beginning or end of the row, switch weave direction
            if (j < 0 || j >= N) {
                d *= -1;
                j += d;
            }
        }
        return permutations;
    }
}

So what's the best strategy to port that to Java? Can I do it with just primitive arrays? Do I need an array of ArrayLists? Or an ArrayList of ArrayLists? Or is there some other data type that's better? Whatever I use, I need to be able to convert it back into a an array of primitive arrays.

Maybe's there a better algorithm that would simplify this for me...

Thank you in advance for your advice!

Answer 1

As you know the number of permutations beforehand (it's N!) and also you want/have to return an int[][] I would go for an array directly. You can declare it right at the beginning with correct dimensions and return it at the end. Thus you don't have to worry about converting it afterwards at all.