Crack a Keycode

Also see:

- Career cup discussion
- https://en.wikipedia.org/wiki/De_Bruijn_sequence


de Bruijn construction by Lyndon Words. See here
Java – De Bruijn
    public static StringBuilder sequence;
    public static int[] a;
    public static int alphabet;
    public static int subLength;

    // De Bruijn Sequence for alphabet k
    // and subsequence of length n
    public String crackSequence(int k, int n) {
        alphabet = k; subLength = n;
        sequence = new StringBuilder();
        a = new int[n + 1];
        db(1, 1);
        return sequence.toString();
    }

    // Lyndon Words
    private void db(int t, int p) {
        if (t > subLength) {
            if (subLength % p == 0)
                for (int i = 1; i < p + 1; ++i) sequence.append(a[i]);
        } else {
            a[t] = a[t - p];
            db(t + 1, p);
            for (int j = a[t - p] + 1; j < alphabet; ++j) {
                a[t] = j;
                db(t + 1, t);
            }
        }
    }