Object-Oriented Permutation Generation

A classic interview coding question is—or at least used to be—to write a program to generate all the permutations of a string.

I used to like to get it because it had a simple and elegant recursive solution that was easy to right the first time, when writing it on the whiteboard. And coming up with a good recursive solution in an interview used to impress interviewers, especially if you explained it nicely in a “mathematical induction” sort of way.

Recently I had two additional thoughts about that easy solution. The first was that recursive solutions were sort of the epitome of procedural programming, but what would be the object-oriented variant, and would it be as easy to write it correctly at the whiteboard?

The second thought was a bit more interesting: suppose you actually needed a permutation generator in your program (I never have) then you probably would not want the recursive solution anyway, which would generate all permutations—and process them—before returning to the caller. Instead, you’d want a demand-oriented, that is, iterator-style, solution that you could pull solutions out of when you wanted to. That sort of solution would be more difficult to express in a procedural language, and you couldn’t easily change a recursive solution into an demand-oriented solution, but the object-oriented solution might be easier to adapt. And could you still do it at the whiteboard?

I was going to make a blog post about this—but it turned into quite the megilla and I put it on CodeProject as a tutorial article, here.

In that article I not only show the object-oriented data-pipeline version that corresponds directly to the procedural (recursive) solution, but I also show two variants of it in “pull-style” as a iterator.

However, here is the object-oriented solution to generating permutations. It is in fact as simple as the recursive solution, and perhaps even easier to get right the first time while standing at the whiteboard. I don’t know why it hasn’t been seen, as an example, earlier.

private static final class PermuteStep implements Action {
    private final Action a;
    private final char c;
    private PermuteStep(char c, Action a) {
        this.c = c;
        this.a = a;
    }
    public void next(String s) {
        for (int i = 0; i <= s.length(); i++) {
            String n = s.substring(0, i)
                     + c
                     + s.substring(i, s.length());
            a.next(n);
        }
    }
}

public static void Permute(Action a, String p) {
     // (Argument validation elided for clarity)
    Action as = a;
    for (char c : p.toCharArray()) {
        as = new PermuteStep(c, as);
    }
    as.next("");
}