Sortable Objects

Advent of Code 2023 has just kicked off, and I'm going to try something a bit different this year, I'm going to try and share useful concepts and patterns that play a role in solving each day's puzzle.

Today, I wanted to talk about making your objects sortable and how you can use this to take advantage of the built-in sort functionality in your language of choice. This is an incredibly useful pattern to know about, and one which I found useful for Day 7 of Advent of Code 2023.

How Sorting Works

When it comes to sorting things, there are two main problems we face: deciding which order things should appear in, and then the algorithm used to perform the actual sorting. In most languages, the algorithm is already taken care of for us as part of the standard library (often implemented using a stable QuickSort) so the main thing we need to worry about is how to decide which order things should appear in.

In many cases, I find folks reaching for the ability to provide a custom sorting callback, which is great for quick and dirty once-off sorting, but when it comes to building reusable code, it can artificially result in a lot of code duplication.

Natively Orderable Objects

Of course, we know that for most language primitives (numbers and strings in particular) sorting "just works" without you needing to provide a custom sorting callback. In an ideal world, this is how our custom objects would work too, and fortunately, most languages provide a way to do just that.

In Rust, we can avail of the std::cmp::Ord and std::cmp::PartialOrd traits to describe how objects should be ordered. In trivial cases, you can use #[derive(...)] to implement these, but let's talk about doing so explicitly.

tip

Rust isn't the only language that supports this type of functionality, and you can achieve similar results in C# by implementing the IComparable interface, in Python by implementing the __lt__ and __gt__ methods, and in Go by implementing the sort.Interface interface.

Sorting enums in Rust

Let's start with a simple enum which we want to be able to sort. In this case, we'll use a Direction enum which represents the four cardinal directions.

enum Direction {
    North,
    East,
    South,
    West,
}

If we wanted to sort these in clockwise order, we could do so by implementing the std::cmp::Ord trait ourselves, or we could instead use #[derive(...)] and define constant values for our enum variants.

#[derive(PartialEq, Eq, PartialOrd, Ord)]
enum Direction {
    North = 0,
    East = 1,
    South = 2,
    West = 3,
}

tip

In order to implement Ord you'll need to implement Eq, same goes for PartialOrd and PartialEq. This is because Ord and PartialOrd are traits which extend Eq and PartialEq respectively, so you'll need to implement the base traits before you can implement the extended ones.

Sorting structs in Rust

Of course, not everything in Rust is an enum, and we'll often want to sort structs too. Let's imagine that we've got a Complex number type as shown below.

#[derive(PartialEq, Eq)]
struct Complex {
    real: f64,
    imaginary: f64,
}

If we'd like to spiral-sort this (i.e. first by distance from the origin, then by angle), we would need to implement our own sort function to perform the necessary transforms. Let's do that, and take the time to implement this in a clean and reusable manner. We'll start by implementing support for converting our Complex type to polar coordinates.

impl Complex {
    pub fn new(real: f64, imaginary: f64) -> Self {
        Self { real, imaginary }
    }
    
    pub fn to_polar(&self) -> (f64, f64) {
        // Don't you just love Rust's lovely math extensions?
        let r = (self.real.powi(2) + self.imaginary.powi(2)).sqrt();
        let theta = self.imaginary.atan2(self.real);

        (r, theta)
    }
}

Now that we can easily retrieve the polar coordinates for our Complex number, we can implement std::cmp::PartialOrd for it.

impl std::cmd::PartialOrd for Complex {
    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
        let (r1, theta1) = self.to_polar();
        let (r2, theta2) = other.to_polar();

        // First, compare the distance from the origin
        let distance = r1.partial_cmp(&r2);
        if distance != Some(std::cmp::Ordering::Equal) {
            return distance;
        }

        // If the distance is the same, compare the angle
        theta1.partial_cmp(&theta2)
    }
}

With this, we can now easily sort our Complex numbers using the built-in sort function.

let mut numbers = vec![
    Complex::new(1.0, 1.0),
    Complex::new(2.0, -1.5),
    Complex::new(1.0, -1.0),
    Complex::new(0.0, 0.0),
    Complex::new(-1.0, -1.0),
    Complex::new(-2.0, 1.5),
    Complex::new(-1.0, 1.0),
];

// Sort the numbers by their position in the spiral
numbers.sort();

Conclusion

I find that incorporating this pattern can help significantly reduce the amount of duplicated sort code lying around your code bases and allows you to take advantage of built-in sort functionality for solving interesting problems (like ordering the winning hands in a game of cards).