Swift collection types that support efficient storage of order-relative values.


Swift collection types that support efficient storage of order-relative values


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All the structures here store relative data. This means that a given value has some kind of dependency on the values that came before. If your data fits into this model, it can help to improve the efficiency of certain operations.

This is very similar to a Rope. And while these structures are just a little more generalized, the terminology used is similar. Data is split into two components: Value and Weight. The Value is independent data. The Weight is the per-element contribution. The full element is reconstructed by combining all preceding elements Weight, along with its independent Value.

To operate on the Weight, these collections need user-defined functions to perform addition, subtraction, as well as finding an initial value. However, if Weight conforms to the AdditiveArithmetic protocol, these can all be inferred.


Let's take a look at some real-world usage of a structure like this. Consider an application that works with text and needs to store information about each line in a document. You might just record the range of each line as (start, length). This is a great example of relative data! The length is the independent value. As long as an edit does not occur within the line, a length is not affected by edits. The relative value is the start - it is defined as the sum of all preceding lengths.

This Metrics type below stores information about a line of text. You could put all kinds of stuff in here, like the height of a line or if it contains any multi-byte UTF-8 data. We'll just record offsets to any leading and trailing whitespace.

This Metrics type will be our independent Value. Line length, expressed as an Int will make up the relative Weight. This works because a line's absolute starting position is the sum of all preceding line lengths.

struct Metrics {
    let leadingWhitespace: Int
    let trailingWhitespace: Int
    init(_ leading: Int, trailing: Int) {
        self.leadingWhitespace = leading
        self.trailingWhitespace = trailing

To get this working, we also need to define a few core operations on the Weight. You can do that through a Configuration property.

let config = RelativeArray<Metrics, Int>.Configuration(
    initial: 0,
    add: { lengthA, lengthB in lengthA + lengthB },
    subtract: { lengthA, lengthB in lengthA - lengthB }

All this ceremony allows for very abstract Weight types. However, we can do better for types that implement AdditiveArithmetic, which Int does! In that case, Configuration has predefined behavior that will automatically do the right thing. Making your own custom types conform to AdditiveArithmetic will allow it to work the same way.

This allows us to define a configuration with a default initializer. And, this is also set as a default for RelativeArray, so in this case we can avoid dealing with configuration entirely.

On to some example data! Let's say we'd like to store metrics for this text:


We can do that by creating our array with the right types and appending some WeightedValue types in.

let array = RelativeArray<Metrics, Int>()

    WeightedValue(value: Metrics(3, 3), weight: 9)

    WeightedValue(value: Metrics(2, 0), weight: 8)

    WeightedValue(value: Metrics(1, 0), weight: 3)

Now that our data is loaded, we can read out values. And with a little work, we can reconstruct our desired values.

let record = array[2]

let start = record.dependency // 17 (9 + 8)
let length = record.weight    // 3
let metrics = record.value    // Metrics(1, 0)



A RelativeArray is the simplest type. It stores a Value and Weight in a plain array. On its own, this type can be handy for many applications. But, it is also used as a building block for more complex structures.

RelativeArray conforms to Sequence and RandomAccessCollection. It supports CoW, just like other Swift collections.


⚠️ Still a WIP ⚠️

This is a position-addressable type, like an array. However, internally it stores data in a B+Tree. That gets you logarithmic insertion and deletion.

RelativeList conforms to Sequence and RandomAccessCollection.

However, this is a reference type and does not support CoW. I started looking into it more, but just getting this to work was hard enough.

Notes on Data Structures

You might be wondering why I didn't use a Red-black tree for this. Red-black tree's are great! They may be the simplest self-balancing tree structure known. And, they can totally be used in this relative-data context. However, they do make some trade-offs. Compared to something like a B-tree, they need a lot more pointers. This adds to memory overhead and isn't great for locality of reference. This is basically why B-Tree's were invented in the first place. They also will compare unfavorably to an array for small N. And as they say, N is usually small. A B+Tree addresses both these limitations, though of course it is a lot more complex internally.

At one point, I got excited about trying out a skip list for this, because skip lists are cool. I had a tough time getting my head around how to do this at all, and skip lists just made it harder.

Typically, when faced with this kind of problem you have to measure. Carefully. But, the allure of optimization-without-rigor is powerful and I gave in. I don't know if this structure is actually faster than a RBTree or standard B-Tree. But I learned a lot. I hope that one day Swift Collections provides a suitable B+Tree or Rope.

Related Projects

Contributing and Collaboration

I'd love to hear from you! Get in touch via an issue or pull request.

I prefer collaboration, and would love to find ways to work together if you have a similar project.

I prefer indentation with tabs for improved accessibility. But, I'd rather you use the system you want and make a PR than hesitate because of whitespace.

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Last updated: Tue Apr 02 2024 00:33:43 GMT-0900 (Hawaii-Aleutian Daylight Time)