Metamorphose

Efficient permutation representations

A permutation is a rearrangement of the elements in an ordered collection. It is a one-to-one mapping—a bijection—and therefore reversible. Lehmer codes provide a mapping between positive integers and permutations, which make it possible to describe a permutation of n elements in O(nlog(n)) space. Metamorphose provides an implementation of this encoding.

Features

• efficient representation of permutations of collection elements
• bijection between positive integers and permutations
• provides a binary serialization of permutations

Availability

Getting Started

Metamorphose primarily provides the Permutation class, which is in the metamorphose package and exported to the soundness package. You can import it with,

import metamorphose.*

or,

import soundness.*

There are two ways to construct a new Permutation. Firstly, from an ordered sequence of distinct indexes, for example,

val permutation = Permutation(Vector(1, 4, 2, 3, 0))

which interprets the ordering of the indexes to yield the permutation with factoradic number 45, i.e. Permutation(Factoradic(45)).

Or, if we already know the factoradic number of the permutation, we can pass that in directly, using the Factoradic costructor, like so:

val permutation = Permutation(Factoradic(45))

To check that this is the same permutation, we can expand it with,

val order: List[Int] = permutation.expansion

which gives the original sequence back: List(1, 4, 2, 3, 0).

It's also possible to see the Lehmer code derived from this permutation with,

permutation.lehmer

which produces, List(1, 3, 1, 1, 0).

We can apply this permutation to a sufficiently long sequence just by applying it to the sequence, i.e. permutation(list).

Permutations are always reversible, and Permutation#inverse will construct a new permutation which will permute a sequence permuted by the original permutation back to the original list.

That is, for all lists and permutations of the right size it is true that,

permutation.inverse(permutation(list)) == list

Status

Metamorphose is classified as fledgling. For reference, Soundness projects are categorized into one of the following five stability levels:

• embryonic: for experimental or demonstrative purposes only, without any guarantees of longevity
• fledgling: of proven utility, seeking contributions, but liable to significant redesigns
• maturescent: major design decisions broady settled, seeking probatory adoption and refinement
• dependable: production-ready, subject to controlled ongoing maintenance and enhancement; tagged as version 1.0.0 or later
• adamantine: proven, reliable and production-ready, with no further breaking changes ever anticipated

Projects at any stability level, even embryonic projects, can still be used, as long as caution is taken to avoid a mismatch between the project's stability level and the required stability and maintainability of your own project.

Metamorphose is designed to be small. Its entire source code currently consists of 223 lines of code.

Building

Metamorphose will ultimately be built by Fury, when it is published. In the meantime, two possibilities are offered, however they are acknowledged to be fragile, inadequately tested, and unsuitable for anything more than experimentation. They are provided only for the necessity of providing some answer to the question, "how can I try Metamorphose?".

1. Copy the sources into your own project

   Read the fury file in the repository root to understand Metamorphose's build structure, dependencies and source location; the file format should be short and quite intuitive. Copy the sources into a source directory in your own project, then repeat (recursively) for each of the dependencies.

   The sources are compiled against the latest nightly release of Scala 3. There should be no problem to compile the project together with all of its dependencies in a single compilation.

2. Build with Wrath

   Wrath is a bootstrapping script for building Metamorphose and other projects in the absence of a fully-featured build tool. It is designed to read the fury file in the project directory, and produce a collection of JAR files which can be added to a classpath, by compiling the project and all of its dependencies, including the Scala compiler itself.

   Download the latest version of wrath, make it executable, and add it to your path, for example by copying it to /usr/local/bin/.

   Clone this repository inside an empty directory, so that the build can safely make clones of repositories it depends on as peers of metamorphose. Run wrath -F in the repository root. This will download and compile the latest version of Scala, as well as all of Metamorphose's dependencies.

   If the build was successful, the compiled JAR files can be found in the .wrath/dist directory.

Contributing

Contributors to Metamorphose are welcome and encouraged. New contributors may like to look for issues marked beginner.

We suggest that all contributors read the Contributing Guide to make the process of contributing to Metamorphose easier.

Please do not contact project maintainers privately with questions unless there is a good reason to keep them private. While it can be tempting to repsond to such questions, private answers cannot be shared with a wider audience, and it can result in duplication of effort.

Author

Metamorphose was designed and developed by Jon Pretty, and commercial support and training on all aspects of Scala 3 is available from Propensive OÜ.

Name

When an insect metamorphoses, it permutes the elements of its body from one form into another.

In general, Soundness project names are always chosen with some rationale, however it is usually frivolous. Each name is chosen for more for its uniqueness and intrigue than its concision or catchiness, and there is no bias towards names with positive or "nice" meanings—since many of the libraries perform some quite unpleasant tasks.

Names should be English words, though many are obscure or archaic, and it should be noted how willingly English adopts foreign words. Names are generally of Greek or Latin origin, and have often arrived in English via a romance language.

Logo

The logo shows a butterfly, which has undergone metamorphosis from a caterpillar.

License

Metamorphose is copyright © 2024 Jon Pretty & Propensive OÜ, and is made available under the Apache 2.0 License.