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https://github.com/postmodern/combinatorics.rb
Bringing (more) Combinatorics to Ruby.
https://github.com/postmodern/combinatorics.rb
combinatorics math ruby
Last synced: 4 days ago
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Bringing (more) Combinatorics to Ruby.
- Host: GitHub
- URL: https://github.com/postmodern/combinatorics.rb
- Owner: postmodern
- License: mit
- Created: 2010-10-03T00:50:32.000Z (over 14 years ago)
- Default Branch: main
- Last Pushed: 2024-01-25T13:12:57.000Z (about 1 year ago)
- Last Synced: 2024-05-01T21:59:34.788Z (10 months ago)
- Topics: combinatorics, math, ruby
- Language: Ruby
- Homepage: http://rubygems.org/gems/combinatorics
- Size: 238 KB
- Stars: 46
- Watchers: 6
- Forks: 2
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- Changelog: ChangeLog.md
- License: LICENSE.txt
Awesome Lists containing this project
README
# Combinatorics
[](https://github.com/postmodern/combinatorics/actions/workflows/ruby.yml)
[](https://codeclimate.com/github/postmodern/combinatorics)
* [Source](https://github.com/postmodern/combinatorics)
* [Issues](https://github.com/postmodern/combinatorics/issues)
* [Documentation](http://rubydoc.info/gems/combinatorics)
## Description
A collection of modules and methods for performing
[Combinatoric](http://en.wikipedia.org/wiki/Combinatoric) calculations.
Methods are defined to compute power sets, Cartesian products, permutations,
combinations, and derangements.
Note: this includes k-combinations and k-permutations, i.e. only generating
resultant sets of a given size. Each set theory operation method supports block
arguments to allow continuous code execution during the combinatoric set
generation process. Each combinatoric operation implementation also supports a
`cardinality` method which determines the total number of subsets that will be
created beforehand (to aid in the avoidance of starting an operation which will
never complete due to exponential computational complexity.)
## Features
* Adds Haskell/Python style list comprehensions via [Array#comprehension].
* Provides reusable Combinatorics Mixins:
* [Combinatorics::CartesianProduct]
* [Combinatorics::Choose]
* [Combinatorics::Derange]
* [Combinatorics::Permute]
* [Combinatorics::PowerSet]
* Adds Combinatorics core extension methods to {Array} and {Set}:
* [cartesian_product]
* [choose]
* [derange]
* [permute]
* [powerset]
* Adds additional core extension methods:
* [Range#&]
* [Range#upto]
* [Range#downto]
* [Math.sigma]
* [Math.pi]
* [Math.factorial]
* [Math.subfactorial]
[Array#comprehension]: https://rubydoc.info/gems/combinatorics/Array#comprehension-instance_method
[Combinatorics::CartesianProduct]: https://rubydoc.info/gems/combinatorics/Combinatorics/CartesianProduct
[Combinatorics::Choose]: https://rubydoc.info/gems/combinatorics/Combinatorics/Choose
[Combinatorics::Derange]: https://rubydoc.info/gems/combinatorics/Combinatorics/Derange
[Combinatorics::Permute]: https://rubydoc.info/gems/combinatorics/Combinatorics/Permute
[Combinatorics::PowerSet]: https://rubydoc.info/gems/combinatorics/Combinatorics/PowerSet
[cartesian_product]: https://rubydoc.info/gems/combinatorics/Combinatorics/CartesianProduct/Mixin#cartesian_product-instance_method
[choose]: https://rubydoc.info/gems/combinatorics/Combinatorics/Choose/Mixin#choose-instance_method
[derange]: https://rubydoc.info/gems/combinatorics/Combinatorics/Derange/Mixin#derange-instance_method
[permute]: https://rubydoc.info/gems/combinatorics/Combinatorics/Permute/Mixin#permute-instance_method
[powerset]: https://rubydoc.info/gems/combinatorics/Combinatorics/PowerSet/Mixin#powerset-instance_method
[Range#&]: https://rubydoc.info/gems/combinatorics/Range#&-instance_method
[Range#upto]: https://rubydoc.info/gems/combinatorics/Range#upto-instance_method
[Range#downto]: https://rubydoc.info/gems/combinatorics/Range#downto-instance_method
[Math.sigma]: https://rubydoc.info/gems/combinatorics/Math#sigma-class_method
[Math.pi]: https://rubydoc.info/gems/combinatorics/Math#pi-class_method
[Math.factorial]: https://rubydoc.info/gems/combinatorics/Math#factorial-class_method
[Math.subfactorial]: https://rubydoc.info/gems/combinatorics/Math#subfactorial-class_method
## Examples
Power-set:
```ruby
Set['ab', 'cd', 'ef'].powerset
# => [#,
#,
#,
#,
#,
#,
#,
#]
```
Cartesian products:
```ruby
require 'combinatorics/cartesian_product'
['a', 'b', 'c'].cartesian_product([0, 1, 2]).to_a
# => [["a", 0],
["b", 0],
["c", 0],
["a", 1],
["b", 1],
["c", 1],
["a", 2],
["b", 2],
["c", 2]]
```
k-combinations:
```ruby
require 'combinatorics/choose'
('a'..'f').to_a.choose(2).to_a
# => [["a", "b"],
["a", "c"],
["a", "d"],
["a", "e"],
["a", "f"],
["b", "c"],
["b", "d"],
["b", "e"],
["b", "f"],
["c", "d"],
["c", "e"],
["c", "f"],
["d", "e"],
["d", "f"],
["e", "f"]]
```
Derangements:
```ruby
require 'combinatorics/derange'
[:_, :q, :z, :x].derange.to_a
# => [[:q, :_, :x, :z],
[:q, :z, :x, :_],
[:q, :x, :_, :z],
[:z, :_, :x, :q],
[:z, :x, :_, :q],
[:z, :x, :q, :_],
[:x, :_, :q, :z],
[:x, :z, :_, :q],
[:x, :z, :q, :_]]
```
Permutation cardinality:
```ruby
require 'combinatorics/permutation'
Combinatorics::Permute.cardinality(128)
# => 8256
```
List comprehensions:
```ruby
require 'combinatorics/list_comprehension'
[(0..10).step(2),('a'..'c')].comprehension.to_a
# => [[0, "a"],
[0, "b"],
[0, "c"],
[2, "a"],
[2, "b"],
[2, "c"],
[4, "a"],
[4, "b"],
[4, "c"],
[6, "a"],
[6, "b"],
[6, "c"],
[8, "a"],
[8, "b"],
[8, "c"],
[10, "a"],
[10, "b"],
[10, "c"]]
```
Find the intersecting sub-range between two ranges:
```ruby
(1..50) & (20..100)
# => (20..50)
```
Enumerate over every sub-range between two ranges:
```ruby
(1..5).upto(2..10).to_a
# => [1..5, 1..6, 1..7, 1..8, 1..9, 1..10,
2..5, 2..6, 2..7, 2..8, 2..9, 2..10]
```
## Requirements
* [ruby](http://www.ruby-lang.org/) >= 2.0.0
## Install
```shell
$ gem install combinatorics
```
## Copyright
See {file:LICENSE.txt} for license information.