# postmodern/combinatorics

### Subversion checkout URL

You can clone with
or
.
Bringing (more) Combinatorics to Ruby.
Ruby

Fetching latest commit…

Cannot retrieve the latest commit at this time

 Failed to load latest commit information. benchmarks lib spec .document .gemtest .gitignore .rspec .yardopts Benchmarks.md ChangeLog.md LICENSE.txt README.md Rakefile combinatorics.gemspec gemspec.yml

# Combinatorics

## Description

A collection of modules and methods for performing 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 conveniance methods to {Array} and {Set}:
• `cartesian_product`
• `choose`
• `derange`
• `permute`
• `powerset`
• Adds conveniance methods:
• {Range#&}
• {Range#upto}
• {Range#downto}
• {Math.sigma}
• {Math.pi}
• {Math.factorial}
• {Math.subfactorial}

## Examples

Power-set:

``````Set['ab', 'cd', 'ef'].powerset
# => [#<Set: {}>,
#<Set: {"ef"}>,
#<Set: {"cd"}>,
#<Set: {"cd", "ef"}>,
#<Set: {"ab"}>,
#<Set: {"ab", "ef"}>,
#<Set: {"ab", "cd"}>,
#<Set: {"ab", "cd", "ef"}>]
``````

Find the intersecting sub-range between two ranges:

``````(1..50) & (20..100)
# => (20..50)
``````

Enumerate over every sub-range between two ranges:

``````(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]
``````

List comprehensions:

``````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"]]
``````

Cartesian products:

``````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:

``````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:

``````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:

``````require 'combinatorics/permutation'

include Combinatorics::Permute

Combinatorics::Permute::cardinality(128)
# => 8256
``````

## Install

``````  \$ sudo gem install combinatorics
``````