# Combinatorics * [Source](https://github.com/postmodern/combinatorics) * [Issues](https://github.com/postmodern/combinatorics/issues) * [Documentation](http://rubydoc.info/gems/combinatorics) * [Email](mailto:postmodern.mod3 at gmail.com) ## 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 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 # => [#, #, #, #, #, #, #, #] 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' Combinatorics::Permute.cardinality(128) # => 8256 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"]] 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] ## Requirements * [ruby](http://www.ruby-lang.org/) >= 1.8.7 ## Install \$ gem install combinatorics ## Copyright Copyright (c) 2010-2012 Hal Brodigan See {file:LICENSE.txt} for license information.