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¶ ↑
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Adds Haskell/Python style list comprehensions via Array#comprehension.
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Provides reusable
Combinatorics
Mixins: -
Adds
Combinatorics
core extension methods to {Array} and {Set}: -
Adds additional core extension methods:
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"}>]
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¶ ↑
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ruby >= 1.8.7
Install¶ ↑
$ gem install combinatorics
Copyright¶ ↑
Copyright © 2010-2022 Hal Brodigan
See {file:LICENSE.txt} for license information.