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:
- 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)
# => 8256List 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 >= 1.8.7
Install
$ gem install combinatoricsCopyright
Copyright (c) 2010-2022 Hal Brodigan
See {file:LICENSE.txt} for license information.