Ruby combinatorics

combs.rb

class Integer
  def !
    if self > 0
      (1..self).reduce :*
    elsif self.zero?
      1
    else
      raise ArgumentError, "No factorial for #{self}"
    end
  end

  alias :"!@" :!
  alias :fact :!

  def choose r
    raise ArgumentError, "r = #{r} is outside 0..#{self}" if r < 0 or r > self
    (self.!).fdiv((self - r).!).fdiv(r.!).to_i
  end

end

def nice n, p=3
  return n unless n.kind_of? Numeric
  i = n.to_i
  f = ((n - i).round(p).to_s)[2..-1]
  i = i.to_s.reverse.gsub(/...(?=.)/, '\& ').reverse
  "#{i}.#{f}"
end

def ncr n, r
  raise ArgumentError, "r = #{r} is outside 0..#{n}" if r < 0 or r > n
  n.choose r
end

def npr n, r
  raise ArgumentError, "r = #{r} is outside 0..#{n}" if r < 0 or r > n
  n.!.fdiv((n - r).!).to_i
end

def binomial(n, x, p)
  raise ArgumentError, "x=#{x} cannot be greater than n=#{n}" if x > n
  n.choose(x) * p ** x * (1 - p) ** (n - x)
end

Fun things to try:

puts 8.! # 40320
puts !8 # 40320, for the sake of fun
puts 8.fact # 40320, for the sake of fun

puts(7.choose 0) # 1
puts(7.choose 1) # 7
puts(7.choose 2) # 21
puts(7.choose 4) # 35
puts(7.choose 5) # 21
puts(7.choose 6) # 7
puts(7.choose 7) # 1

puts(npr 7, 6) # 5040

puts(binomial(8, 3, 0.4)) # 0.27869184

Also, to use the nice function, remember the special variable underscore, i.e. _! (Only works in irb 😢)

> nice 4345.34535
=> "4 345.345"
> 8379.44
=> 8379.44
> nice _
=> "8 379.44"