ダイスで組分け・解答例

d:id:Nabetani:20070820#p1 を解くスクリプトを書いてみました。

#!/usr/bin/ruby
require 'mathn' # for gcd

class Groups < Hash
  def initialize
    super(0)
    self[[0, 0, 0, 0, 0, 0]] = 1
    @members=0
  end

  def iterate
    tmp = self.dup
    self.clear
    tmp.each{|groups, frequency|
      (0..5).each{|i|
         x = groups.dup
         x[i] += 1
         x.sort!
         self[x] += frequency
      }
    }
    @members += 1
  end

  def numerator
    self.inject(0){|sum, item| sum + (item[0].index(1) ? item[1] : 0) }
  end

  def denominator
    self.inject(0){|sum, item| sum + item[1] }
  end

  def show_probability
    n = self.numerator
    d = self.denominator
    g = n.gcd(d)
    puts sprintf("n=%2d: %8.6f (%d/%d)\n", @members,
                  n.to_f/d.to_f, (n/g).to_s, (d/g).to_s)
  end
end

groups = Groups.new
ARGV[0].to_i.times {
  groups.iterate
  groups.show_probability
}

> ruby ./dicegroup.rb 20
n= 1: 1.000000 (1/1)
n= 2: 0.833333 (5/6)
n= 3: 0.972222 (35/36)
n= 4: 0.925926 (25/27)
n= 5: 0.960648 (415/432)
n= 6: 0.945216 (1225/1296)
n= 7: 0.948967 (44275/46656)
n= 8: 0.940358 (32905/34992)
n= 9: 0.931418 (173825/186624)
n=10: 0.918691 (4629145/5038848)
n=11: 0.901407 (18168205/20155392)
n=12: 0.879292 (2953745/3359232)
n=13: 0.851716 (1853999485/2176782336)
n=14: 0.818071 (5342289715/6530347008)
n=15: 0.778281 (20329774345/26121388032)
n=16: 0.732966 (21539352185/29386561536)
n=17: 0.683323 (642576334555/940369969152)
n=18: 0.630864 (197748653015/313456656384)
n=19: 0.577167 (58617086216815/101559956668416)
n=20: 0.523683 (79777892481245/152339935002624)
>