勝敗経緯パターンの試行

perm.rb

module Static
  refine Array do
    # 平均
    def mean
      self.inject(&:+) / self.length
    end

    # 標準偏差
    def sdev
      m = self.mean
      Math.sqrt(self.inject(0.0) {|s,e| s += (e-m)**2} / (self.length-1))
    end

    alias :_permutation :permutation

    # 順列生成
    # count なし: すべての場合, あり: 乱数で count 回生成
    def permutation(count=nil, &block)
      if count && count > self.length
        count.times do
          random = self.dup
          perm = []
          until random.empty?
            perm << random.delete_at(rand(0...random.length))
          end
          block.call(perm)
        end
      else
        self._permutation(count, &block)
      end
    end
  end
end

using Static

# 勝敗経緯パターンに対応する順位の配列
def order(perm)
  cases = Hash.new {|h,k| h[k]=[]}
  cases[''] = perm.dup
  rest = perm.length
  while rest > 1 do
    cases.keys.each do |k|
      v = cases.delete(k)
      until v.empty? do
        a, b, *v = v
        cases[k + '○'] << [a,b].min
        cases[k + '×'] << [a,b].max
      end
    end
    rest /= 2
  end
  cases
end

# 勝敗経緯パターンの試行
def trial(n, count=nil)
  trials = Hash.new {|h,k| h[k] = []}
  (2..2**n).to_a.map(&:to_f).permutation(count) do |perm|
    order([1.0]+perm).each_pair do |k, v|
      trials[k] << v.first
    end
  end
  trials
end

# ８人櫓 (全順列網羅)
trials = trial(3)
trials.length.times do |i|
  puts ' %2d %s %7.4f %7.4f' %  [i+1, trials.keys[i],
        trials.values[i].mean, trials.values[i].sdev] # =>
# 1 ○○○  1.0000  0.0000
# 2 ○○×  2.6000  0.8001
# 3 ○×○  3.0571  0.8601
# 4 ○××  5.3429  0.9841
# 5 ×○○  3.6571  0.9841
# 6 ×○×  5.9429  0.8601
# 7 ××○  6.4000  0.8001
# 8 ×××  8.0000  0.0000
end

# 16人櫓 (10万回試行)
trials = trial(4,100000)
trials.length.times do |i|
  puts ' %2d %s %7.4f %7.4f' %  [i+1, trials.keys[i],
        trials.values[i].mean, trials.values[i].sdev] # =>
#  1 ○○○○  1.0000  0.0000
#  2 ○○○×  2.7772  1.0512
#  3 ○○×○  3.3264  1.1702
#  4 ○○××  6.4880  1.8770
#  5 ○×○○  4.0833  1.4004
#  6 ○×○×  7.4572  1.8547
#  7 ○××○  8.2784  1.8964
#  8 ○××× 11.9042  1.7225
#  9 ×○○○  5.0948  1.7260
# 10 ×○○×  8.7218  1.8861
# 11 ×○×○  9.5457  1.8576
# 12 ×○×× 12.9170  1.4003
# 13 ××○○ 10.5087  1.8749
# 14 ××○× 13.6717  1.1694
# 15 ×××○ 14.2254  1.0497
# 16 ×××× 16.0000  0.0000
end