Dice sum probability calculator

dice_sum_probability_calc.rb

require 'bigdecimal'
require 'benchmark'

class DiceSumProbabilityCalc
  DEFAULT_SIDES_COUNT = 6

  def initialize(sum, dices_count, dice_sides_count = DEFAULT_SIDES_COUNT)
    @sum = sum
    @dices_count = dices_count
    @dice_sides_count = dice_sides_count
  end

  def call
    coefficient * single_probability
  end

  private

  def coefficient
    (0..max_limit).reduce(0) do |acc, i|
      acc + summand(i)
    end
  end

  def summand(i)
    (-1)**i * factorial_formula(@dices_count, i) * factorial_formula(@sum - @dice_sides_count * i - 1, @dices_count - 1)
  end

  def max_limit
    (@sum - @dices_count) / @dice_sides_count
  end

  def single_probability
    1.0 / (@dice_sides_count**@dices_count)
  end

  def factorial_formula(n, k)
    BigDecimal.new(factorial(n)) / factorial(k) / factorial(n - k)
  end

  def factorial(n)
    factorial_builder[n]
  end

  def factorial_builder
    @factorial_builder ||= Hash.new { |memo, value| memo[value] = (1..value).reduce(1, :*) }
  end
end

Benchmark.bm do |x|
  x.report("M=300 N=100") { DiceSumProbabilityCalc.new(300, 100).call }
  x.report("M=600 N=100") { DiceSumProbabilityCalc.new(600, 100).call }
  x.report("M=900 N=300") { DiceSumProbabilityCalc.new(900, 300).call }
  x.report("M=1800 N=300") { DiceSumProbabilityCalc.new(1800, 300).call }
  x.report("M=2100 N=600") { DiceSumProbabilityCalc.new(2100, 600).call }
end