Created
July 31, 2015 20:49
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Dice sum probability calculator
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| 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 |
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