#!/usr/bin/env ruby
#==========================================================================
# Initial author of this file: Martin.Vahi@softf1.com
# This file is in public domain.
#--------------------------------------------------------------------------
# The Bash line and the command line output:
=begin

ruby ./2017_10_29_randomness_and_the_e.rb 10000000

Histogram Column Label | Histogram Column Height
---------------------- | -----------------------
                     0 | 0
                     1 | 0
                     2 | 5001315
                     3 | 3331379
                     4 | 1250445
                     5 | 333403
                     6 | 69654
                     7 | 11837
                     8 | 1736
                     9 | 208
                    10 | 22
                    11 | 1
                    12 | 0
                    13 | 0
                    14 | 0
                    15 | 0
                    16 | 0
  more_than_max_bucket | 0
------------------------------------------------
Approximate arithmetic mean of 
the n of selections: 2.7182336
------------------------------------------------

=end
#--------------------------------------------------------------------------

# According to Dr. Alexander Flint's tweet at
#
#     https://twitter.com/neuroicudoc/status/924331454036811776
#     (archival copy: https://archive.fo/uVpVa )
#
# which I noticed due to the re-tweet of the Joanna Rutkowska
#
#     https://twitter.com/rootkovska/status/924541577686634496
#     (archival copy: https://archive.fo/ih4mB )
#
# it takes about e=2.71828...
# random number selections from the range of [0,1]
# till the sum of those selections is greater than 1.
#
# This Ruby class is created to check that claim.
class The_experiment

   def initialize
      @ht_histogram_of_the_number_of_selections_till_sum_is_greater_than_1=Hash.new
      @i_histogram_highest_numbered_bucket=16 # the lowest is 0
      (@i_histogram_highest_numbered_bucket+1).times do |i| # i==0 at first iteration
         # As the random numbers are chosen from range [0,1], which
         # includes 1, but the sum must be greater than 1, then
         # the histogram buckets with labels 0 and 1 are guaranteed to
         # have 0 entries. However, to keep this Ruby code simpler, the
         # 0 and 1 are added to the histogram. No off-by-1-s at the lower end.
         @ht_histogram_of_the_number_of_selections_till_sum_is_greater_than_1[i]=0
      end # loop
      @lc_s_more_than_max_bucket="more_than_max_bucket" # to avoid reinitialization of that string
      @ht_histogram_of_the_number_of_selections_till_sum_is_greater_than_1[@lc_s_more_than_max_bucket]=0
      @lc_linebreak="\n"
   end # initialize

   private


   # (b_failed_to_top_1, i_n)
   def b_i_n_of_selections_till_the_sum_of_elections_is_greater_than_1()
      b_failed_to_top_1=true
      i_n=0
      r_sum=0
      r_0=nil
      while((r_sum<1)&&(i_n<@i_histogram_highest_numbered_bucket)) do
         i_n+=1
         r_0=Random::rand().to_r
         r_sum+=r_0
      end # loop
      b_failed_to_top_1=false if (1<r_sum)
      return b_failed_to_top_1,i_n
   end # b_i_n_of_selections_till_the_sum_of_elections_is_greater_than_1


   def fd_approximate_arithmetic_mean_of_the_n_of_selections()
      ht_hist=@ht_histogram_of_the_number_of_selections_till_sum_is_greater_than_1
      i_numerator=0
      i_denominator=0
      (@i_histogram_highest_numbered_bucket+1).times do |i| # i==0 at first iteration
         i_column_label=i
         i_column_height=ht_hist[i]
         if i_column_height<0
            raise(Exception.new("GUID=='24071e27-e7b3-42df-b47d-034061d1a1e7'"))
         end # if
         i_denominator+=i_column_height
         i_numerator+=(i_column_height*i_column_label)
      end # loop
      r_0=Rational(i_numerator,i_denominator)
      fd_out=r_0.to_f
      return fd_out
   end # fd_approximate_arithmetic_mean_of_the_n_of_selections()

   def s_results_formatted()
      ht_hist=@ht_histogram_of_the_number_of_selections_till_sum_is_greater_than_1
      s_0="Histogram Column Label"
      s_1=" | "
      s_2="Histogram Column Height"
      lc_linebreak=@lc_linebreak
      #--------
      i_s_0_len=s_0.size
      #--------
      s_out=""+lc_linebreak
      s_out<<(s_0+s_1+s_2+lc_linebreak)
      s_out<<(("-"*s_0.size)+s_1+"-"*s_2.size+lc_linebreak)
      (@i_histogram_highest_numbered_bucket+1).times do |i| # i==0 at first iteration
         s_label=i.to_s
         i_height=ht_hist[i]
         s_height=i_height.to_s
         i_0=(i_s_0_len-s_label.size)
         if i_0<0
            raise(Exception.new("GUID=='e029292d-da7a-420b-b37d-034061d1a1e7'"))
         end # if
         s_out<<((" "*i_0)+s_label+s_1+s_height+lc_linebreak)
      end # loop
      #----------
      s_label=@lc_s_more_than_max_bucket
      s_height=ht_hist[@lc_s_more_than_max_bucket].to_s
      i_0=(i_s_0_len-s_label.size)
      if i_0<0
         raise(Exception.new("GUID=='927e335b-8858-4a6c-917d-034061d1a1e7'"))
      end # if
      s_out<<((" "*i_0)+s_label+s_1+s_height+lc_linebreak)
      #----------
      s_line=("-"*(s_0.size+s_1.size+s_2.size)+lc_linebreak)
      s_out<<s_line
      fd_0=fd_approximate_arithmetic_mean_of_the_n_of_selections()
      s_out<<("Approximate arithmetic mean of "+lc_linebreak)
      s_out<<("the n of selections: "+fd_0.to_s+lc_linebreak)
      s_out<<s_line
      s_out<<lc_linebreak
      return s_out
   end # s_results_formatted()


   public

   def run_experiment(i_n_of_selection_series=100)
      i_n_of_selection_series=ARGV[0].to_i if ARGV[0]!=nil
      if i_n_of_selection_series<1
         raise(Exception.new("GUID=='aa084b43-0da9-4f02-b57d-034061d1a1e7'"))
      end # if
      ht_hist=@ht_histogram_of_the_number_of_selections_till_sum_is_greater_than_1
      i_n_of_selection_series.times do
         b_failed_to_top_1,i_n=b_i_n_of_selections_till_the_sum_of_elections_is_greater_than_1()
         if i_n<2
            raise(Exception.new("GUID=='141f3f55-a941-4e20-956d-034061d1a1e7'"))
         end # if
         if b_failed_to_top_1
            ht_hist[@lc_s_more_than_max_bucket]+=1
         else
            ht_hist[i_n]+=1
         end # if
      end # loop
      puts s_results_formatted()
   end # run_experiment

end # class The_experiment

The_experiment.new.run_experiment()