Divide amount equally using pairwise equalization

balancing.rb

#!/usr/bin/env ruby

# balancing.rb : Divide amount equally using pairwise equalization
#  by takehikom

class Balancing
  def initialize(n_, rep_ = 5)
    @n = n_
    @rep = rep_

    @zero = Rational(0, 1)
    @one = Rational(1, 1)
    @minus = Rational(-1, 1)
    @average = Rational(1, @n)

    @cups = [@zero] * @n
    @cups[0] = @one
  end

  def to_s
    emax = error
    lines = []
    @cups.each_with_index do |cup, i|
      lines << "#{diff(cup) == emax ? '*' : ' '}[#{i + 1}] #{cup} = #{cup.to_f}"
    end
    lines << "error: #{emax} = #{emax.to_f}"
    lines.join("\n")
  end

  def equalize(i, j)
    sum = @cups[i] + @cups[j]
    avg = sum / 2
    @cups[i] = @cups[j] = avg
  end

  def diff(cup)
    (cup < @average) ? (@average - cup) : (cup - @average)
  end

  def error
    pos = 0
    emax = @zero

    @cups.each_with_index {|cup, i|
      e = diff(cup)
      if emax < e
        pos = i
        emax = e
      end
    }

    emax
  end

  def balanced?
    error == 0
  end

  def find_min_and_max
    pos_min = pos_max = -1
    min = @one
    max = @minus

    @cups.each_with_index {|cup, i|
      if cup < min
        pos_min = i
        min = cup
      end
      if max < cup
        pos_max = i
        max = cup
      end
    }

    raise if pos_min == -1
    raise if pos_max == -1
    raise if min >= max

    [pos_min, pos_max]
  end

  def start
    puts "==== Step 0 ===="
    puts to_s

    @rep.times do |trial|
      i, j = find_min_and_max
      equalize(i, j)
      puts "==== Step #{trial + 1} ===="
      puts to_s

      if balanced?
        puts "==== End of operation ===="
        break
      end
    end
  end
end

if __FILE__ == $0
  n = (ARGV.shift || 3).to_i
  rep = (ARGV.shift || 5).to_i
  Balancing.new(n, rep).start
end