max_plus.rb

row = [ 5, 6, 3, 7, 4, 6, 3, 8 ]

def max_plus(row)
  return row unless row.length > 1

  row = get_maximums_and_differences row

  split_row = get_halves row
  # transform first half
  split_row[0] = max_plus(split_row[0])
  power = Math::log(row.length, 2) - 1
  # multiply second half with sqrt(2) in power
  split_row[1] = multiply_with_sqrt_of_two(split_row[1], power)

  return split_row.flatten
end

def get_halves(row)
  return row.each_slice( (row.size/2.0).round ).to_a
end

def get_maximums_and_differences(row)

  maximums    = []
  differences = []

  row.each_slice 2 do |pair|
    maximums.push(pair.max)
    differences.push(pair.first - pair.last)
  end

  return maximums + differences
end

def multiply_with_sqrt_of_two(row, power)
  sqrt_two_in_power = Math::sqrt(2) ** power
  return row.map { |number| (number * sqrt_two_in_power).round }
end

row = max_plus(row)

puts row.to_s