olivernn

require 'enumerator'

class Coefficient
  
  def initialize(term, index, highest_power)
    @term = term
    @index = index
    @highest_power = highest_power
  end
  
  def to_s
    multiplier.to_s + exponent.to_s unless @term == 0 # if the term is 0 then there should be no coefficient
  end
  
  private
  
  def multiplier
    if @term == -1
      "-" # the coefficient should be -x^a rather than -1x^a
    elsif @term == 1
      "+" unless first_term? # because we don't need a leading +
    elsif @term < -1
      @term.to_s # the negative sign will aready be there for us
    elsif @term > 1
      "+" + @term.to_s
    end
  end
  
  def exponent
    if power == 1
      "x" # because x^1 is just x
    elsif power != 0
      "x^" + power.to_s
    end
  end
  
  def first_term?
    @index == 0
  end
  
  def power
    @highest_power - @index
  end
end

class Polynomial
  
  def initialize(terms)
    @terms = terms
    enough_terms?
    
    @highest_power = (terms.size - 1)
    @coefficients = coefficients.delete_if {|x| x.nil?}
  end
  
  def to_s
    if @coefficients.size == 0
      "0"
    else
      @coefficients.join
    end
  end
  
  private  
  
  def coefficients
    @terms.enum_with_index.map do |term, index|
      Coefficient.new(term, index, @highest_power).to_s
    end
  end
  
  def enough_terms?
    raise ArgumentError, "Need at least 2 coefficients" if @terms.size < 2
  end
end