Ryan Glass Ryan Glass - 1 month ago 22
Ruby Question

Harmonic series in ruby

I am trying to write a program that calculates a Harmonic series from a whole number. Such as 5 and calculates it until it reaches that argument.

So essentially it looks like:

h1: 1 / 1
h2: 3 / 2
h3: 11 / 6
h4: 25 / 12
h5: 137 / 60

This is what I have.

my question is, is there a formula that will calculate a harmonic series in ruby?

class Fraction

attr_accessor :numerator, :denominator

def initialize(n, d)
@numerator = n
@denominator = d
end

def +(rhs)
n = @numerator*rhs.denominator + @denominator*rhs.numerator
d = @denominator*rhs.denominator
n, d = reduce(n, d)
return Fraction.new(n, d)
end

def print
puts "#{@numerator} / #{@denominator}"
end

def reduce(n, d)
r = gcd(n, d)
return n / r, d / r
end

def gcd(a, b)
if a % b == 0
return b
else
return gcd(b, a % b)
end
end
private :reduce, :gcd
end

Answer

The harmonic series isn't implemented in Ruby standard library, but Rational is :

def harmonic_sum(n)
  (1..n).inject(Rational(0,1)) {|r, i| r + Rational(1,i) }
end

puts harmonic_sum(5)
#=> 137/60
puts harmonic_sum(50)
#=> 13943237577224054960759/3099044504245996706400
puts harmonic_sum(10_000).to_f
#=> 9.787606036044382

NOTE: Your code is fine BTW. Here are some slight modifications and a few TODOS ;)

class Fraction
  attr_reader :numerator, :denominator

  def initialize(n, d)
    @numerator = n
    @denominator = d
  end

  def to_f
    numerator.to_f/denominator
  end

  #TODO: Add *
  #TODO: Define - and / with + and *
  #TODO: Check that rhs is a Fraction, convert self to float otherwise.

  def +(rhs)
    n = @numerator*rhs.denominator + @denominator*rhs.numerator
    d = @denominator*rhs.denominator
    n, d = reduce(n, d)
    return Fraction.new(n, d)
  end

  def to_s
    "#{@numerator} / #{@denominator}"
  end

  private

  def reduce(n, d)
    r = gcd(n, d)
    return n / r, d / r
  end

  def gcd(a, b)
    if a % b == 0
      return b
    else
      return gcd(b, a % b)
    end
  end
end

def harmonic_sum(n)
  (1..n).inject(Fraction.new(0,1)) {|r, i| r + Fraction.new(1,i) }
end

puts harmonic_sum(100)
#=> 14466636279520351160221518043104131447711 / 2788815009188499086581352357412492142272