angelikatyborska's solution to Nth Prime on the Ruby track

Instructions

Test suite

Solution

Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

Given a number n, determine what the nth prime is.

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

If your language provides methods in the standard library to deal with prime numbers, pretend they don't exist and implement them yourself.

For installation and learning resources, refer to the exercism help page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

gem install minitest

If you would like color output, you can require 'minitest/pride' in the test file, or note the alternative instruction, below, for running the test file.

Run the tests from the exercise directory using the following command:

ruby nth_prime_test.rb

To include color from the command line:

ruby -r minitest/pride nth_prime_test.rb

Source

A variation on Problem 7 at Project Euler http://projecteuler.net/problem=7

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

nth_prime_test.rb

require 'minitest/autorun'
require_relative 'nth_prime'

# Common test data version: 1.0.0 016d65b
class NthPrimeTest < Minitest::Test
  def test_first_prime
    # skip
    assert_equal 2, Prime.nth(1)
  end

  def test_second_prime
    skip
    assert_equal 3, Prime.nth(2)
  end

  def test_sixth_prime
    skip
    assert_equal 13, Prime.nth(6)
  end

  def test_big_prime
    skip
    assert_equal 104743, Prime.nth(10001)
  end

  def test_there_is_no_zeroth_prime
    skip
    assert_raises(ArgumentError) { Prime.nth(0) }
  end

  # Problems in exercism evolve over time, as we find better ways to ask
  # questions.
  # The version number refers to the version of the problem you solved,
  # not your solution.
  #
  # Define a constant named VERSION inside of the top level BookKeeping
  # module, which may be placed near the end of your file.
  #
  # In your file, it will look like this:
  #
  # module BookKeeping
  #   VERSION = 1 # Where the version number matches the one in the test.
  # end
  #
  # If you are curious, read more about constants on RubyDoc:
  # http://ruby-doc.org/docs/ruby-doc-bundle/UsersGuide/rg/constants.html

  def test_bookkeeping
    skip
    assert_equal 1, BookKeeping::VERSION
  end
end

class Prime
  def self.nth(n)
    if n < 1 || !(n.is_a? Integer)
      raise ArgumentError.new "#{n}:#{n.class} is not a positive integer"
    end

    primes = sieve(nth_prime_upper_bound(n))
    primes[n - 1]
  end

  private

  def self.nth_prime_upper_bound(n)
    return nth_prime_upper_bound(6) if n < 6

    (n * Math.log(n * Math.log(n))).ceil
  end

  # the sieve of Eratosthenes
  def self.sieve(n)
    sieve = Array.new(n + 1, true)

    exclude_zero_and_one!(sieve)
    exclude_composite_numbers!(sieve)

    primes = sieve.map.with_index { |prime, integer| integer if prime }
    primes.compact
  end

  def self.exclude_zero_and_one!(sieve)
    sieve[0] = false
    sieve[1] = false
  end

  def self.exclude_composite_numbers!(sieve)
    upper_bound = Math.sqrt(sieve.length).ceil

    (2..upper_bound).to_a.each do |integer|
      exclude_multiples!(sieve, integer) if sieve[integer]
    end
  end

  def self.exclude_multiples!(sieve, n)
    multiple = n**2

    while multiple < sieve.length
      sieve[multiple] = false
      multiple += n
    end
  end
end

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angelikatyborska's solution

to Nth Prime in the Ruby Track