Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.
The square of the sum of the first ten natural numbers is (1 + 2 + ... + 10)² = 55² = 3025.
The sum of the squares of the first ten natural numbers is 1² + 2² + ... + 10² = 385.
Hence the difference between the square of the sum of the first ten natural numbers and the sum of the squares of the first ten natural numbers is 3025 - 385 = 2640.
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:
To include color from the command line:
ruby -r minitest/pride difference_of_squares_test.rb
Problem 6 at Project Euler http://projecteuler.net/problem=6
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
require 'minitest/autorun' require_relative 'difference_of_squares' # Common test data version: 1.1.0 7a1108b class DifferenceOfSquaresTest < Minitest::Test def test_square_of_sum_1 # skip assert_equal 1, Squares.new(1).square_of_sum end def test_square_of_sum_5 skip assert_equal 225, Squares.new(5).square_of_sum end def test_square_of_sum_100 skip assert_equal 25_502_500, Squares.new(100).square_of_sum end def test_sum_of_squares_1 skip assert_equal 1, Squares.new(1).sum_of_squares end def test_sum_of_squares_5 skip assert_equal 55, Squares.new(5).sum_of_squares end def test_sum_of_squares_100 skip assert_equal 338_350, Squares.new(100).sum_of_squares end def test_difference_of_squares_1 skip assert_equal 0, Squares.new(1).difference end def test_difference_of_squares_5 skip assert_equal 170, Squares.new(5).difference end def test_difference_of_squares_100 skip assert_equal 25_164_150, Squares.new(100).difference 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 4, BookKeeping::VERSION end end
class Squares attr_reader :n def initialize(n) @n = n end def square_of_sums ((n + 1) * n / 2)**2 end def sum_of_squares n * (n + 1) * (2*n + 1) / 6 end def difference # Fun: # If you like you can factor out a term of sum to make this marginally # faster to compute: # n(n + 1) / 2 <- sum # n(n + 1)(2n + 1) / 6 <- sum_of_squares # n(n + 1)/2 * ((2n+1)/3) # sum * (2n + 1)/3 # ------------------------------------------------ # sum * sum - sum * (2n + 1)/3 = sum - (2n + 1)/3 <- difference square_of_sums - sum_of_squares end end
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.