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:
ruby difference_of_squares_test.rb
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
def initialize(how_many)
@how_many = how_many
end
def difference
square_of_sums - sum_of_squares
end
def square_of_sums
# n*(n+1)/2 is standard formula for sum(1..n)
(@how_many * (@how_many + 1) / 2) ** 2
end
def sum_of_squares
# from https://en.wikipedia.org/wiki/Square_pyramidal_number
(2 * @how_many**3 + 3 * @how_many**2 + @how_many) / 6
end
end
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Community comments
What drove me in the direction of using formulae for the square_of_sums and vice-versa was the performance geek in me. :-) This makes the performance constant-time rather than linear. That was actually the last thing I did after making all the tests pass. Up until then, it was driven by just making the tests pass....
I really like the formulae! Two thumbs up.
Thanks! I wasted a good bit of time trying to figure out the second formula, and then Googling it, before I finally realized that the term "square pyramidal number", which I had glossed over in the list of Google hits, perfectly described what I was after.