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caterwall's solution

to Difference Of Squares in the Ruby Track

Published at Jul 13 2018 · 4 comments
Instructions
Test suite
Solution

Note:

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

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

Source

Problem 6 at Project Euler http://projecteuler.net/problem=6

Submitting Incomplete Solutions

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

difference_of_squares_test.rb

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(number)
    @number = number
  end

  def square_of_sums
    sum = 0
    (0..@number).each do |num|
      sum += num
    end
    sum * sum
  end

  def sum_of_squares
    sum = 0
    (0..@number).each do |num|
      temp = num * num
      sum += temp
    end
    sum
  end

  def difference
    self.square_of_sums - self.sum_of_squares
  end


end

Community comments

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Avatar of orangejulius

Whenever you have a loop that is modifying a variable in each iteration of the loop, consider a functional programming approach. It will usually result in less code setting up and returning variables, which makes the code that actually does the intersting stuff stand out more.

Any time you are taking every element of an array and want to produce another array with modified variables, you can use map. And any time you have an array and want to use each value in the array to construct a single result at the end, you want reduce.

Also, you can almost always call methods on an object from other methods on that object without self

Avatar of caterwall
Solution Author (Anonymous Mode)
commented about 4 years ago

Thanks for commenting!

When you mention functional programming, are you suggesting that I create a method for iterating over the the arrays, and calling that method within #square_of_sums and #sum_of_squares?

Thanks for the nitpick, this is so helpful!

Avatar of orangejulius

You don't have to create a method, but you could if you wanted. Ruby's block syntax is helpful, and you're already using it correctly with .each :)

To explain the difference, let's imagine you have a short array of integers, and you want to create a new array with all those integers incremented by one. You might do it like this: def add_one_to_array(old_array) new_array = []

old_array.each do |element| new_array<< element+1 end new_array end

That will work just fine. And because you've probably written tons of loops just like that one, it feels intuitive. But I would argue you can make the code much clearer, while doing the same thing, and reducing the chance of bugs sneaking in. Here's how: def add_one_to_array(old_array) old_array.map do |element| element + 1 end end

When you call .each on an Enumerable (the module that handles all sorts of stuff regarding working with arrays and other collections), all .each does is do whatever is in the block (everything inside the do...end in each method is a block) you passed it. thats why the block code in the first example has to actually do the heavy lifting of pushing data into the new_array variable.

The .map method on Enumerable does a bit more for you: it uses the return value of the block you pass to it, and collects all the return values from running the block with each element, turning that into a new array. You don't have to bother creating a variable and assigning it into an empty array, explitly updating the array, or even returning the array (because the return value of .map is the array that results).

It also tells everyone reading the code something very important: the code that follows takes some code and uses it to transform one array into another. With .each, it could do anything, so you have to carefully read the code to ensure it doesn't do something weird.

There's a whole bunch of helpful methods defined on Enumerable, and the docs are quite helpful. They all do different things, but the idea is similar: they all work on a collection of some sort, and each one can be thought of as a single, specialized, powerful tool. Go read through them and fool around with a couple.

Avatar of caterwall
Solution Author (Anonymous Mode)
commented about 4 years ago

Right, makes perfect sense. Thanks you for your input!

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