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pfertyk's solution

to Difference Of Squares in the Python Track

Published at Jul 13 2018 · 1 comment
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.

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.

Exception messages

Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.

To raise a message with an exception, just write it as an argument to the exception type. For example, instead of raise Exception, you should write:

raise Exception("Meaningful message indicating the source of the error")

Running the tests

To run the tests, run the appropriate command below (why they are different):

  • Python 2.7: py.test difference_of_squares_test.py
  • Python 3.4+: pytest difference_of_squares_test.py

Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version): python -m pytest difference_of_squares_test.py

Common pytest options

  • -v : enable verbose output
  • -x : stop running tests on first failure
  • --ff : run failures from previous test before running other test cases

For other options, see python -m pytest -h

Submitting Exercises

Note that, when trying to submit an exercise, make sure the solution is in the $EXERCISM_WORKSPACE/python/difference-of-squares directory.

You can find your Exercism workspace by running exercism debug and looking for the line that starts with Workspace.

For more detailed information about running tests, code style and linting, please see the help page.

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.py

import unittest

from difference_of_squares import difference, square_of_sum, sum_of_squares


# Tests adapted from `problem-specifications//canonical-data.json` @ v1.2.0

class DifferenceOfSquaresTest(unittest.TestCase):
    def test_square_of_sum_1(self):
        self.assertEqual(square_of_sum(1), 1)

    def test_square_of_sum_5(self):
        self.assertEqual(square_of_sum(5), 225)

    def test_square_of_sum_100(self):
        self.assertEqual(square_of_sum(100), 25502500)

    def test_sum_of_squares_1(self):
        self.assertEqual(sum_of_squares(1), 1)

    def test_sum_of_squares_5(self):
        self.assertEqual(sum_of_squares(5), 55)

    def test_sum_of_squares_100(self):
        self.assertEqual(sum_of_squares(100), 338350)

    def test_difference_of_squares_1(self):
        self.assertEqual(difference(1), 0)

    def test_difference_of_squares_5(self):
        self.assertEqual(difference(5), 170)

    def test_difference_of_squares_100(self):
        self.assertEqual(difference(100), 25164150)


if __name__ == '__main__':
    unittest.main()
def difference(n):
    return square_of_sum(n) - sum_of_squares(n)


def square_of_sum(n):
    return (n*(n+1)/2)**2


def sum_of_squares(n):
    return n*(n+1)*(2*n+1)/6

Community comments

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Avatar of behrtam

I agree that the first version was a little bit more self-explanatory than the formula based one. But performance and memory wise it really makes a difference.

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