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Published at Jul 13 2018
·
1 comment

Instructions

Test suite

Solution

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)Â² = 55Â² = 3025.

The sum of the squares of the first ten natural numbers is 1Â² + 2Â² + ... + 10Â² = 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.

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")
```

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`

`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`

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.

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.

```
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
```

A huge amount can be learned from reading other peopleâ€™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.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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## Community comments

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.