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Published at Jun 12 2020
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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.

You are not expected to discover an efficient solution to this yourself from first principles; research is allowed, indeed, encouraged. Finding the best algorithm for the problem is a key skill in software engineering.

If you don't know how to run Vader tests, see: Tests.

For general information about the Vim script track, see: Help.

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.

```
"
" Version: 1.2.0
"
Execute (square of sum 1):
let number = 1
let expected = 1
AssertEqual expected, SquareOfSum(number)
Execute (square of sum 5):
let number = 5
let expected = 225
AssertEqual expected, SquareOfSum(number)
Execute (square of sum 100):
let number = 100
let expected = 25502500
AssertEqual expected, SquareOfSum(number)
Execute (sum of squares 1):
let number = 1
let expected = 1
AssertEqual expected, SumOfSquares(number)
Execute (sum of squares 5):
let number = 5
let expected = 55
AssertEqual expected, SumOfSquares(number)
Execute (sum of squares 100):
let number = 100
let expected = 338350
AssertEqual expected, SumOfSquares(number)
Execute (difference of squares 1):
let number = 1
let expected = 0
AssertEqual expected, DifferenceOfSquares(number)
Execute (difference of squares 5):
let number = 5
let expected = 170
AssertEqual expected, DifferenceOfSquares(number)
Execute (difference of squares 100):
let number = 100
let expected = 25164150
AssertEqual expected, DifferenceOfSquares(number)
```

```
"
" Find the difference between the square of the sum and the sum of the squares
" of the first N natural numbers.
"
" Examples:
"
" :echo SquareOfSum(3)
" 36
" :echo SumOfSquares(3)
" 14
" :echo DifferenceOfSquares(3)
" 22
"
function! DifferenceOfSquares(number) abort
return abs(SquareOfSum(a:number) - SumOfSquares(a:number))
endfunction
function! SquareOfSum(number) abort
let n = a:number
let sum = n * (n + 1) / 2
return sum * sum
" Alternatively:
" return float2nr(pow((n * (n + 1) / 2), 2))
endfunction
function! SumOfSquares(number) abort
let n = a:number
return n * (n + 1) * (2 * n + 1) / 6
endfunction
```

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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