Published at Jun 18 2019
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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)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.

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.

Refer to the Installing Elm page for information about installing elm.

The first time you start an exercise, you'll need to ensure you have the appropriate dependencies installed. Thankfully, Elm makes that easy for you and will install dependencies when you try to run tests or build the code.

Execute the tests with:

```
$ elm-test
```

Automatically run tests again when you save changes:

```
$ elm-test --watch
```

As you work your way through the test suite, be sure to remove the `skip <|`

calls from each test until you get them all passing!

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

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

```
module Tests exposing (tests)
import DifferenceOfSquares exposing (difference, squareOfSum, sumOfSquares)
import Expect
import Test exposing (..)
tests : Test
tests =
describe "DifferenceOfSquares"
[ describe "square the sum of the numbers up to the given number"
[ test "square of sum 5" <|
\() -> Expect.equal 225 (squareOfSum 5)
, skip <|
test "square of sum 10" <|
\() -> Expect.equal 3025 (squareOfSum 10)
, skip <|
test "square of sum 100" <|
\() -> Expect.equal 25502500 (squareOfSum 100)
]
, describe "sum the squares of the numbers up to the given number"
[ skip <|
test "sum of squares 5" <|
\() -> Expect.equal 55 (sumOfSquares 5)
, skip <|
test "sum of squares 10" <|
\() -> Expect.equal 385 (sumOfSquares 10)
, skip <|
test "sum of squares 100" <|
\() -> Expect.equal 338350 (sumOfSquares 100)
]
, describe "subtract sum of squares from square of sums"
[ skip <|
test "difference of squares 0" <|
\() -> Expect.equal 0 (difference 0)
, skip <|
test "difference of squares 5" <|
\() -> Expect.equal 170 (difference 5)
, skip <|
test "difference of squares 10" <|
\() -> Expect.equal 2640 (difference 10)
, skip <|
test "difference of squares 100" <|
\() -> Expect.equal 25164150 (difference 100)
]
]
```

```
module DifferenceOfSquares exposing (difference, squareOfSum, sumOfSquares)
squareOfSum : Int -> Int
squareOfSum n =
List.range 1 n
|> List.sum
|> square
sumOfSquares : Int -> Int
sumOfSquares n =
List.range 1 n
|> List.foldl addSquare 0
difference : Int -> Int
difference n =
squareOfSum n - sumOfSquares n
-- PRIVATE
addSquare : Int -> Int -> Int
addSquare n acc =
acc + square n
square : Int -> Int
square n =
n ^ 2
```

A huge amount can be learned from reading other people’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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