Published at Feb 25 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.

To run the tests run the command `go test`

from within the exercise directory.

If the test suite contains benchmarks, you can run these with the `--bench`

and `--benchmem`

flags:

```
go test -v --bench . --benchmem
```

Keep in mind that each reviewer will run benchmarks on a different machine, with different specs, so the results from these benchmark tests may vary.

For more detailed information about the Go track, including how to get help if you're having trouble, please visit the exercism.io Go language 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.

```
package diffsquares
import "testing"
var tests = []struct{ n, sqOfSum, sumOfSq int }{
{5, 225, 55},
{10, 3025, 385},
{100, 25502500, 338350},
}
func TestSquareOfSum(t *testing.T) {
for _, test := range tests {
if s := SquareOfSum(test.n); s != test.sqOfSum {
t.Fatalf("SquareOfSum(%d) = %d, want %d", test.n, s, test.sqOfSum)
}
}
}
func TestSumOfSquares(t *testing.T) {
for _, test := range tests {
if s := SumOfSquares(test.n); s != test.sumOfSq {
t.Fatalf("SumOfSquares(%d) = %d, want %d", test.n, s, test.sumOfSq)
}
}
}
func TestDifference(t *testing.T) {
for _, test := range tests {
want := test.sqOfSum - test.sumOfSq
if s := Difference(test.n); s != want {
t.Fatalf("Difference(%d) = %d, want %d", test.n, s, want)
}
}
}
// Benchmark functions on just a single number (100, from the original PE problem)
// to avoid overhead of iterating over tests.
func BenchmarkSquareOfSum(b *testing.B) {
for i := 0; i < b.N; i++ {
SquareOfSum(100)
}
}
func BenchmarkSumOfSquares(b *testing.B) {
for i := 0; i < b.N; i++ {
SumOfSquares(100)
}
}
func BenchmarkDifference(b *testing.B) {
for i := 0; i < b.N; i++ {
Difference(100)
}
}
```

```
package diffsquares
// SquareOfSum returns the square of the sum of the first n natural numbers (https://brilliant.org/wiki/sum-of-n-n2-or-n3/)
func SquareOfSum(n int) int {
sum := n * (n + 1) / 2
return sum * sum
}
// SumOfSquares returns the sum of the squares of the first n natural numbers (https://brilliant.org/wiki/sum-of-n-n2-or-n3/)
func SumOfSquares(n int) int {
return n * (n + 1) * (2*n + 1) / 6
}
// Difference returns the difference between the square of the sum of the first n natural numbers and the sum of the squares of the first n natural numbers
func Difference(n int) int {
return SquareOfSum(n) - SumOfSquares(n)
}
```

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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