The Problem

The sum of the squares of the first ten natural numbers is,

1² + 2² + … + 10² = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + … + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

F# Solution

I used to hate writing sequence-based algorithms in C#. Everything always just seemed so clunky. Then LINQ came along and make it much nicer.

Since sequences are first-class citizens in F#, it makes working with them very easy.

To solve this problem, we first need a function to produce the sum of the squares of the elements in a sequence.

let sumOfSquares nums =
    nums
    |> Seq.map (fun n -> n * n)
    |> Seq.sum

We use Seq.map to transform each element into its square, and then Seq.sum to get the sum.

Contrast that with this:

public static int SumOfSquares(IEnumerable<int> nums)
{
    var sum = 0;
    foreach (var n in nums)
    {
        sum += (n*n);
    }
    return sum;
}

or this:

public static int SumOfSquares(IEnumerable<int> nums)
{
    return nums.Sum(n => (n*n));
}

Both C# functions get the job done, but the F# code reads much better to me.

Next, we need a function to produce the square of the sum of a sequence of numbers.

let squareOfSum nums =
    nums
    |> Seq.sum
    |> fun n -> n * n

And finally, put those functions together to get the answer:

(seq { 1..100 } |> squareOfSum) - (seq { 1..100 } |> sumOfSquares)