Project Euler in F#, Problems 1 and 2

I recently stumbled across the Project Euler website. From wikipedia: “Project Euler (named after Leonhard Euler) is a website dedicated to a series of computational problems intended to be solved with computer programs”.

I thought this would be a good opportunity to continue working with F# and have some material for writing more blog articles.

Problem 1 is very straight forward.

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

I went with the most logical algorithm I could think of.

1. Enumerate though each of the numbers 1-999.
2. Filter the values that are multiples of either 3 or 5.
3. Add up the resulting values.

The resulting F# code is quite elegant:

let problem1 = 
    [1..999] |> Seq.filter (fun i -> i % 3 = 0 || i % 5 = 0) |> Seq.sum

After looking at other algorithms people had used, there are more efficient methods using summations. But not bad for my first solution. On to problem 2…

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Again, there is a pretty obvious solution here.

1. Generate the Fibonacci sequence up to 4 million.
2. Filter the values that are even.
3. Add up the resulting values.

The resulting F# code:

let Problem2 =
    Seq.unfold (fun state ->
        if (snd state > 4000000) then None
        else Some(fst state + snd state, (snd state, fst state + snd state))) (1,1)
            |> Seq.filter (fun x -> x % 2 = 0) |> Seq.sum

Again, a more efficient solution can be found but this is at least semantically easy to follow.

I’m planning on continuing this series of blog articles with a problem or 2 for each entry, and seeing how many of the problems I can get through.  I’ll also provide the source code.   If you’re interested in more in this series stay tuned!

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