Project Euler Problem 9 in F#

In the continuing series of solving Project Euler problems with F#, here is problem 9 with my solution:

A Pythagorean triplet is a set of three natural numbers, a b c, for which,

a² + b² = c²
For example, 3² + 4² = 9 + 16 = 25 = 5².

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

1. Enumerate from 1 to 1000.  Create tuples of all sets (m, n) where m > n.
2. Create Pythagorean triplets using Euclid’s formula from the tuples.
3. Find the set where a + b + c = 1000.
4. Find the product of this set.

let problem9 =
    let pythagorean_triplets(m:int, n:int) =
        let a = m*m-n*n
        let b = 2*m*n
        let c = m*m+n*n
        [a;b;c]
    let tops = 1000
    [for m in [1..tops] do
        for n in [1..m-1] do yield (m, n)] |> Seq.map (fun t -> pythagorean_triplets((fst t, snd t)))
            |> Seq.filter (fun x -> x |> Seq.sum = tops) |> Seq.head |> Seq.fold (fun acc elem -> acc * elem) 1

Download the source code with unit tests.

Advertisement