Project Euler - Problem #2

Description

Problem #2 is to find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed four million.

General Order

• calculate Fibonacci series up to 4MM
• filter list for evens
• sum filtered list

Solution (Improved)

The fundamental improvement is a updated Fibonacci series function, rewritten as a tail-recursion.

let rec fibsRec a b max arr =

    if a + b > max then

        arr

    else

        let current = a + b

        let newArr = List.append arr [current]

        fibsRec b current max newArr

let evenArray = (1::2::(fibsRec 1 2 4000000 [])) |> List.filter (fun x -> x % 2 = 0) |> List.sum

Solution (Original)

//fibonacci via recursion

let rec fibsRec a b max =

    if a + b < max then

        let current = a + b

        let rest = fibsRec b current max

        current :: rest

    else

        []

//generate list with 1, 2 and all other larger fibonaccis

let fibs = 1::2::(fibsRec 1 2 4000000)

//filter for even only

let evenArray = fibs |> List.filter (fun x -> x % 2 = 0)

//sum evens

let sumArray = List.sum evenArray