Project Euler - Problem 26

Description

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

• 1/2 = 0.5
• 1/3 = 0.(3)
• 1/4 = 0.25
• 1/5 = 0.2
• 1/6 = 0.1(6)
• 1/7 = 0.(142857)
• 1/8 = 0.125
• 1/9 = 0.(1)
• 1/10 = 0.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

Solution

let rec remainders (num:int) (rem:int) (arr:list) =
    let filteredList = arr |> List.filter (fun x -> x = num)
    if filteredList.Length > 1 || num = 0 then
        arr.Length - 1
    elif (num*10) < rem then
        remainders (num*10) rem arr
    else
        let newRem = (num*10) % rem
        let newArr = List.append arr [newRem]
        remainders newRem rem newArr

let testRemainders =
    let results = [1..999] |> List.map (fun x -> remainders 1 x [])
    let max = List.max results
    let idx = results |> List.findIndex (fun x -> x = max)
    (idx+1, max)