pe008.ml

open Core.Std

let number = "73167176531330624919225119674426574742355349194934\
96983520312774506326239578318016984801869478851843\
85861560789112949495459501737958331952853208805511\
12540698747158523863050715693290963295227443043557\
66896648950445244523161731856403098711121722383113\
62229893423380308135336276614282806444486645238749\
30358907296290491560440772390713810515859307960866\
70172427121883998797908792274921901699720888093776\
65727333001053367881220235421809751254540594752243\
52584907711670556013604839586446706324415722155397\
53697817977846174064955149290862569321978468622482\
83972241375657056057490261407972968652414535100474\
82166370484403199890008895243450658541227588666881\
16427171479924442928230863465674813919123162824586\
17866458359124566529476545682848912883142607690042\
24219022671055626321111109370544217506941658960408\
07198403850962455444362981230987879927244284909188\
84580156166097919133875499200524063689912560717606\
05886116467109405077541002256983155200055935729725\
71636269561882670428252483600823257530420752963450"

let chr_to_digit c = (Char.to_int c) - (Char.to_int '0')

module Rolling_product : sig
    type t

    val create : unit -> t
    val add : t -> int -> t
    val remove : t -> int -> t
    val get : t -> int
end = struct
    type t = (int * int)

    let create () = (1, 0)

    let add (prod, nr0) = function
        | 0 -> (prod, nr0 + 1)
        | n -> (prod * n, nr0)

    let remove (prod, nr0) = function
        | 0 -> (prod, nr0 - 1)
        | n -> (prod / n, nr0)

    let get (prod, nr0) =
        match nr0 with
        | 0 -> prod
        | _ -> 0
end

let max_product range =
    String.foldi number
        ~init:(0, Rolling_product.create ())
        ~f:(fun i (max, cur) chr ->
            let nxt = Rolling_product.add cur (chr_to_digit chr) in
            if i < range then
                if i = range - 1 then
                    (Rolling_product.get nxt, nxt)
                else
                    (0, nxt)
            else
                let nxt = Rolling_product.remove nxt
                    (String.get number (i - range) |> chr_to_digit) in
                let nxt_val = Rolling_product.get nxt in
                let nxt_max = if nxt_val > max then nxt_val else max in
                (nxt_max, nxt))
    |> (fun (max, _cur) -> max)

let () = Printf.printf "%d\n" (max_product 13)