[ProjectEuler.net] 14

n按照下面的規則產生的序列：

n  n/2 (n is even)
n  3n + 1 (n is odd)

比如13：

13  40  20  10  5  16  8  4  2  1 求在100萬以下的數中，哪個數產出的序列最長。產出的序列中會包含很多以前計算過的，所以要緩衝起來，以下使用了字典。要注意的是當一個數很大的時候，如果是奇數，那麼下一個數可能會超出類型的最大值。所以以下F#就用int64了其實下面代碼是haskell直接轉型過來的，唉，haskell怎麼寫才快起來呢..

let isEven (n:int64) =
    n % 2L = 0L

let next n=
match isEven n with
    | true -> n/2L
    | false -> 3L*n+1L


open System.Collections.Generic 

let dict =new Dictionary<int64 ,int64 list>()

let rec gen (n:int64)=
if n =1L then [1L]
    elif dict.ContainsKey n then dict.[n]
else 
let x =gen<| next n in
        dict.Add(n,n::x)
        n::x

let mapToLen xs =
    List.map (fun x-> 
let xs = gen x 
match xs with
                    | h:: t->(h, List.length xs)) xs

List.maxBy (fun (v,l)->l) <| mapToLen [1L..1000000L]           

  --haskell

import qualified Data.Map as Map

longlength ::[a] -> Integer
longlength =fromIntegral . length

isEven :: Integer -> Bool
isEven x
  | x `mod`2 == 0 = True
  | otherwise     =False

next :: Integer -> Integer
next n
  | isEven n =n `div` 2
  | otherwise =3*n+1
tree =Map.empty
--使用Map緩衝
gen' :: Integer ->Map.Map Integer [Integer] -> ([Integer],Map.Map Integer [Integer])
gen' 1 t =([1],t)
gen' n t =
  case Map.lookup n t of
    Just v -> (v,t)
    Nothing ->(ret,Map.insert n ret t')
    where (nxts,t') =gen' (next n) t
          ret =n:nxts

mapToLen:: [Integer]->Map.Map Integer [Integer]->[Integer]
mapToLen [] t =[]  
mapToLen (x:xs) t =
let (lst,t')=gen' x t in
  (longlength lst):mapToLen xs t'
--Ghci中 maximum $ rang 1 1000000
range a b =
  mapToLen [a.. b] tree