Project Euler Problem 001

import Control.Arrow
import Control.Monad
import Control.Applicative
import Data.Function

-- 5パターンの解
divs x = x `rem` 3 ==0 || x `rem` 5 == 0
ans0 = sum $ filter divs [1..999]
ans1 :: Integer
ans1 = sum $ filter (((`rem`3)&&&(`rem`5))>>>(join(***)(==0))>>>(liftA2(||)fst snd)) [1..999]
ans2 :: Integer
ans2 = sum $ filter( ((||)<$>((==0).(`rem`3)))<*>((==0).(`rem`5)))[1..999]

-- 包摂原理(inclusion-exclusion principle)の利用
-- http://en.wikipedia.org/wiki/Project_Euler
-- n未満ではなく、n以下で考えたほうが-1とかないのでわかりやすい
sumk :: Integral a => a -> a -> a
sumk n k= sum [k*i|i<-[1..(n`quot`k)]]
sumk' :: Integral a => a -> a -> a
sumk' n k = k*(d*(d+1))`quot`2 where d = n`quot`k
ans3 :: Integer
ans3 = (sk 3) + (sk 5) - (sk 15) where sk = sumk 999 -- O(N)
ans4 :: Integer
ans4 = (sk 3) + (sk 5) - (sk 15) where sk = sumk' 999 -- O(1)

--233168
main = print ans1