「HaskellでProject Euler(Problem 46～48)」ブログ用

euler46.hs

import Data.List (find)
import Data.Maybe (fromJust, isJust)
import Zaneli.Euler (primesLimitNum)

main = print $ fromJust $ find (not . isGoldbachConjecture) oddComposites

oddComposites :: [Integer]
oddComposites = filter isComposite [3,5..]
  where
    -- これだけでは 0 や 1 も True と判定されるが、今回3から始めると分かっているのでそれ以前の値は考慮しない
    isComposite n = n /= (head $ primesLimitNum n)

isGoldbachConjecture :: Integral a => a -> Bool
isGoldbachConjecture n = isJust $ find (\m -> n == m) [f x y | x <- primesLimitNum (n-2), y <- [halfSqrt n, (halfSqrt n)-1 .. 1]]
  where
    f n m = truncate $ (fromIntegral n) + 2 * (fromIntegral m) ** 2
    halfSqrt n = truncate $ sqrt $ fromIntegral $ n`div`2

euler47.hs

import Data.List (find, unfoldr)
import Data.Maybe (fromJust)
import Zaneli.Euler (primeFactors)

main = print $ head $ fromJust $ distinctPrimesFactors 4

distinctPrimesFactors :: Integral a => Int -> Maybe [a]
distinctPrimesFactors n = find (all (\m -> (length $ primeFactors m) >= n)) $ consecutives n

consecutives :: (Enum a, Num a) => Int -> [[a]]
consecutives n = unfoldr (\ns -> Just (take n ns, tail ns)) [1..]

euler48-1.hs

import Zaneli.Euler (listToNum, numToList)

main = print $ sumOfSelfPowers [1..1000]

limit :: Int
limit = 10

sumOfSelfPowers :: [Int] -> Int
sumOfSelfPowers ns = foldl (\acc n -> drop' $ acc + selfPower n) 0 ns

selfPower :: Int -> Int
selfPower n = foldl (\acc n -> drop' $ acc * n) 1 $ replicate n n

drop' :: Int -> Int
drop' n | (length n') <= limit = n
        | otherwise            = listToNum $ drop (length n' - limit) n'
          where n' = numToList n

euler48-2.hs

main = print $ drop' $ sum $ map selfPower [1..1000]

selfPower :: Int -> Int
selfPower n = iterate (drop' . (* n)) 1 !! n

drop' :: Integral a => a -> a
drop' n = n `mod` 10 ^ limit
  where limit = 10