「HaskellでProject Euler(Problem 55～57)」ブログ用

euler55.hs

main = print $ length $ filter isLychrel [1..9999]

isLychrel :: Integer -> Bool
isLychrel = not . any isPalindrome . take 49 . tail . iterate addReverseNum

addReverseNum :: (Show a, Read a, Num a) => a -> a
addReverseNum n = n + reverseNum n
  where reverseNum = read . reverse . show

isPalindrome :: Show a => a -> Bool
isPalindrome n = let s = show n in s == reverse s

euler56.hs

import Data.Char (digitToInt)
 
main = print $ maximum [digitSum a b | a <- [1..100], b <- [1..100]]

digitSum :: (Show a, Num a, Integral b) => a -> b -> Int
digitSum n m = sum $ map digitToInt $ show $ n ^ m

euler57-1.hs

import Data.Ratio ((%), denominator, numerator, Ratio)

limit = 1000

main = print $ length $ filter (\n -> size (numerator n) > size (denominator n)) $ take limit $ sqrt2
  where size = length . show

sqrt2 :: [Ratio Integer]
sqrt2 = map (1 +) $ iterate (\n -> reciprocal (2 + n)) (1 % 2)

reciprocal :: Integral a => Ratio a -> Ratio a
reciprocal n = denominator n % numerator n

euler57-2.hs

import Data.Function (on)
import Data.Ratio ((%), denominator, numerator, Ratio)

limit = 1000

main = (print . length . filter (\n -> (numerator n) `exceed` (denominator n)) . take limit) sqrt2
  where exceed = (>) `on` size
          where size = length . show

sqrt2 :: [Ratio Integer]
sqrt2 = iterate (\n -> 1 + 1 / (1 + n)) (3 % 2)