「HaskellでProject Euler(Problem 28～30)」ブログ用

euler28-1.hs

main = print $ 1 + addDiags [2..1001*1001] 0 1 0

addDiags :: (Num a, Num b, Eq b) => [a] -> a -> Int -> b -> a
addDiags [] sum _ _          =  sum
addDiags list sum step count = let (n:ns) = drop step' list in
                               addDiags ns (sum + n) step' count'
  where
    (step', count') | count == 4 = (step + 2, 1)
                    | otherwise  = (step, count + 1)

euler28-2.hs

main = print $ sumDiags 1001

sumDiags :: (Enum a, Eq a, Num a) => a -> a
sumDiags n = sum $ map sumDiag [1,3..n]

sumDiag :: (Enum a, Eq a, Num a) => a -> a
sumDiag 1 = 1
sumDiag n = let list = [((n-2)^2+1)..n^2] in sumDiag' ((length list `div` 4) - 1) list []
  where
    sumDiag' n xs result
      | length xs > n = let (y:ys) = drop n xs in
                        sumDiag' n ys $ y:result
      | otherwise = sum result

euler28-3.hs

main = print $ sumDiags 1001
 
sumDiags :: (Enum a, Num a) => a -> a
sumDiags n = 1 + sum [4*m^2-6*(m-1) | m <- [3,5..n]]

euler29.hs

import Data.List (nub, sort)

main = print $ length $ nub $ sort [a^b | a <- [2..100], b <- [2..100]]

euler30.hs

import Data.Char (digitToInt)
import Data.List (find)

main = print $ answer 5

answer :: Integral a => a -> Int
answer n = sum $ filter (\n -> n == f n) [2..limit n]
  where f = sum . map ((^n) . digitToInt) . show

limit :: Integral a => a -> Int
limit x = maybe 0 f $ find (\n -> f n < fill 9 n) [1..]
  where f n = (n * (9 ^ x))

fill :: Num a => a -> Int -> a
fill n c = foldl1 (\a b -> a * 10 + b) $ take c $ repeat n