「HaskellでProject Euler(Problem 7～9)」ブログ用

euler7-1.hs

main = print $ prime 10001

prime :: Integral a => Int -> a
prime 1 = 2
prime n = head $ prime' 3 []
  where
    prime' m list | length list >= (n-1) = list
                  | isPrime list         = prime' (m + 2) (m:list)
                  | otherwise            = prime' (m + 2) list
                    where isPrime = all (\x -> m `mod` x /= 0) . dropWhile (\x -> x ^ 2 > m)

euler7-2.hs

main = print $ prime 10001

prime :: Integral a => Int -> a
prime n = head $ prime' 3 [2] []
  where
    prime' m list list' | length list >= n = list
                        | isPrime list'    = prime' (m + 2) (m:list) (list'++[m])
                        | otherwise        = prime' (m + 2) list list'
                          where isPrime = all (\x -> m `mod` x /= 0) . takeWhile (\x -> x ^ 2 <= m)

euler7-3.hs

main = print $ prime 10001

prime :: Integral a => Int -> a
prime 1 = 2
prime n = prime' 3 [] (n - 1) -- (n - 1) から 0 までデクリメントするカウンタ。最初に -1 しているのは、2番目の素数である3からはじめるため。 
  where
    prime' m list cnt | cnt' <= 0 = m
                      | otherwise = prime' (m + 2) list' cnt'
                        where
                          (cnt', list') | isPrime list = (cnt - 1, list ++ [m])
                                        | otherwise    = (cnt, list)
                          isPrime = all (\x -> m `mod` x /= 0) . takeWhile (\x -> x ^ 2 <= m)

euler8.hs

main = print $ maxProduct number 5

maxProduct :: (Show a, Num b, Ord b, Read b) => a -> Int -> b
maxProduct n digit = maxProduct' (show n) 0
  where
    maxProduct' numStr@(_:rest) maxNum
      | (length numStr) < digit = maxNum
      | any (== '0') num        = maxProduct' rest maxNum
      | otherwise               = maxProduct' rest $ max currentNum maxNum
        where
          currentNum = product $ map (\x -> (read [x])) num
          num = take digit numStr

number = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450

euler9-1.hs

main = print $ pythagorean 1000

pythagorean :: (Enum a, Eq a, Num a) => a -> a
pythagorean n = pythagorean' $ [(a, b, 1000 - a - b) | a <- [1..(n-3)], b <- [2..(n-2)]]
  where
    pythagorean' []             = 0
    pythagorean' ((a, b, c):xs)
      | (a^2) + (b^2) == c^2    = a * b * c
      | otherwise               = pythagorean' xs

euler9-2.hs

main = print $ pythagorean 1000

pythagorean :: (Enum a, Eq a, Num a) => a -> a
pythagorean n =
  let (a, b, c) = head $ [(a, b, c) | a <- [1..(n-3)], b <- [2..(n-2)], c <- [1000 - a - b], a^2 + b^2 == c^2]
  in a * b * c