euler.hs

-- Project Euler in Haskell --
--   by cloudhead           --

-- "there's some real nasty code in here"

import Char

-- Some useful functions
--
prime :: Integer -> Bool
prime n = if null [ x | x <- [2..(ceiling $ sqrt (fromInteger n))], n `mod` x == 0 ]
          then True
          else False

factorial :: (Integral a) => a -> a
factorial 0 = 1
factorial n = n * factorial (n - 1)
--

euler1 :: Int
euler1 = sum [ x | x <- [0 .. 999], mod x 3 == 0 || mod x 5 == 0 ]

euler2 :: Int
euler2 = sum [ x | x <- (take 40 fib), (mod x 2) == 0, x < 4000000 ]
  where fib = 0 : 1 : zipWith (+) fib (tail fib)

euler3 :: Integer -> Integer
euler3 x = head [ y | y <- [r, r - 1 .. 2], x `mod` y == 0, prime y ]
  where r = ceiling $ sqrt (fromInteger x)    

euler4 :: Integer
euler4 = maximum [ x * y
                 | x <- [1..999]
                 , y <- [x..999] 
                 , palindromic (x * y)
                 ] where
                     palindromic x = (show x) == reverse (show x)

euler5 :: Integer
euler5 = f 1
  where f 20 = 20
        f x  = lcm x (f (x + 1))
        
euler6 :: Integer
euler6 = sum [ x | x <- [1..100] ] ^ 2 - sum [ x ^ 2 | x <- [1..100] ]

euler7 :: Integer
euler7 = last $ take 10001 [ x | x <- [1..], prime x ]

euler8 :: Integer
euler8 = maximum [ product (digitize xs) | xs <- take5 number ]
  where take5 :: String -> [String]
        take5 xs
          | length xs <= 5 = [xs]
          | otherwise      = take 5 xs : take5 (tail xs)
        digitize :: String -> [Integer]
        digitize xs = [ toInteger (digitToInt x) | x <- xs ]
        number = "7316717653133062" -- actual number is *way* longer