haskell_exam, Haskell

haskell_exam

-- 1.(a)
f a b = sum [x | (x, y) <- zip a b, x `mod` y == 0]

-- 1.(b)
g [] _ = 0
g _ [] = 0
g [x] [y] = if x `mod` y == 0 then x else 0
g (x:xs) (y:ys) = g [x] [y] + g xs ys

-- 2.(a)
p a 
    | intList == [] = 0
    | otherwise = maximum intList
    where intList = [read [x] :: Int | x <- a, x `elem` "0123456789"]

-- 2.(b)
q [] = 0
q [x] = if x `elem` "0123456789" then read[x] :: Int else 0
q (x:xs) = max (q [x]) (q xs)

-- 2.(c)
r a
    | intList == [] = 0
    | otherwise = maximum intList
    where intList = [read [x] :: Int | x <- filter (`elem` "0123456789") a]
    
-- 3.(a)
data Move =
    Go Int -- move the given distance in the current direction
    | Turn -- reverse direction
    | Dance -- dance in place, without changing direction
    deriving (Show,Eq)
    
data Command =
    Nil -- do nothing
    | Command :#: Move -- do a command followed by a move
    deriving (Show,Eq)
    
type Position = Int
data Direction = L | R deriving (Show,Eq)
type State = (Position, Direction)

--isFacingLeft L = True
--isFacingLeft R = False
reverseDirection L = R
reverseDirection R = L

state :: Move -> State -> State
state (Go x) (p, d) = if d == L then (p - x, L) else (p + x, R)
state Turn (p, d) = (p, reverseDirection d)
state Dance s = s

-- 3.(b)
trace :: Command -> State -> [State]
trace Nil s = [s]
trace (c :#: m) s = t ++ [state m (last t)]
    where t = trace c s

-- 3.(c)
visited :: State -> [State] -> Bool
visited (p, _) ss = p `elem` (map fst ss)

dancify :: Command -> Command
dancify Nil = Nil
dancify (c :#: Dance) = (dancify c) :#: Dance
dancify (c :#: m) 
    | visited (state m (last t)) t = (dancify c) :#: m :#: Dance
    | otherwise = (dancify c) :#: m
    where t = trace c (0,R)

main = print $ dancify (Nil :#: Go 3 :#: Turn :#: Go 2 :#: Go 1 :#: Turn :#: Go 4)


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