-- 4. cvičení

{- Akumulacni funkce na seznamech -}
foldr_my :: (a -> b -> b) -> b -> [a] -> b
foldr_my f last []     = last
foldr_my f last (x:xs) = x `f` (foldr_my f last xs)

foldl_my :: (a -> b -> a) -> a -> [b] -> a
foldl_my f accum []     = accum
foldl_my f accum (x:xs) = foldl_my f (accum `f` x) xs

length_2 :: [a] -> Integer
length_2 xs = foldr_my (\y ys_len -> 1 + ys_len) 0 xs
length_3 :: [a] -> Integer
length_3 xs = foldl_my (\acc _ -> acc + 1) 0 xs

foldr1_my :: (a -> a -> a) -> [a] -> a
foldr1_my f []     = error "foldr1_my: empty list"
foldr1_my f (x:[]) = x
foldr1_my f (x:xs) = x `f` foldr1_my f xs

foldl1_my :: (a -> a -> a) -> [a] -> a
foldl1_my f []     = error "foldl1_my: empty list"
foldl1_my f (x:xs) = foldl_my f x xs

sum_2 :: [Integer] -> Integer
sum_2 xs = foldr (+) 0 xs

-- vyzkoušejte si tyto příklady:
-- https://www.fi.muni.cz/~xukrop/ib015/excercise_listfold.html

{- pomoci akumulačních funkcí:
 - length, sum, product, minimum, maximum, min-max,
 - id_list, reverse, map, filter -}
{-
product :: [Integer] -> Integer
minimum, maximum :: [Integer] -> Integer
minmax :: [Integer] -> (Integer, Integer)
id_list :: [a] -> [a]
reverse :: [a] -> [a] -- pomocí foldl
map :: (a -> b) -> [a] -> [b]  -- pomocí foldr
filter :: (a -> Bool) -> [a] -> [a] -- pomocí foldr
-}

length_1 :: [a] -> Integer
length_1 []     = 0
length_1 (x:xs) = 1 + length_1 xs

length_my_l :: [a] -> Integer
length_my_l xs = foldl_my (\acc x -> acc + 1) 0 xs

sum_1 :: [Integer] -> Integer
sum_1 []     = 0
sum_1 (x:xs) = x + sum_1 xs

-- length_my_l [1,2] ~> foldl_my (\acc x -> acc + 1) 0 [1,2] ~>     foldl_my (\acc x -> acc + 1) ( (\acc x -> acc + 1) 0 1) [2] ~> foldl_my (\acc x -> acc + 1) 1 [2] ~> foldl_my (\acc x -> acc + 1) ( (\acc x -> acc + 1) 1 2) [] ~> foldl_my (\acc x -> acc + 1) 2 [] ~> 2

{- pomoci akumulačních funkcí:
 - length, sum, product, minimum, maximum, min-max,
 - id_list, reverse, map, filter -}

data Teleso
    = Kvadr Double Double Double  -- a,b,c
    | Valec Double Double         -- r,v
    | Kuzel Double Double         -- r,v
    | Koule Double                -- r
    deriving ( Show )

-- objem, povrch