FLOLAC-24-Tasks.hs

-- This exercise covers the first 6 and the 8th chapters of "Learn You a Haskell for Great Good!"

-- Chapter 1 - http://learnyouahaskell.com/introduction
-- Chapter 2 - http://learnyouahaskell.com/starting-out
-- Chapter 3 - http://learnyouahaskell.com/types-and-typeclasses
-- Chapter 4 - http://learnyouahaskell.com/syntax-in-functions
-- Chapter 5 - http://learnyouahaskell.com/recursion
-- Chapter 6 - http://learnyouahaskell.com/higher-order-functions
-- Chapter 8 - http://learnyouahaskell.com/making-our-own-types-and-typeclasses 

-- Download this file and then type ":l FLOLAC-24-Tasks.hs" in GHCi to load this exercise
-- Some of the definitions are left "undefined", you should replace them with your answers.

-- 0. Example: find the penultimate (second-to-last) element in list xs
penultimate xs = last (init xs)

-- 1. Find the antepenultimate (third-to-last) element in list xs
antepenultimate xs = undefined

-- 2. Left shift list xs by n
--    For example, "rotateLeft 2 [1, 2, 3]" should return "[3, 1, 2]"
rotateLeft n xs = undefined

-- 3. Insert element x in list xs at index k
--    For example, "insertElem 100 3 [0,0,0,0,0]" should return [0,0,0,100,0,0]
insertElem x k xs = undefined

-- 4. Determine whether a given list is a palindrome
--    For example, "palindrome []" or "palindrome [1, 3, 1]" should return "True"
palindrome :: Eq a => [a] -> Bool
palindrome xs = undefined

-- 5. Raise x to the power y using recursion
--    For example, "power 3 4" should return "81"
power :: Int -> Int -> Int
power x y = undefined

-- 6. Convert a list of booleans (big-endian) to a interger using recursion
--    For example, "convertBinaryDigit [True, False, False]" should return 4
convertBinaryDigit :: [Bool] -> Int
convertBinaryDigit bits = undefined

-- 7. Create a fibbonaci sequence of length N in reverse order
--    For example, "fib 5" should return "[3, 2, 1, 1, 0]"
fib :: Int -> [Int]
fib = undefined

-- 8. Map the first component of a pair with the given function
--    For example, "mapFirst (+3) (4, True)" should return "(7, True)"
mapFirst :: (a -> b) -> (a, c) -> (b, c)
mapFirst f pair = undefined

-- 9. Devise a function that has the following type
someFunction :: (a -> (b -> c) -> d) -> (b -> a -> c) -> a -> d
someFunction = undefined

-- Here we have a type for 10 Heavenly Stems ("天干"), 12 Earthly Branches ("地支"), and a pair type of them.
-- Try typeclass functions like "show" or "maxBound" on them
data Stems = Chia | Yi | Bing | Ding | Wu | Ji | Geng | Xin | Ren | Gui
         deriving (Eq, Ord, Show, Bounded, Enum)

data Branches = Zi | Chou | Yin | Mao | Chen | Si | Wu' | Wei | Shen | You | Shu | Hai
         deriving (Eq, Ord, Show, Bounded, Enum)

type StemsAndBranches = (Stems , Branches)

-- 10. Note that if you try "succ Gui" or "succ Hai", you should get an error, because "succ" is not defined on either "Gui" or "Hai"
--     Define "next" for "StemsAndBranches", which shift both the stem and the branch to the next one, and cycle to the first one if it meets the end.
--     For example, "next (Bing, Yin)" should be "(Ding, Mao)", and "next (Ding, Hai)" should be "(Wu, Zi)".
next :: StemsAndBranches -> StemsAndBranches
next (stem, branch) = undefined

-- 11. If you keep iterating with "next", you will be in a sexagenary cycle.
--     Only half of the pairs will be traversed (60 pairs in total.)
--     Determine whether a pair is in the cycle that starts from "(Chia, Zi)". Return "True" if the pair is in the cycle, otherwise return "False".
inCycle :: StemsAndBranches -> Bool
inCycle (stem, branch) = undefined

-- Here is an algebraic datatype representing trees.
-- Be careful, these trees are somehow different from those defined in the book!
-- Apparently our trees are better, they have leaves, and data is stored on leaves.
data Tree a = Leaf a | Node (Tree a) (Tree a)

-- 12. What is the map function as well as the Functor instance for this tree?
--     (You may want to lookup the Functor typeclass.)
instance Functor Tree where
  fmap = undefined

-- We say a tree is flattenable if it can be turned into a list
-- which contains all elements originally in the tree.
data List a = Nil | Cons a (List a)

-- We can define a typeclass to express that.
class Flattenable t where
  flatten :: t a -> List a

-- 13. Show that our Tree is flattenable:
instance Flattenable Tree where
  flatten = undefined

-- 14. Define a type of trees that have leaves and two kinds of nodes:
--     one with two branches and another with three branches.
--     Your tree should have three constructors.
--     You can choose where to store data (either on leaves, nodes, or both).
--
--   data TwoThreeTree = ...

-- 15. Show that the datatype you just defined is flattenable:
--
--   instance Flattenable TwoThreeTree where
--     flatten = ...