FLOLAC-22-Tasks.hs

import Data.List (sortBy)
-- 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-22-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 = last $ init $ init xs

-- 2. Left shift list xs by 1
--    For example, "shiftLeft [1, 2, 3]" should return "[2, 3, 1]"
shiftLeft xs = tail xs ++ [head xs]

-- 3. Left shift list xs by n
--    For example, "rotateLeft 2 [1, 2, 3]" should return "[3, 1, 2]"
rotateLeft 0 xs = xs
rotateLeft n xs = rotateLeft (n-1) (shiftLeft xs)

-- 4. 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 = (take k xs) ++ x:(drop k xs)

-- Here we have a type for the 7 days of the week
-- Try typeclass functions like "show" or "maxBound" on them
data Day = Mon | Tue | Wed | Thu | Fri | Sat | Sun
         deriving (Eq, Ord, Show, Bounded, Enum)   

-- 5. Note that if you try "succ Sun", you should get an error, because "succ" is not defined on "Sun"
--    Define "next", which is like "succ", but returns "Mon" on "next Sun"
next :: Day -> Day
next Sun = Mon
next day = succ day

-- 6. Return "True" on weekend
isWeekend :: Day -> Bool
isWeekend day = day > Fri

data Task = Work | Shop | Play deriving (Eq, Show)

-- You are given a schedule, which is a list of pairs of Tasks and Days
schedule :: [(Task, Day)]
schedule = [(Shop, Fri), (Work, Tue), (Play, Mon), (Play, Fri)]

-- 7. However, the schedule is a mess
--    Sort the schedule by Day, and return only a list of Tasks. 
--    If there are many Tasks in a Day, you should keep its original ordering
--    For example, "sortTask schedule" should return "[(Play, Mon), (Work, Tue), (Shop, Fri), (Play, Fri)]"
sortTask :: [(Task, Day)] -> [(Task, Day)]
sortTask xs = sortBy (\(_, d1) (_, d2) -> d1 `compare` d2) xs

-- 8. This function converts days to names, like "show", but a bit fancier
--    For example, "nameOfDay Mon" should return "Monday"
nameOfDay :: Day -> String
nameOfDay Mon = "Monday"
nameOfDay Tue = "Tuesday"
nameOfDay Wed = "Wednesday"
nameOfDay Thu = "Thursday"
nameOfDay Fri = "Friday"
nameOfDay Sat = "Saturday"
nameOfDay Sun = "Sunday"

-- 9. You shouldn't be working on the weekends
--     Return "False" if the Task is "Work" and the Day is "Sat" or "Sun"
labourCheck :: Task -> Day -> Bool
labourCheck Work day = not (isWeekend day)
labourCheck _    _   = True

-- 10. Raise x to the power y using recursion
--     For example, "power 3 4" should return "81"
power :: Int -> Int -> Int
power _ 0 = 1
power x y = x * (power x (y - 1))

-- 11. 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 (x:[]) = fromEnum x
convertBinaryDigit bits = fromEnum (last bits) + 2 * (convertBinaryDigit (init bits))

-- 12. 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 1 = [0]
fib 2 = [1, 0]
fib n = (sum (take 2 previous)):(previous) where previous = fib (n - 1)

-- 13. 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 (x:[])  = True
palindrome (x:y:[]) = x == y
palindrome xs = (head xs) == (last xs) && (palindrome (init (tail xs)))

-- 14. 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 = (f (fst pair), snd pair)

-- 15. Devise a function that has the following type
someFunction :: (a -> b -> c) -> (a -> b) -> a -> c
someFunction r f x = r x (f x)

-- 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) deriving (Show)

-- 16. 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 f (Leaf a) = Leaf (f a)
  fmap f (Node a b) = Node (fmap f a) (fmap f b)

-- 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) deriving Show

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

-- 17. Show that our Tree is flattenable:
instance Flattenable Tree where
  flatten (Leaf a) = Cons a Nil
  flatten (Node (Leaf a) b) = Cons a (flatten b)
  flatten (Node (Node a b) c) = flatten (Node a (Node b c))

-- 18. 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 a = TLeaf a |
  TNode2 (TwoThreeTree a) (TwoThreeTree a) |
  TNode3 (TwoThreeTree a) (TwoThreeTree a) (TwoThreeTree a)
  deriving (Show)

-- 19. Show that the datatype you just defined is flattenable:
--
instance Flattenable TwoThreeTree where
  flatten (TLeaf a)  = Cons a Nil
  flatten (TNode3 a b c) = flatten (TNode2 a (TNode2 b c))
  flatten (TNode2 (TLeaf a) b) = Cons a (flatten b)
  flatten (TNode2 (TNode2 a b) c) = flatten (TNode2 a (TNode2 b c))
  flatten (TNode2 (TNode3 a b c) d) = flatten (TNode2 a (TNode3 b c d))