{-
 Haskell exercises from Fall 2016
-}

-- 10 points, should be the same as a function with different name on cheat sheet
-- exercise 1
myElem:: Eq a => a -> [a] -> Bool
myElem _ [] = False
myElem anItem (x:xs) = 
       if anItem == x then True
       else myElem anItem xs
 
-- 15 points
-- can also do this with recursion and a cons operator :
-- exercise 2
myReplicate:: Int -> a -> [a]
myReplicate n anItem = [anItem | i <- [1..n]] 

-- 20 points
-- can use a loop for this, too
-- if they use `div` instead of fromIntegral, that's okay
-- exercise 3
halve:: [a] -> ([a],[a])
halve [] = ([],[])
halve aList = (take firstHalf aList, drop firstHalf aList)
  where firstHalf = ceiling (fromIntegral (length aList)/2)

-- 15 points
-- the predicate a<b is optional, but nice
-- can also use loops and brute force, but that's not so nice
-- exercise 4
pyths:: Int -> [(Int,Int,Int)]
pyths n = [(a,b,c) | a <- [1..n], b <- [1..n], c <- [1..n],
      a<b, a^2 + b^2 == c^2]

-- 20 points
-- exercise 5
-- merge
-- the list@(x:xs) notation is quite useful
merge:: Ord a => [a] -> [a] -> [a]
merge aList [] = aList
merge [] aList = aList
merge aList@(a:as) bList@(b:bs) =
  if a < b then
    [a] ++ merge as bList
  else [b] ++ merge aList bs

-- exercise 6
-- 20 points
-- next time, I will teach fromIntegral
-- mergesort
msort:: Ord a => [a] -> [a]
msort aList = 
      if length aList <= 1 then aList
      else merge (msort (take n aList)) (msort (drop n aList))
        where	   
    	  n = ceiling (fromIntegral (length aList)/2)

-- having a demonstration function like this is optional
-- but I found it convenient
main = do
  putStrLn "Haskell Exercises for CMSC 331, Fall 2016"

  putStrLn "Exercise 1 myElem"
  putStrLn (show(myElem 2 [1,2,3]))
  putStrLn "should be True"
  putStrLn (show(myElem 4 [1,2,3]))
  putStrLn "should be False"

  putStrLn "Exercise 2 myReplicate"
  putStrLn (show(myReplicate 3 "tsk"))

  putStrLn "Exercise 3 halve"
  putStrLn (show(halve [31,41,5,9,26]))

  putStrLn "Exercise 4 Pythagorean Triples"
  putStrLn (show(pyths 20))

  putStrLn "Exercise 5 Merge two lists"
  putStrLn (show(merge [1,3,5] [2,4,6,8]))
  putStrLn "that should be sorted"

  putStrLn "Exercise 6 Mergesort"
  putStrLn (show(msort [31,41,5,9,26]))

  putStrLn "That's all"