{-# LANGUAGE ParallelListComp #-}
import Text.Printf

addTwo :: Num a => a -> a
addTwo x = x + 2

threeParam :: Num a => a -> a -> a -> a
threeParam x y z = let w = x+y in w*z

myFirst :: (a,b) -> a
myFirst t = let (x,y)=t in x

okko :: [Int] -> [[Char]]
okko xs = [if x<10 then "OK" else "KO" | x <- xs]

addList :: [Int] -> [Int] -> [Int]
addList xs ys = [x+y | x <- xs, y <- ys]


length2 :: [a] -> Int
length2 xs = last [n | _ <- xs | n <- [2,4..]]

greaterTwo :: [Char] -> Bool
greaterTwo "one" = False
greaterTwo "two" = False
greaterTwo _ = True

divide :: Fractional a => Eq a => a -> a -> a
divide _ 0 = -9999
divide p q = p/q

myand :: Bool -> Bool -> Bool
myand False False = False
myand True False = True
myand False True = True
myand True True = False

myand2 :: Bool -> Bool -> Bool
myand2 False b = b
myand2 True b = not b

compVectOld :: (Double,Double) -> (Double,Double) -> Double
compVectOld u v = ((fst u) + (fst v)) * ((snd u) + (snd v))

compVect :: Real a => (a,a) -> (a,a) -> a
compVect (x,y) (w,z) = (x+y)*(w+z)

myFst :: (a,a,a) -> a
myFst (x,y,z) = x

mySnd :: (a,a,a) -> a
mySnd (x,y,z) = y

myThd :: (a,a,a) -> a
myThd (x,y,z) = z

listPat :: Num a => [(a,a,a)] -> [a]
listPat [] = []
listPat ((x,y,z):s) = (x+y*z):(listPat s)

myHead :: [a] -> a
myHead [] = error "The list is empty !"
myHead (x:_) = x

twoEq :: Eq a => [a] -> [a] -> Bool
twoEq (x:_) (y:_) = (x==y)
twoEq [] [] = True
twoEq _ _ = False

myLength :: PrintfType r => [a] -> r
myLength [] = printf "The list has no elements\n"
myLength [x] = printf "The list has one element\n"
myLength [x,y] = printf "The list has two elements\n"
myLength _ = printf "The list has more than two elements\n"

myLengthShow :: PrintfType r => Show a => [a] -> r
myLengthShow [] = printf "The list has no elements\n"
myLengthShow [x] = printf "The list has one element: %s\n" (show x)
myLengthShow [x,y] = printf "The list has two elements: %s and %s\n" (show x) (show y)
myLengthShow _ = printf "The list has more than two elements\n"


goodStudent :: Real a => a -> String
goodStudent m
    | m>12 = "You are a good student"
    | m>=10 = "You can be do what you want to do"
    | otherwise = "You are a bad student"


myMin :: Ord a => a -> a -> a
myMin a b
    | a<b = a
    | otherwise = b
    
maxVect :: Ord a => (a,a) -> (a,a) -> (a,a)
maxVect (x,y) (x',y')
    | x>=x' &&    y>=y' = (x,y)
    | x>=x' = (x,y')
    | y>=y' = (x',y)
    | otherwise = (x',y')

myMean :: Fractional a => Real a => a -> a -> String
myMean x y
    | (x+y)/2>12 = "You are a good student"
    | (x+y)/2>=10 = "You can be do what you want to do"
    | otherwise = "You are a bad student"

myMean2 :: Fractional a => Real a => a -> a -> String
myMean2 x y
    | moy>12 = "You are a good student"
    | moy>=10 = "You can be do what you want to do"
    | otherwise = "You are a bad student"
    where moy=(x+y)/2

myMean3 :: Fractional a => Real a => a -> a -> String
myMean3 x y
    | moy>=acceptable = "You are a good student"
    | moy>=pass = "You can be do what you want to do"
    | otherwise = "You are a bad student"
    where 
    moy=(x+y)/2
    pass=10
    acceptable=12


myMean4 :: Fractional a => Real a => a -> a -> String
myMean4 x y
    | moy>=acceptable = "You are a good student"
    | moy>=pass = "You can be do what you want to do"
    | otherwise = "You are a bad student"
    where (moy,pass,acceptable)=((x+y)/2,10,12)

whereList :: Show a => Show b => [a] -> [b] -> String
whereList l1 l2
    | length l1 > 1 && length l2 > 1 = show secondl1 ++ " " ++ show lastl2
    | length l1 <= 1  && length l2 <= 1 = "The lengths of l1 and l2 are too short"
    | length l1 <= 1 = "The length of l1 is too short"
    | length l2 <= 1 = "The length of l2 is too short"
    where 
    _:secondl1:_ = l1
    lastl2 = last l2
    
listMean :: [(Double,Double)] -> [Double]
listMean l = [moy x y | (x,y) <- l]
    where moy u v = (u+v)/2

listMeanlet :: [(Double,Double)] -> [Double]
listMeanlet l = [moy x y | d<-l, let (x,y) =d]
    where moy u v = (u+v)/2

listMeanlet2 :: [(Double,Double)] -> [Double]
listMeanlet2 l = [let (x,y) =d in moy x y | d<-l]
    where moy u v = (u+v)/2

listMeanlet3 :: [(Double,Double)] -> [Double]
listMeanlet3 l = [m| d<-l, let (x,y) =d, let m = moy x y, m>=12]
    where moy u v = (u+v)/2

modifStrings :: [[Char]] -> [[Char]]
modifStrings l = [ case s of {
        [] -> "null";
        [e] -> "indefini";
        [e,f] -> [e];
        _ -> [last s]
    } | s<-l]

allMin :: Ord a => [a] -> a
allMin [e] = e
allMin (e:s) = min e (allMin s)

fact :: Num a => Eq a => a -> a
fact 0 = 1
fact n = n*(fact (n-1))

replicate' :: (Num i, Ord i) => i -> a -> [a]
replicate' n x
    | n <= 0 = [ ]
    | otherwise = x : replicate' (n - 1) x

ssum :: Num a => [a] -> a
ssum [] = 0
ssum (e:s) = e+(ssum s)

ppea :: Ord a => a -> [a] -> [a]
ppea x [] = []
ppea x (e:s)
    | e<=x = e:(ppea x s)
    | otherwise = (ppea x s)
    
pgq :: Ord a => a -> [a] -> [a]
pgq x [] = []
pgq x (e:s)
    | e>x = e:(pgq x s) 
    | otherwise = (pgq x s)

triPivot :: Ord a => [a] -> [a]
triPivot [] = []
triPivot (x:s) = (triPivot (ppea x s)) ++ [x] ++ (triPivot (pgq x s))

apply3 :: (a -> a) -> a -> a
apply3 f x = f (f (f x))

applyN :: Int -> (a->a) -> a -> a
applyN 0 f x = x
applyN n f x = f (applyN (n-1) f x)

myMap :: (a -> b) -> [a] -> [b]
myMap f l = [f x | x <- l]

myMap2 :: (a->b)->[a]->[b]
myMap2 f [] = []
myMap2 f (e:s) = (f e):(myMap2 f s)

myFilter :: (a -> Bool) -> [a] -> [a]
myFilter f [] = []
myFilter f (e:s)
    | f e = e:(filter f s)
    | otherwise = filter f s

myZipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
myZipWith o l l' = map applicateur (zip l l')
    where applicateur (x,y) = o x y

minimum' :: [Float] -> Float
minimum' [e] = e
minimum' (e:s) = min e (minimum' s)

minimum'' :: [Float] -> Float
minimum'' (u:l) = go l u
    where go [] x = x
          go (e:s) x
              | e>x = go s x
              | otherwise = go s e


and' :: [Bool] -> Bool
and' [] = True
and' (e:s) = e && (and' s)

and'' :: [Bool] -> Bool
and'' l = go l True
    where go [] x = x
          go (e:s) x = go s (e && x)

reduce :: (t->t->t) -> [t] -> t
reduce f [e] = e
reduce f (e:s) = f e (reduce f s)

reduce' :: (t->t->t) -> [t] -> t
reduce' f (e:s) = go s e
    where go [] x = x
          go (h:t) x = go t (f h x)

rminimum l = reduce' min l
rand l = reduce' (&&) l

reduceTotal :: (t->t->t) -> t -> [t] -> t
reduceTotal f x0 [] = x0
reduceTotal f x0 (e:s) = f e (reduceTotal f x0 s)

reduceTotal' :: (t->t->t) -> t -> [t] -> t
reduceTotal' f x0 l = go l x0
    where go [] x = x
          go (h:t) x = go t (f h x)


    
data Vector = Vec3 Float Float Float

magnitude :: Vector -> Float
magnitude (Vec3 a b c) = sqrt (a*a+b*b+c*c)

data Arbre t = Noeud t (Arbre t) (Arbre t) | Feuille

arbreSomme :: Num t => Arbre t -> t
arbreSomme Feuille = 0
arbreSomme (Noeud v a b) = v + (arbreSomme a) + (arbreSomme b)

headSafe :: [t] -> Maybe t
headSafe [] = Nothing
headSafe (e:s) = Just e