import Data.List

gcd' a b = if a == b 
  then a 
  else if a > b 
      then gcd' (a-b) b 
      else gcd' a (b-a)
fib n = if n < 1 then 1
        else fib (n-1) + fib (n-2)

fib' n = f n 0 1 
        where   f 0 a b = b
                f n a b = f (n-1) b (a+b)
fibs = fib' `map` [0..]

lfibs =  filter (\a -> mod a 2 == 1) fibs

quicksort [] = []
quicksort (h:tail) = let smaller = quicksort $filter (<h) tail
                         bigger = quicksort $filter (>=h) tail
                     in
                         smaller ++ [h] ++ bigger

mergesort l = let
                  ll = map (\a -> [a]) l
                  merge :: Ord a => [a] -> [a] -> [a]
                  merge [] [] = []
                  merge [] x = x
                  merge x [] = x
                  merge xx@(x:xs) yy@(y:ys) = 
                        if x < y then x:(merge xs yy)
                        else y:(merge xx ys)
                  glue [] = []
                  glue [a] = [a]
                  glue (x:y:s) = merge x y:glue s
                  ms [] = []
                  ms [a] = a
                  ms a = ms(glue a) 
               in
                  ms ll
secti l = foldr (+) 0 l

fact 0 = 1
fact n = n * fact (n-1)

fact' n = product [1..n]




--cv8

rozdily s = zipWith (-) s (tail s)
fs = [(+1), (*2), (* 10)]

tails' s = take (length s) $ map ($ s) (map drop [0..])

rle s = 
  let g = group s
  in zip (map head g) (map length g)

lookup' e (x:xs) = let (x1,x2) = x in 
  if e==x1 then Just x2
  else lookup' e xs
lookup' _ [] = Nothing

fib'' = 0:1: zipWith (+) fib'' (tail fib'')

primes = 2:3: filter isPrime [4..]
  where isPrime n = all (/= 0) $ map (mod n) $takeWhile (\i -> i * i <= n) primes

  
data Complex = C Int Int deriving Show

cMult:: Complex -> Complex -> Complex
cMult (C ax ay) (C bx by) = C (ax*bx-ay*by) ( ay*bx + ax*by) 

data Tree a = Nil | Branch (Tree a) a (Tree a) deriving Show

tInsert value Nil = Branch Nil value Nil
tInsert value (Branch lt v rt) = if value > v then Branch lt v (tInsert value rt)
                                            else Branch (tInsert value lt) v rt
											
tFind value Nil = False
tFind value (Branch lt v rt) = 
    if value == v then True 
    else if value < v then tFind value lt 
	     else tFind value rt
		 
treeToList Nil = []
treeToList (Branch lt v rt) = treeToList lt++[v]++treeToList rt