add recursion

Author: EpsilonX

README.md

@@ -6,6 +6,7 @@ By <b>Jeffrey Liu</b>
 Contents
 ---
 1. [Basic Typeclass](#title1)
+2. [Elegent of Haskell](#title2)
 
 ### <a name="title1"></a> Basic Typeclass
 ----
@@ -41,3 +42,24 @@ Contents
   * Use **fromIntegral** to parse Integral to Num, ```fromIntegral (length [1,2,3,4]) + 3.2```
 9. Floating
   * Types in this class: Float, Double
+
+<br />
+
+
+### <a name="title2"></a> Elegant of Haskell
+----
+1. Fibonacci
+```haskell
+fibs :: [Integer]
+fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
+```
+
+2. QuickSort
+```haskell
+quicksort :: (Ord a) => [a] -> [a]
+quicksort []     = []
+quicksort (x:xs) =
+    let smallerSorted = quicksort [a | a <- xs , a <= x]
+        biggerSorted = quicksort [a | a <- xs, a > x]
+    in smallerSorted ++ [x] ++ biggerSorted
+```

recursion.hs

@@ -0,0 +1,46 @@
+maximum' :: (Ord a) => [a] -> a
+maximum' [] = error "maximum of empty list"
+maximum' [x] = x
+maximum' (x:xs) = max x (maximum' xs)
+{-    | x > maxTail = x
+    | otherwise = maxTail
+    where maxTail = maximum' xs -}
+
+replicate' :: (Num i, Ord i) => i -> a -> [a]
+replicate' i a
+    | i <= 0    = []
+    | otherwise = a:replicate' (i-1) a 
+
+take' :: (Num i, Ord i) => i -> [a] -> [a]
+take' n _
+    | n <= 0   = []
+take' _ []     = []
+take' n (x:xs) = x : take' (n-1) xs
+
+reverse' :: [a] -> [a]
+reverse' [] = []
+reverse' (x:xs) = reverse' xs ++ [x]
+
+repeat' :: a -> [a]
+repeat' x = x : repeat' x
+
+zip' :: [a] -> [a] -> [(a,a)]
+zip' _ [] = []
+zip' [] _ = []
+zip' (x:xs) (y:ys) = (x,y) : zip' xs ys
+
+elem' :: (Eq a) => a -> [a] -> Bool
+elem' a []     = False
+elem' a (x:xs) = if (a == x) then True
+                 else elem' a xs
+{- elem' a (x:xs)
+    | a == x    = True
+    | otherwise = a `elem'` xs -}
+
+-- Classic QuickSort!
+quicksort :: (Ord a) => [a] -> [a]
+quicksort []     = []
+quicksort (x:xs) =
+    let smallerSorted = quicksort [a | a <- xs , a <= x]
+        biggerSorted = quicksort [a | a <- xs, a > x]
+    in smallerSorted ++ [x] ++ biggerSorted