implemented exercises upto capitalize

exercises/Set3a.hs

@@ -28,8 +28,10 @@ import Data.List
 --  maxBy head   [1,2,3] [4,5]  ==>  [4,5]
 
 maxBy :: (a -> Int) -> a -> a -> a
-maxBy measure a b = todo
-
+maxBy measure a b = if a_val > b_val then a else b
+    where
+        a_val = measure a
+        b_val = measure b
 ------------------------------------------------------------------------------
 -- Ex 2: implement the function mapMaybe that takes a function and a
 -- Maybe value. If the value is Nothing, it returns Nothing. If it is
@@ -40,7 +42,8 @@ maxBy measure a b = todo
 --   mapMaybe length (Just "abc") ==> Just 3
 
 mapMaybe :: (a -> b) -> Maybe a -> Maybe b
-mapMaybe f x = todo
+mapMaybe f Nothing = Nothing
+mapMaybe f (Just x) = Just (f x)
 
 ------------------------------------------------------------------------------
 -- Ex 3: implement the function mapMaybe2 that works like mapMaybe
@@ -54,7 +57,8 @@ mapMaybe f x = todo
 --   mapMaybe2 div (Just 6) Nothing   ==>  Nothing
 
 mapMaybe2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c
-mapMaybe2 f x y = todo
+mapMaybe2 f (Just x) (Just y) = Just (f x y)
+mapMaybe2 _ _ _ = Nothing
 
 ------------------------------------------------------------------------------
 -- Ex 4: define the functions firstHalf and palindrome so that
@@ -76,9 +80,13 @@ mapMaybe2 f x y = todo
 palindromeHalfs :: [String] -> [String]
 palindromeHalfs xs = map firstHalf (filter palindrome xs)
 
-firstHalf = todo
-
-palindrome = todo
+firstHalf :: String -> String
+firstHalf x = take (halfLength x) x
+    where
+        halfLength x = (length x) `div` 2 + ((length x) `mod` 2)
+    
+palindrome :: String -> Bool
+palindrome x = (reverse x) == x
 
 ------------------------------------------------------------------------------
 -- Ex 5: Implement a function capitalize that takes in a string and
@@ -96,7 +104,9 @@ palindrome = todo
 --   capitalize "goodbye cruel world" ==> "Goodbye Cruel World"
 
 capitalize :: String -> String
-capitalize = todo
+capitalize xs = unwords (map capitalizeWord (words xs))
+    where
+        capitalizeWord (x:xs) = toUpper x : xs
 
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 -- Ex 6: powers k max should return all the powers of k that are less