data Tree = Empty | Node Integer Tree Tree
tree1 = Node 2 (Node 3 (Node 1 Empty Empty)
                       (Node 4 Empty Empty))
               (Node 1 Empty
                       (Node 5 Empty Empty))
{-  2
  3    1
 1 4    5-}

sumMaxPath :: Tree -> Integer
sumMaxPath Empty = 0
sumMaxPath (Node v l r) = v + max (sumMaxPath l)
                                  (sumMaxPath r)


type Point = (Double, Double)

dist :: Point -> Point -> Double
dist (x1,y1) (x2,y2) = sqrt $ (x1-x2)^2 + (y1-y2)^2

maxDistance :: [Point] -> Double
maxDistance points = maximum [ dist x y | x<-points, y<-points ]
--distances x points = map (`dist` x) points
--maxDistance points = maximum . concat $ map (\x -> (map (\y -> dist x y) points)) points

count :: (Eq a) => a -> [a] -> Int
count x l = length $ filter (==x) l

remove :: (Eq a) => a -> [a] -> [a]
remove x l = filter (/=x) l

removeDuplicates :: (Eq a) => [a] -> [a]
removeDuplicates [] = []
removeDuplicates (head:tail) = head : removeDuplicates (remove head tail)

histogram :: (Eq a) => [a] -> [(a,Int)]
histogram l = map (\x -> (x, count x l)) $ removeDuplicates l