Sumlen.hs

module Sumlen where

sumList :: (Num a) => [a] -> a
sumList = foldr (+) 0

lenList :: (Num b) => [a] -> b
lenList = foldr (\_ y->y+1) 0

sumlenList :: (Num a, Num b) => [a] -> (a,b)
sumlenList = foldr (\x (y,z)->(x+y,z+1)) (0,0)

averageList :: (Fractional a) => [a] -> a
averageList xs = y / z
  where (y,z) = sumlenList xs


data Tree a = Leaf a | Fork (Tree a) (Tree a) deriving Show

foldTree :: (a -> b) -> (b -> b -> b) -> Tree a -> b
foldTree f _ (Leaf x)     = f x
foldTree f g (Fork xt yt) = g (foldTree f g xt) (foldTree f g yt)

sumTree :: (Num a) => Tree a -> a
sumTree = foldTree id (+)

lenTree :: (Num b) => Tree a -> b
lenTree = foldTree (\_->1) (+)

sumlenTree :: (Num a, Num b) => Tree a -> (a,b)
sumlenTree = foldTree (\x -> (x,1)) (\(x0,y0) (x1,y1)->(x0+x1,y0+y1))

averageTree :: (Fractional a) => Tree a -> a
averageTree xs = y / z
  where (y,z) = sumlenTree xs

xt :: (Num a) => Tree a
xt = Fork (Fork (Leaf 5) (Fork (Leaf 1) (Leaf 2))) (Fork (Leaf 4) (Leaf 3))