import Mpi


-- some auxiliary functions

-- uncurried multiplication, mult (x,y) = x*y
mult = uncurry (*)

-- uncurried sum
add = uncurry (+)

-- uncurried max
maxi = uncurry max

-- isZero n = n==0
isZero = (==0)




-- Arvores Binarias etiquetadas nas folhas

data LTree a = Leaf a | LNode (LTree a) (LTree a)


inLTree :: Either a (LTree a , LTree a) -> LTree a

inLTree = either Leaf (uncurry LNode)


outLTree :: LTree a -> Either a (LTree a , LTree a) 

outLTree (Leaf x)    = i1 x
outLTree (LNode e d) = i2 (e,d)





alturaL = (either (const 0) (succ.maxi.(alturaL >< alturaL))) . outLTree

alturaL' = (either (const 0) (succ.maxi)) . 
	   (id -|- alturaL' >< alturaL') . outLTree


somaFolhas = (either id add) .
	     (id -|- somaFolhas >< somaFolhas) . outLTree




-- Arvores Binarias etiquetadas nos nos.

data BTree a = Empty | BNode a (BTree a) (BTree a)


inBTree :: Either () ((a, BTree a) , BTree a) -> BTree a

inBTree = either (const Empty) (uncurry (uncurry BNode))


outBTree :: BTree a -> Either () ((a, BTree a), BTree a) 

outBTree Empty         = i1 ()
outBTree (BNode x e d) = i2 ((x,e),d)





alturaB = (either (const 0) (succ.maxi.(snd >< id))) . 
	  (id -|- (id >< alturaB) >< alturaB) . outBTree


somaNodos = (either (const 0) (add.(add >< id))) .
	    (id -|- (id >< somaNodos) >< somaNodos) . outBTree
	    






t :: LTree Integer
t = LNode (Leaf 1) (LNode (Leaf 2) (Leaf 3))
t' = LNode t t 



a :: BTree Integer
a = BNode 1 (BNode 2 Empty Empty) (BNode 3 Empty Empty)
a'= BNode 0 a a