-- Level Order Traversal of a labelled binary tree
-- Objective: Print each "level" of the tree on a separate line
--
-- NOTICE: This demo relies on tricu base library functions
-- 
-- We model labelled binary trees as sublists where values act as labels. We
-- require explicit notation of empty nodes. Empty nodes can be represented 
-- with an empty list, `[]`, which is equivalent to a single node `t`. 
--
-- Example tree inputs:
-- [("1") [("2") [("4") t t] t] [("3") [("5") t t] [("6") t t]]]]
-- Graph:
--       1
--      / \
--     2   3
--    /   /  \
--   4   5    6
--

isLeaf = (\node : lOr (emptyList node) (emptyList (tail node)))
getLabel = (\node : head node)
getLeft = (\node : if (emptyList node) [] (if (emptyList (tail node)) [] (head (tail node))))
getRight = (\node : if (emptyList node) [] (if (emptyList (tail node)) [] (if (emptyList (tail (tail node))) [] (head (tail (tail node))))))

processLevel = y (\self queue : if (emptyList queue) [] (pair (map getLabel queue) (self (filter (\node : not (emptyList node)) (lconcat (map getLeft queue) (map getRight queue))))))
levelOrderTraversal = (\a : processLevel (t a t))
toLineString = y (\self levels : if (emptyList levels) "" (lconcat (lconcat (map (\x : lconcat x " ") (head levels)) "") (if (emptyList (tail levels)) "" (lconcat (t (t 10 t) t) (self (tail levels))))))
levelOrderToString = (\s : toLineString (levelOrderTraversal s))

flatten = foldl (\acc x : lconcat acc x) ""
flatLOT = (\s : lconcat (t 10 t) (flatten (levelOrderToString s)))

exampleOne = flatLOT [("1") [("2") [("4") t t] t] [("3") [("5") t t] [("6") t t]]]]
exampleTwo = flatLOT [("1") [("2") [("4") [("8") t t] [("9") t t]] [("6") [("10") t t] [("12") t t]]] [("3") [("5") [("11") t t] t] [("7") t t]]]