Level Order Traversal demo

demos/LevelOrderTraversal.tri

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+-- 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]]]