Update Binary Search Tree

binary-search-tree.hs

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+module BinarySearchTree(BSTree(Void,BSNode), subTree, Tree(Node), count, labels, height) where
+
+{- Binary Search Trees
+
+   Void represents an empty tree. BSNode l x r represents a tree with
+   left subtree l, root label x, and right subtree r.
+
+   INVARIANT: in every tree of the form BSNode l x r, all labels in l
+              are < x, and all labels in r are > x.
+ -}
+data BSTree = Void | BSNode BSTree Integer BSTree  -- do not modify this line
+
+{-  subTree a b t
+
+    Takes two integers and the Binary Search Tree
+
+    RETURNS: The sub-tree where the nodes are greater than or equal to a but smaller than b
+    EXAMPLES: subTree 5 8 (BSNode (BSNode (BSNode Void 0 (BSNode Void 2 Void))
+                            3
+                            (BSNode Void 5 Void))
+                    6
+                    (BSNode Void
+                            7
+                            (BSNode Void 8 (BSNode Void 9 Void)))) == BSNode (BSNode Void 5 Void) 6 (BSNode Void 7 Void)
+-}
+subTree :: Integer -> Integer -> BSTree -> BSTree
+
+subTree a b (Void) = Void
+subTree a b (BSNode Void x Void) 
+    | x >= a && x < b   = BSNode Void x Void
+    | otherwise         = Void
+
+subTree a b (BSNode Void x r) 
+    | x >= a && x < b   = subTree a b (BSNode Void x (subTree a b r))
+    | otherwise         = subTree a b r
+
+subTree a b (BSNode l x Void) 
+    | x >= a && x < b   = subTree a b (BSNode (subTree a b l) x Void)
+    | otherwise         = subTree a b l
+
+subTree a b (BSNode l x r) 
+    | x >= a && x < b   = BSNode (subTree a b l) x (subTree a b r)
+    | otherwise         = subTree a b (BSNode (subTree a b l) x (subTree a b r))
+
+
+data Tree a = Node a [Tree a]
+
+tree1 = Node "hej" []
+tree2 = Node 1 [Node 2 []]
+tree3 = Node "hej" [Node "hello" [Node "ni hao" [Node "ahoj" []]],
+                    Node "bonjour" [Node "privet" [Node "guten tag" []]],
+                    Node "namaste" [Node "ciao" [Node "as-salam alaykom" [Node "saluton" [Node "hei" [Node "halo" []]],
+                                                                          Node "kon-nichiwa" [Node "an-nyong ha-se-yo " [Node "ola" []]],
+                                                                          Node "sa-wat-dee" [Node "selam" [Node "jambo" []]]]]]]
+
+{-  count t
+
+    Takes a tree of type Tree a
+
+    RETURNS: The number of nodes of that tree
+    EXAMPLES: count (Node "hej" []) == 1
+              count (Node 1 [Node 2 []]) == 2
+-}
+count :: Tree a -> Integer
+count (Node _ []) = 1
+count (Node r (n:xn)) = count (n) + count (Node r xn)
+
+{-  labels t
+
+    Takes a tree of type Tree a
+
+    RETURNS: The list of all node labels of that tree
+    EXAMPLES: labels (Node "hej" []) == ["hej"]
+              labels (Node 1 [Node 2 []]) == [1, 2]
+-}
+labels :: Tree a -> [a]
+labels (Node n []) = [n]
+labels (Node n xn) = n : concatMap labels xn
+
+{-  height t
+
+    Takes a tree of type Tree a
+
+    RETURNS: The height of tree
+    EXAMPLES: height (Node "hej" []) == 1
+              height (Node 1 [Node 2 []]) == 2
+-}
+height :: Tree a -> Integer
+height (Node _ []) = 1
+height (Node _ xn) = 1 + maximum (map height xn)