Simple tree functions

src/BinaryTree/BinarySearchTree.hs

@@ -14,6 +14,16 @@ inorderWalk :: (Eq a, Ord a) => BTree a -> [a]
 inorderWalk Empty = []
 inorderWalk (Node x l r) = (inorderWalk l) ++ [x] ++ (inorderWalk r)
 
+-- Perform preorder walk of the binary search tree
+preorderWalk :: (Eq a, Ord a) => BTree a -> [a]
+preorderWalk Empty = []
+preorderWalk (Node x l r) = [x] ++ preorderWalk l ++ preorderWalk r
+
+-- Perform postorder walk of the binary search tree
+postorderWalk :: (Eq a, Ord a) => BTree a -> [a]
+postorderWalk Empty = []
+postorderWalk (Node x l r) = preorderWalk l ++ preorderWalk r ++ [x]
+
 -- Function to insert a value into the tree. Returns the new tree.
 -- Cormen, Thomas H., et al. Introduction to algorithms.  pg. 294, MIT press, 2009.
 bstInsert :: (Eq a, Ord a) => BTree a -> a -> BTree a
@@ -54,4 +64,12 @@ isBST Empty = True
 isBST (Node x Empty Empty) = True
 isBST (Node x Empty r) = (x < (nkey r)) && (isBST r) where nkey = (\(Node n ll rr) -> n)
 isBST (Node x l Empty) = (x >= (nkey l)) && (isBST l) where nkey = (\(Node n ll rr) -> n)
-isBST (Node x l r) = (x >= (nkey l)) && (x < (nkey r)) && (isBST l) && (isBST r) where nkey = (\(Node n ll rr) -> n)
+isBST (Node x l r) = (x >= (nkey l)) && (x < (nkey r)) && (isBST l) && (isBST r) where nkey = (\(Node n ll rr) -> n)
+
+isElementInBST :: (Ord a, Eq a) => BTree a -> a -> Bool
+isElementInBST Empty _ = False
+isElementInBST (Node x l r) ele = 
+    x == ele ||
+    if x < ele 
+        then isElementInBST r ele
+        else isElementInBST l ele

src/BinaryTree/BinaryTree.hs

@@ -2,7 +2,7 @@ module BinaryTree.BinaryTree where
 
 import qualified Data.List as L
 
-data BTree a = Empty | Node a (BTree a) (BTree a) deriving (Show)
+data BTree a = Empty | Node a (BTree a) (BTree a) deriving (Show, Eq)
 data Side = LeftSide | RightSide deriving (Eq, Show)
 
 -- Get subtree on specified side
@@ -68,4 +68,30 @@ numNodes t = length $ bfsList t
 -- Pretty Print a Binary Tree
 simplePrint :: (Show a) => BTree a -> String
 simplePrint Empty = ""
-simplePrint t = (nodeShow t) ++ " " ++ (simplePrint $ getLeftTree t) ++ (simplePrint $ getRightTree t)
+simplePrint t = (nodeShow t) ++ " " ++ (simplePrint $ getLeftTree t) ++ (simplePrint $ getRightTree t)
+
+-- Find count of element occurrence in binary tree
+elementCountInTree :: (Ord a, Eq a) => BTree a -> a -> Int
+elementCountInTree Empty _ = 0
+elementCountInTree (Node x l r) ele =
+    (if ele == x then 1 else 0) + 
+    elementCountInTree l ele    +
+    elementCountInTree r ele
+
+-- Find whether tree is symmetric at root
+-- Uses Haskell Eq instance to compare BTree datatype
+isSymmetric :: (Eq a) => BTree a -> Bool
+isSymmetric Empty = True
+isSymmetric (Node _ l r) = l == r
+
+-- Get sum of all elements in tree
+sumTree :: BTree Int -> Int
+sumTree Empty = 0
+sumTree (Node x l r) = x + sumTree l + sumTree r 
+
+-- Get an array of leaf nodes in a binary tree
+getLeafNodes :: (Eq a, Show a) => BTree a -> [a]
+getLeafNodes Empty = []
+getLeafNodes (Node x l r)
+    | l == Empty && r == Empty = [x]
+    | otherwise = getLeafNodes l ++ getLeafNodes r