Added programming language fundamentals code. More to come.

OSU Coursework/CS 381 - Programming Language Fundamentals/Homework 1/Tree.perrenc.hs

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+module Tree where
+
+
+--
+-- * Part 1: Binary trees
+--
+
+-- | Integer-labeled binary trees.
+data Tree = Node Int Tree Tree   -- ^ Internal nodes
+          | Leaf Int             -- ^ Leaf nodes
+  deriving (Eq,Show)
+
+
+-- | An example binary tree, which will be used in tests.
+t1 :: Tree
+t1 = Node 1 (Node 2 (Node 3 (Leaf 4) (Leaf 5)) (Leaf 6)) (Node 7 (Leaf 8) (Leaf 9))
+
+-- | Another example binary tree, used in tests.
+t2 :: Tree
+t2 = Node 6 (Node 2 (Leaf 1) (Node 4 (Leaf 3) (Leaf 5)))
+            (Node 8 (Leaf 7) (Leaf 9))
+
+
+-- | The integer at the left-most node of a binary tree.
+--
+--   >>> leftmost (Leaf 3)
+--   3
+--
+--   >>> leftmost (Node 5 (Leaf 6) (Leaf 7))
+--   6
+--
+--   >>> leftmost t1
+--   4
+--
+--   >>> leftmost t2
+--   1
+--
+leftmost :: Tree -> Int
+leftmost (Leaf i)     = i
+leftmost (Node _ l _) = leftmost l
+
+
+-- | The integer at the right-most node of a binary tree.
+--
+--   >>> rightmost (Leaf 3)
+--   3
+--
+--   >>> rightmost (Node 5 (Leaf 6) (Leaf 7))
+--   7
+--
+--   >>> rightmost t1
+--   9
+--
+--   >>> rightmost t2
+--   9
+--
+rightmost :: Tree -> Int
+rightmost (Leaf i) = i
+rightmost (Node _ _ r) = rightmost r
+
+
+-- | Get the maximum integer from a binary tree.
+--
+--   >>> maxInt (Leaf 3)
+--   3
+--
+--   >>> maxInt (Node 5 (Leaf 4) (Leaf 2))
+--   5
+--
+--   >>> maxInt (Node 5 (Leaf 7) (Leaf 2))
+--   7
+--
+--   >>> maxInt t1
+--   9
+--
+--   >>> maxInt t2
+--   9
+--
+maxInt :: Tree -> Int
+maxInt (Leaf i) = i
+maxInt (Node x l r) = max x (max (maxInt l) (maxInt r))
+
+
+-- | Get the minimum integer from a binary tree.
+--
+--   >>> minInt (Leaf 3)
+--   3
+--
+--   >>> minInt (Node 2 (Leaf 5) (Leaf 4))
+--   2
+--
+--   >>> minInt (Node 5 (Leaf 4) (Leaf 7))
+--   4
+--
+--   >>> minInt t1
+--   1
+--
+--   >>> minInt t2
+--   1
+--
+minInt :: Tree -> Int
+minInt (Leaf i) = i
+minInt (Node x l r) = min x (min (minInt l) (minInt r))
+
+
+-- | Get the sum of the integers in a binary tree.
+--
+--   >>> sumInts (Leaf 3)
+--   3
+--
+--   >>> sumInts (Node 2 (Leaf 5) (Leaf 4))
+--   11
+--
+--   >>> sumInts t1
+--   45
+--
+--   >>> sumInts (Node 10 t1 t2)
+--   100
+--
+sumInts :: Tree -> Int
+sumInts (Leaf i) = i
+sumInts (Node x l r) = sum ([x] ++ [sumInts l] ++ [sumInts r])
+
+
+-- | The list of integers encountered by a pre-order traversal of the tree.
+--
+--   >>> preorder (Leaf 3)
+--   [3]
+--
+--   >>> preorder (Node 5 (Leaf 6) (Leaf 7))
+--   [5,6,7]
+--
+--   >>> preorder t1
+--   [1,2,3,4,5,6,7,8,9]
+--
+--   >>> preorder t2
+--   [6,2,1,4,3,5,8,7,9]
+--
+preorder :: Tree -> [Int]
+preorder (Leaf i) = [i]
+preorder (Node x l r) = [x] ++ preorder l ++ preorder r
+
+-- | The list of integers encountered by an in-order traversal of the tree.
+--
+--   >>> inorder (Leaf 3)
+--   [3]
+--
+--   >>> inorder (Node 5 (Leaf 6) (Leaf 7))
+--   [6,5,7]
+--
+--   >>> inorder t1
+--   [4,3,5,2,6,1,8,7,9]
+--
+--   >>> inorder t2
+--   [1,2,3,4,5,6,7,8,9]
+--
+inorder :: Tree -> [Int]
+inorder (Leaf i) = [i]
+inorder (Node x l r) =  inorder l ++ [x] ++ inorder r
+
+
+-- | Check whether a binary tree is a binary search tree.
+--
+--   >>> isBST (Leaf 3)
+--   True
+--
+--   >>> isBST (Node 5 (Leaf 6) (Leaf 7))
+--   False
+--
+--   >>> isBST t1
+--   False
+--
+--   >>> isBST t2
+--   True
+--
+isBST :: Tree -> Bool
+isBST (Leaf _) = True
+isBST (Node x (Leaf l) (Leaf r))
+    | l > x = False
+    | r < x = False
+    | otherwise = True
+isBST (Node x (Node l al ar) (Node r bl br))
+    | l > x = False
+    | r < x = False
+    | isBST al && isBST ar && isBST bl && isBST br == True = True
+    | otherwise = True
+-- | Check whether a number is contained in a binary search tree.
+--   (You may assume that the given tree is a binary search tree.)
+--
+--   >>> inBST 2 (Node 5 (Leaf 2) (Leaf 7))
+--   True
+--
+--   >>> inBST 3 (Node 5 (Leaf 2) (Leaf 7))
+--   False
+--
+--   >>> inBST 4 t2
+--   True
+--
+--   >>> inBST 10 t2
+--   False
+--
+inBST :: Int -> Tree -> Bool
+inBST i (Leaf x) = x == i
+inBST i (Node x l r) = elem True ([x == i] ++ [inBST i l] ++ [inBST i r])