new: Solved problems 61 to 63

Problems 61-69/problem_61.hs

@@ -0,0 +1,8 @@
+data Tree a = Empty | Branch a (Tree a) (Tree a)
+  deriving (Show, Eq)
+
+countLeaves :: Tree a -> Int
+countLeaves Empty = 0
+countLeaves (Branch _ Empty Empty) = 1
+countLeaves (Branch _ branch1 branch2) =
+  countLeaves branch1 + countLeaves branch2

Problems 61-69/problem_61a.hs

@@ -0,0 +1,8 @@
+data Tree a = Empty | Branch a (Tree a) (Tree a)
+  deriving (Show, Eq)
+
+leaves :: Tree a -> [a]
+leaves Empty = []
+leaves (Branch a Empty Empty) = [a]
+leaves (Branch _ branch1 branch2) =
+  leaves branch1 ++ leaves branch2

Problems 61-69/problem_62.hs

@@ -0,0 +1,8 @@
+data Tree a = Empty | Branch a (Tree a) (Tree a)
+  deriving (Show, Eq)
+
+internals :: Tree a -> [a]
+internals Empty = []
+internals (Branch _ Empty Empty) = []
+internals (Branch a branch1 branch2) =
+  (a : internals branch1) ++ internals branch2

Problems 61-69/problem_62b.hs

@@ -0,0 +1,8 @@
+data Tree a = Empty | Branch a (Tree a) (Tree a)
+  deriving (Show, Eq)
+
+atLevel :: Tree a -> Int -> [a]
+atLevel Empty _ = []
+atLevel (Branch a _ _) 1 = [a]
+atLevel (Branch _ branch1 branch2) n =
+  atLevel branch1 (n - 1) ++ atLevel branch2 (n - 1)

Problems 61-69/problem_63.hs

@@ -0,0 +1,32 @@
+data Tree a = Empty | Branch a (Tree a) (Tree a)
+  deriving (Show, Eq)
+
+completeBinaryTreeNumbered :: Int -> Int -> Tree Int
+completeBinaryTreeNumbered m n =
+  Branch m branch1 branch2
+  where
+    branch1 =
+      if 2 * m <= n
+        then completeBinaryTreeNumbered (2 * m) n
+        else Empty
+    branch2 =
+      if 2 * m + 1 <= n
+        then completeBinaryTreeNumbered (2 * m + 1) n
+        else Empty
+
+useSameCharLabel :: Char -> Tree a -> Tree Char
+useSameCharLabel _ Empty = Empty
+useSameCharLabel c (Branch _ branch1 branch2) =
+  Branch c branch1' branch2'
+  where
+    branch1' = useSameCharLabel c branch1
+    branch2' = useSameCharLabel c branch2
+
+completeBinaryTree :: Int -> Tree Char
+completeBinaryTree n = useSameCharLabel 'x' $ completeBinaryTreeNumbered 1 n
+
+isCompleteBinaryTree :: Tree a -> Bool
+isCompleteBinaryTree Empty = True
+isCompleteBinaryTree (Branch _ _ Empty) = True
+isCompleteBinaryTree (Branch _ branch1 branch2) =
+  isCompleteBinaryTree branch1 && isCompleteBinaryTree branch2