What is the minimum number of nodes in an AVL tree of height 8? Let N(H) be the minimum number of nodes in an AVL tree of height h. What is the minimum number of nodes in an AVL tree of height 8? Let N(H) be the minimum number of nodes in an AVL tree of height h. Solution (* contains(t,x) is whether x is in the tree *) fun contains(t: tree, x: value): bool = case t of Empty => false | Node{value, left, right} => (case compare(x, value) of EQUAL => true | LESS => contains(left, x) | GREATER => contains(right, x)) (* add(t,x) is a BST with the same values as t, plus x *) fun add(t: tree, x: value): tree = let fun balance(t: tree): tree = t (* what to write here? *) in case t of Empty => Node{value=x, left=Empty, right=Empty} | Node {value, left, right} => (case compare(x, value) of EQUAL => Node{value=x, left=left, right=right} | LESS => Node{value=value, left=add(left, x), right=right} | GREATER => Node{value=value, left=left, right=add(right,x) } ) end .

1. What is the minimum number of nodes in an AVL tree of height 8? Let N(H) be the minimum
number of nodes in an AVL tree of height h.
What is the minimum number of nodes in an AVL tree of height 8? Let N(H) be the minimum
number of nodes in an AVL tree of height h.
Solution
(* contains(t,x) is whether x is in the tree *) fun contains(t: tree, x: value): bool = case t of Empty
=> false | Node{value, left, right} => (case compare(x, value) of EQUAL => true | LESS =>
contains(left, x) | GREATER => contains(right, x)) (* add(t,x) is a BST with the same values as
t, plus x *) fun add(t: tree, x: value): tree = let fun balance(t: tree): tree = t (* what to write here?
*) in case t of Empty => Node{value=x, left=Empty, right=Empty} | Node {value, left, right} =>
(case compare(x, value) of EQUAL => Node{value=x, left=left, right=right} | LESS =>
Node{value=value, left=add(left, x), right=right} | GREATER => Node{value=value, left=left,
right=add(right,x) } ) end