CMSC 330, Spring 2009, Quiz 3 Practice Problem Solutions
1. OCaml Polymorphic Types
Consider a OCaml module Bst that implements a binary search tree:
module Bst = struct
type bst =
Empty
| Node of int * bst * bst
let empty = Empty (* empty binary search tree *)
let is_empty = function (* return true for empty bst *)
Empty -> true
| Node (_, _, _) -> false
let rec insert n = function (* insert n into binary search tree *)
Empty -> Node (n, Empty, Empty)
| Node (m, left, right) ->
if m = n then Node (m, left, right)
else if n < m then Node(m, (insert n left), right)
else Node(m, left, (insert n right))
(* Implement the following functions
val min : bst -> int
val remove : int -> bst -> bst
val fold : ('a -> int -> 'a) -> 'a -> bst -> 'a
val size : bst -> int
*)
let rec min = (* return smallest value in bst *)
let rec remove n t = (* tree with n removed *)
let rec fold f a t = (* apply f to nodes of t in inorder *)
let size t = (* # of non-empty nodes in t *)
end
a. Is insert tail recursive? Explain why or why not.
No, since the return value for recursive call to insert cannot be used as
the return value of the original call to insert. The return value is used to
create a Node data type first, and the Node value is returned.
b. Implement min as a tail-recursive function. Raise an exception for an empty bst.
Any reasonable exception is fine.
let rec min = function
Empty -> (raise (Failure "min"))
| Node (m, left, right) ->
if (is_empty left) then m
else min left
