Binary Search Tree Assignment

We will implement a binary search tree data structure as well as a few Higher Order Function Hall of Fame inductees.

Background

order

SML's General structure's order

datatype order = LESS | EQUAL | GREATER

Values of type order are used when comparing elements of a type that has a linear ordering.

list

We will implement some of the higher ordered functions list provides on our binary tree.

traversal order

LNR would produce: ABCDEFGHI
RNL would produce: IHGFEDCBA

In-order LNR

Reverse in-order RNL

 datatype traversal_order = LNR | RNL

BinaryTree

file:	src/main/sml/binary_tree/binary_tree.sml
functions:	insert remove find ...

datatype 'a tree = LEAF | BRANCH of 'a tree * 'a * 'a tree

core

insert

note: this function is curried.

fun insert (compare_function:(('a * 'a) -> order)) (t:'a tree) (item:'a) : 'a tree = 
    raise NotYetImplemented

remove

note: this function is curried.

fun remove (equal_less_greater_function:'a -> order) (t:'a tree) : 'a tree =
    raise NotYetImplemented

find

reference: List.find

note: this function is curried.

fun find (equal_less_greater_function : 'a -> order) (t:'a tree) : 'a option = 
    raise NotYetImplemented

fun

to_first_and_last

This function is useful for find_order_hof and fold_order_hof.

It simply returns the left and right tree as a 2-tuple in the appropriate order based on the specified traversal_order.

fun to_first_and_last(order:traversal_order, left:'a tree, right:'a tree) =
    raise NotYetImplemented

find_order_hof

reference: List.find

Instead of a binary search style find, here we create a find based on a traversal order and a predicate. It returns the first item node value it encounters which passes the predicate function.

note: this function is curried.

fun find_order_hof (order:traversal_order) (predicate:'a->bool) (t:'a tree) : 'a option =
    raise NotYetImplemented

fun find_lnr (predicate:'a->bool) (t:'a tree) : 'a option = 
   find_order_hof LNR predicate t
fun find_rnl (predicate:'a->bool) (t:'a tree) : 'a option = 
   find_order_hof RNL predicate t

fold_order_hof

reference: List.foldl

note: this function is curried.

fun fold_order_hof (order:traversal_order) (f : 'a * 'b -> 'b) (init : 'b) (t : 'a tree) : 'b = 
    raise NotYetImplemented

fun fold_lnr f init t = 
   fold_order_hof LNR f init t
fun fold_rnl f init t = 
   fold_order_hof RNL f init t

filter (Not Required)

reference: List.filter

note: this function is curried.

fun filter (predicate : 'a -> bool) (t : 'a tree) : 'a tree = 
    raise NotYetImplemented

filter_civil_war_style

note: this function is curried.

fun filter_civil_war_style (predicate : 'a -> bool) (t : 'a tree) : 'a tree = 
    raise NotYetImplemented

map_to_tree_of_questionable_validity

reference: List.map note: this function is curried.

 fun map_to_tree_of_questionable_validity (f : 'a -> 'b) (t : 'a tree) : 'b tree = 
    raise NotYetImplemented

map_to_tree_hof (Not Required)

note: this function is curried.

fun map_to_tree_hof (order:traversal_order) (compare_function:(('b * 'b) -> order)) (f : 'a -> 'b) (t : 'a tree) : 'b tree =
    raise NotYetImplemented

fun map_to_tree_lnr compare_function f t = 
   map_to_tree_hof LNR compare_function f t
fun map_to_tree_rnl compare_function f t = 
   map_to_tree_hof RNL compare_function f t

map_to_list_hof (Not Required)

note: this function is curried.

fun map_to_list_hof (order:traversal_order) (f : 'a -> 'b) (t : 'a tree) : 'b list =
   raise NotYetImplemented

fun map_to_list_lnr f t = 
   map_to_list_hof LNR f t
fun map_to_list_rnl f t = 
   map_to_list_hof RNL f t

Applications

file:	src/main/sml/binary_tree/apps_using_binary_tree.sml
functions:	max_height sum_int_tree

max_height

fun max_height(t : 'a BinaryTree.tree) : int = 
 	raise NotYetImplemented

sum_int_tree

fun sum_int_tree(t : int BinaryTree.tree) : int =
 	raise NotYetImplemented

Testing

file:	unit_test_binary_tree_and_apps.sml
source folder:	src/test/sml/binary_tree

Pledge, Acknowledgments, Citations

file:

studio-binary-tree-pledge-acknowledgments-citations.txt

More info about the Honor Pledge