Binary Search Tree Assignment
We will implement a binary search tree data structure as well as Higher Order Function Hall of Fame inductees: find and fold.
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.
Functions which take (('k * 'k) -> order) functions behave as Int.compare does:
- compare (i, j)
- returns LESS, EQUAL, or GREATER when i is less than, equal to, or greater than j, respectively.
list
We will implement some of the higher ordered functions list provides on our binary tree.
traversal order
datatype traversal_order = LNR | RNL
Code to Implement
file: | src/main/sml/binary_tree/binary_tree.sml | |
functions: | create_empty_tree insert remove find fold_order_hof to_string |
signature BINARY_SEARCH_TREE = sig type 'k compare_function = (('k * 'k) -> order) type ('a,'k) to_key_function = 'a -> 'k type ('a,'k) tree; val create_empty_tree : ('k compare_function * ('a,'k) to_key_function) -> ('a,'k) tree val create_empty_simple_tree : ('a compare_function) -> ('a,'a) tree val insert : (('a,'k) tree * 'a) -> (('a,'k) tree * 'a option) val remove : (('a,'k) tree * 'k) -> (('a,'k) tree * 'a option) val find : (('a,'k) tree * 'k) -> 'a option val fold_lnr : (('a * 'b) -> 'b) -> ('b) -> (('a,'k) tree) -> 'b val fold_rnl : (('a * 'b) -> 'b) -> ('b) -> (('a,'k) tree) -> 'b val to_string : ('a -> string) -> (('a,'k) tree) -> string end
(* TODO: replace unit with the type you decide upon *) type ('a,'k) tree = unit
create_empty_tree
fun create_empty_tree(cmp : 'k compare_function, to_key : ('a,'k) to_key_function) : ('a,'k) tree = raise NotYetImplemented
insert
fun insert(t:('a,'k) tree, item:'a) : (('a,'k) tree * 'a option) = raise NotYetImplemented
NOTE: if the key for the specified item matches a key already in the tree, the previous item is replaced.
insert
returns a pair containing the new tree and the (optional) replaced value.
remove
fun remove(t:('a,'k) tree, item_key:'k) : (('a,'k) tree * 'a option) = raise NotYetImplemented
remove
the item whose key matches item_key
, if it is found.
returns a pair of the modified tree and the (optional) removed item.
Remove contains the most challenging aspect of this studio. When instructed to remove a node from a tree, there are several cases:
not found
What will indicate that you reached the point where you know the node is not found in the tree?
note: this has a trivial solution.
no child in the left tree
How will you detect this pattern?
note: this has a trivial solution.
no child in the right tree
how will you detect this pattern?
note: this has a trivial solution.
no children are present
If you need to remove a node and it has both children, now you have a legit problem. You must maintain a correct binary search tree.
A common approach is to choose one of the following:
- remove the right most descendant in the left child, and promote it to be the node at the current level, or
- remove the left most descendant in right left child, and promote it to be the node at the current level
The image below shows finding the left most child in the right subtree for promotion:
Building a helper function will likely be helpful.
find
reference: List.find
fun find(t:('a,'k) tree, item_key:'k) : 'a option = raise NotYetImplemented
fold_order_hof
reference: List.foldl foldr
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
Testing
file: | unit_test_binary_search_tree.sml | |
source folder: | src/test/sml/binary_search_tree |
Pledge, Acknowledgments, Citations
file: | studio-binary-search-tree-pledge-acknowledgments-citations.txt |
More info about the Honor Pledge