This is a module for using red-black trees in OCaml. It can be used to
store simple elements that can be compared with (<), (=), and (>), or
for more complicated types in real-world applications. Aside from an
exception used in the remove functions to indicate failure, all of the
functions are purely functional.
User's guide
type 'a t: the type of red-black trees
empty: an empty tree
insert e t: add an element to a tree and return the new tree
insert_new e t: don't insert if the element is already in the tree
remove e t: remove one node containing the element and return the new tree
remove_all e t: remove all nodes containing the element
size t: the number of nodes in a tree (takes O(N) time)
black_height t: the black height of the tree
is_member e t: whether an element is in a tree
of_list l: create a tree from a list
to_list t: create a list from a tree
merge t1 t2: all the nodes in the two trees, together in one tree
union t1 t2: merge with no duplication (uses insert_new instead of insert)
Duplicates are eliminated from the smaller of the two trees
(based on black height), but not from the larger one.
fold_left f x0 t: in-order fold
fold_right f x0 t: reverse in-order fold
map f t: map for trees
mapi f t: map with in-order numbering of nodes
iter f t: in-order iteration
iteri f t: iter with in-order numbering
Make (E): a functor to create modules for complex elements
In modules generated by Make, is_member and the removal functions take a key
instead of an element. Those modules have concrete types, along with two
additional functions:
type element = E.t
type t = element RedBlackTree.t
find k t: returns an optional element from a tree with a specified key
value k t: calls find and extracts the value from the element
User-defined modules don't have map or mapi, but you can use the ones in
RedBlackTree.
To create a module with Make, you'll need to write your own module describing
the elements in the tree:
Typeof_Element: the type of element modules that can be passed to Make
Your module must contain these items:
t: the type of the elements in the tree
tkey: the type of element keys
tval: the type of element values
key e: returns an element's key
value e: returns an element's value
compare k1 k2: the comparison function. Returns zero for equal keys,
a negative integer when k1 belongs before k2, and
a positive integer when k1 belongs after k2.
Once you've defined an element module, you can create your own tree module:
module MyRedBlackTree = RedBlackTree.Make (MyElement)