67 lines
2.2 KiB
OCaml
67 lines
2.2 KiB
OCaml
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(* Red-black trees according to the following classic paper:
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Chris Okasaki, Red-Black Trees in a Functional
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Setting. J. Funct. Program. 9(4): 471-477 (1999)
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*)
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type colour = Red | Black
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type 'a t = private
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Ext
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| Int of colour * 'a t * 'a * 'a t
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val empty: 'a t
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val is_empty: 'a t -> bool
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(* The value of the call [add ~cmp choice x t] is a red-black tree
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augmenting the tree [t] with a node containing the element [x],
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using the comparison function [cmp] (following the same convention
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as [Pervasives.compare]) and, if a value [y] such that [x = y] is
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already present in a node of [t], then the value [choice] denotes
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whether [x] ([New]) or [y] ([Old]) remains in the value of the
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call. Moreover, if [x == y], then [add ~cmp choice x t == t]. *)
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type choice = Old | New
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val add: cmp:('a -> 'a -> int) -> choice -> 'a -> 'a t -> 'a t
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(* The value of the call [find ~cmp x t] is the element [y] belonging
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to a node of the tree [t], such that [cmp x y = true]. If none, the
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exception [Not_found] is raised. *)
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exception Not_found
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val find: cmp:('a -> 'b -> int) -> 'a -> 'b t -> 'b
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(* The value of call [find_opt ~cmp x t] is [Some y] if there is an
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element [y] in a node of the tree [t] such that [cmp x y = true],
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and [None] otherwise. *)
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val find_opt: cmp:('a -> 'b -> int) -> 'a -> 'b t -> 'b option
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(* The value of the call [elements t] is the list of elements in the
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nodes of the tree [t], sorted by increasing order. *)
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val elements: 'a t -> 'a list
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(* The side-effect of evaluating the call [iter f t] is the successive
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side-effects of the calls [f x], for all elements [x] belonging to
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the nodes of [t], visited in increasing order. *)
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val iter: ('a -> unit) -> 'a t -> unit
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(* The value of the call [fold_inc f ~init t] is the iteration of the
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function [f] on increasing elements of the nodes of tree [t],
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accumulating the partial results from the initial value of
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[init]. *)
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val fold_inc: (elt:'a -> acc:'b -> 'b) -> init:'b -> 'a t -> 'b
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(* The value of the call [fold_dec f ~init t] is the iteration of the
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function [f] on decreasing elements of the nodes of tree [t],
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accumulating the partial results from the initial value of
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[init]. *)
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val fold_dec: (elt:'a -> acc:'b -> 'b) -> init:'b -> 'a t -> 'b
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