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(*
* Copyright (c) Facebook, Inc. and its affiliates.
*
* This source code is licensed under the MIT license found in the
* LICENSE file in the root directory of this source tree.
*)
(** Qset - Set with (signed) rational multiplicity for each element *)
open Import0
module type S = sig
type elt
type t
val compare : t -> t -> int
val equal : t -> t -> bool
val hash_fold_t : elt Hash.folder -> t Hash.folder
val sexp_of_t : t -> Sexp.t
val t_of_sexp : (Sexp.t -> elt) -> Sexp.t -> t
val pp : (unit, unit) fmt -> (elt * Q.t) pp -> t pp
(* constructors *)
val empty : t
(** The empty multiset over the provided order. *)
val of_ : elt -> Q.t -> t
val add : t -> elt -> Q.t -> t
(** Add to multiplicity of single element. [O(log n)] *)
val remove : t -> elt -> t
(** Set the multiplicity of an element to zero. [O(log n)] *)
val union : t -> t -> t
(** Sum multiplicities pointwise. [O(n + m)] *)
val map : t -> f:(elt -> Q.t -> elt * Q.t) -> t
(** Map over the elements in ascending order. Preserves physical equality
if [f] does. *)
val map_counts : t -> f:(elt -> Q.t -> Q.t) -> t
(** Map over the multiplicities of the elements in ascending order. *)
(* queries *)
val is_empty : t -> bool
val length : t -> int
(** Number of elements with non-zero multiplicity. [O(1)]. *)
val count : t -> elt -> Q.t
(** Multiplicity of an element. [O(log n)]. *)
val choose : t -> (elt * Q.t) option
(** Find an unspecified element. [O(1)]. *)
val pop : t -> (elt * Q.t * t) option
(** Find and remove an unspecified element. [O(1)]. *)
val min_elt : t -> (elt * Q.t) option
(** Minimum element. [O(log n)]. *)
val pop_min_elt : t -> (elt * Q.t * t) option
(** Find and remove minimum element. [O(log n)]. *)
val classify : t -> [`Zero | `One of elt * Q.t | `Many]
(** Classify a set as either empty, singleton, or otherwise. *)
val find_and_remove : t -> elt -> (Q.t * t) option
(** Find and remove an element. *)
val to_list : t -> (elt * Q.t) list
(** Convert to a list of elements in ascending order. *)
(* traversals *)
val iter : t -> f:(elt -> Q.t -> unit) -> unit
(** Iterate over the elements in ascending order. *)
val exists : t -> f:(elt -> Q.t -> bool) -> bool
(** Search for an element satisfying a predicate. *)
val for_all : t -> f:(elt -> Q.t -> bool) -> bool
(** Test whether all elements satisfy a predicate. *)
val fold : t -> f:(elt -> Q.t -> 's -> 's) -> init:'s -> 's
(** Fold over the elements in ascending order. *)
end