(* * 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. *) (** Multiset - Set with (signed) rational multiplicity for each element *) open NS0 module type MULTIPLICITY = sig type t [@@deriving compare, equal, hash, sexp] val zero : t val add : t -> t -> t val sub : t -> t -> t val neg : t -> t end module type S = sig type mul 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 * mul) pp -> t pp (* constructors *) val empty : t (** The empty multiset over the provided order. *) val of_ : elt -> mul -> t val add : t -> elt -> mul -> 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 (** Add multiplicities pointwise. [O(n + m)] *) val diff : t -> t -> t (** Subtract multiplicities pointwise. [O(n + m)] *) val map : t -> f:(elt -> mul -> elt * mul) -> t (** Map over the elements in ascending order. Preserves physical equality if [f] does. *) val map_counts : t -> f:(mul -> mul) -> t (** Map over the multiplicities of the elements in ascending order. *) val mapi_counts : t -> f:(elt -> mul -> mul) -> t (** Map over the multiplicities of the elements in ascending order. *) val flat_map : t -> f:(elt -> mul -> t) -> t (** Flat map over the elements in ascending order. Preserves physical equality if [f e m] is a singleton [(e', m')] with [e == e'] and [Mul.equal m m'] for all elements. *) val partition : t -> f:(elt -> mul -> bool) -> t * t (* queries *) val is_empty : t -> bool val is_singleton : t -> bool val length : t -> int (** Number of elements with non-zero multiplicity. [O(1)]. *) val count : t -> elt -> mul (** Multiplicity of an element. [O(log n)]. *) val only_elt : t -> (elt * mul) option (** The only element of a singleton multiset. [O(1)]. *) val choose_exn : t -> elt * mul (** Find an unspecified element. [O(1)]. *) val choose : t -> (elt * mul) option (** Find an unspecified element. [O(1)]. *) val pop : t -> (elt * mul * t) option (** Find and remove an unspecified element. [O(1)]. *) val min_elt : t -> (elt * mul) option (** Minimum element. [O(log n)]. *) val pop_min_elt : t -> (elt * mul * t) option (** Find and remove minimum element. [O(log n)]. *) val classify : t -> [`Zero | `One of elt * mul | `Many] (** Classify a set as either empty, singleton, or otherwise. *) val find_and_remove : t -> elt -> (mul * t) option (** Find and remove an element. *) val to_list : t -> (elt * mul) list (** Convert to a list of elements in ascending order. *) (* traversals *) val iter : t -> f:(elt -> mul -> unit) -> unit (** Iterate over the elements in ascending order. *) val exists : t -> f:(elt -> mul -> bool) -> bool (** Search for an element satisfying a predicate. *) val for_all : t -> f:(elt -> mul -> bool) -> bool (** Test whether all elements satisfy a predicate. *) val fold : t -> init:'s -> f:(elt -> mul -> 's -> 's) -> 's (** Fold over the elements in ascending order. *) end