71 lines
3.0 KiB
OCaml
71 lines
3.0 KiB
OCaml
(** This module offers the abstract data type of a partition of
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classes of equivalent items (Union & Find). *)
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(** The items are of type 't, they have to obey a total order,
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but also they must be printable to ease debugging. *)
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type 'item partition
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type 'item t = 'item partition
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(** {1 Creation} *)
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(** The value [empty] is an empty partition. *)
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val empty : ('a -> string) -> ('a -> 'a -> int) -> 'a partition
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(** The value of [equiv i j p] is the partition [p] extended with
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the equivalence of items [i] and [j]. If both [i] and [j] are
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already known to be equivalent, then [equiv i j p == p]. *)
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val equiv : 'item -> 'item -> 'item t -> 'item partition
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(** The value of [alias i j p] is the partition [p] extended with
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the fact that item [i] is an alias of item [j]. This is the
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same as [equiv i j p], except that it is guaranteed that the
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item [i] is not the representative of its equivalence class in
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[alias i j p]. *)
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val alias : 'item -> 'item -> 'item partition -> 'item partition
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(** {1 Projection} *)
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(** The value of the call [repr i p] is [j] if the item [i] is in
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the partition [p] and its representative is [j]. If [i] is not
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in [p], then the value is [i]. *)
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val repr : 'item -> 'item partition -> 'item
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(** The value of the call [get_or_set i p] is [j, p] if the item [i] is
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in the partition [p] and its representative is [j]. If [i] is not
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in [p], then the value is [i, p'], where p' is the partition [p]
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extended with the fact that item [i] is a singleton partition. *)
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val get_or_set : 'item -> 'item t -> 'item * 'item t
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(** The value of the call [mem i p] is [Some j] if the item [i] is
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in the partition [p] and its representative is [j]. If [i] is
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not in [p], then the value is [None]. *)
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val mem : 'item -> 'item partition -> 'item option
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(** The value of the call [elements p] is a list of the elements of p,
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ordered in ascending order *)
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val elements : 'item partition -> 'item list
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(** The value of the call [partitions p] is a list of the partitions
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of p. A partition is a list of elements. The elements and
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partitions are returned with a deterministic order (regardless of
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the way the aliases have been made, the same partition will always
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have the same order). *)
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val partitions : 'item partition -> 'item list list
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(** The call [print p] is a value of type [Buffer.t] containing
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strings denoting the partition [p], based on
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[Ord.to_string]. *)
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val print : Format.formatter -> 'item partition -> unit
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(** {1 Predicates} *)
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(** The value of [is_equiv i j p] is [true] if, and only if, the
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items [i] and [j] belong to the same equivalence class in the
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partition [p], that is, [i] and [j] have the same
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representative. In particular, if either [i] or [j] do not
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belong to [p], the value of [is_equiv i j p] is [false]. See
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[mem] above. *)
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val is_equiv : 'item -> 'item -> 'item partition -> bool
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