package containers

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package containers
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Parameters

module E : PARTIAL_ORD

Signature

type elt = E.t
type t
exception Empty

Basic heap operations

val empty : t

empty returns the empty heap.

val is_empty : t -> bool

is_empty h returns true iff the heap h is empty.

val merge : t -> t -> t

merge h1 h2 merges the two heaps h1 and h2. If one heap is empty, the result is physically equal to the other heap. Complexity: O(log (m+n)) where m and n are the number of elements in each heap.

val insert : elt -> t -> t

insert x h inserts an element x into the heap h. Complexity: O(log n) where n is the number of elements in h.

val add : t -> elt -> t

add h x is insert x h.

val find_min : t -> elt option

find_min h returns the minimal element of h, or None if h is empty. Complexity: O(1).

val find_min_exn : t -> elt

find_min_exn h is akin to find_min, but it raises Empty when the heap is empty.

  • raises Empty

    if the heap is empty.

val take : t -> (t * elt) option

take h returns the minimum element of h and the new heap without this element, or None if h is empty. Complexity: O(log n).

val take_exn : t -> t * elt

take_exn h is akin to take, but it raises Empty when the heap is empty.

  • raises Empty

    if the heap is empty.

val size : t -> int

size h is the number of elements in the heap h. Complexity: O(n).

Deleting elements

val delete_one : (elt -> elt -> bool) -> elt -> t -> t

delete_one eq x h deletes an occurrence of the value x from the heap h, if there is some. If h does not contain x, then h itself is returned. Elements are identified by the equality function eq. Complexity: O(n).

  • since 2.0
val delete_all : (elt -> elt -> bool) -> elt -> t -> t

delete_all eq x h deletes all occurrences of the value x from the heap h. If h does not contain x, then h itself is returned. Elements are identified by the equality function eq. This function is more efficient than filter because it avoids considering elements greater than x. Complexity: O(n).

  • since 2.0
val filter : (elt -> bool) -> t -> t

filter p h filters the elements of h, only retaining those that satisfy the predicate p. If no element in h satisfies p, then h itself is returned. Complexity: O(n).

Iterating on elements

val iter : (elt -> unit) -> t -> unit

iter f h invokes f on every element of the heap h.

val fold : ('a -> elt -> 'a) -> 'a -> t -> 'a

fold f acc h folds on all elements of h.

Adding many elements at once

val add_list : t -> elt list -> t

add_list h l adds the elements of the list l into the heap h. An element occurring several times will be added that many times to the heap. Elements need not be given in any particular order. This function is more efficient than repeated insertions. Complexity: O(log m + n) where m and n are the number of elements in h and l, respectively.

  • since 0.16
val add_iter : t -> elt iter -> t

add_iter h iter is akin to add_list, but taking an iter of elements as input.

  • since 2.8
val add_seq : t -> elt Stdlib.Seq.t -> t

add_seq h seq is akin to add_list, but taking a Seq.t of elements as input. Renamed from add_std_seq since 3.0.

  • since 3.0
val add_gen : t -> elt gen -> t

add_gen h gen is akin to add_list, but taking a gen of elements as input.

  • since 0.16
val add_iter_almost_sorted : t -> elt iter -> t

add_iter_almost_sorted h iter is equivalent to merge h (of_iter_almost_sorted iter). See of_iter_almost_sorted. Complexity: O(log m + n).

  • since 3.14

Conversions

val of_list : elt list -> t

of_list l builds a heap from the list of elements l. Elements need not be given in any particular order. This function is more efficient than repeated insertions. It is equivalent to add_list empty l. Complexity: O(n).

val of_iter : elt iter -> t

of_iter iter is akin to of_list, but taking an iter of elements as input.

  • since 2.8
val of_seq : elt Stdlib.Seq.t -> t

of_seq seq is akin to of_list, but taking a Seq.t of elements as input. Renamed from of_std_seq since 3.0.

  • since 3.0
val of_gen : elt gen -> t

of_gen gen is akin to of_list, but taking a gen of elements as input.

val of_iter_almost_sorted : elt iter -> t

of_iter iter builds a heap from the iter sequence of elements. Elements need not be given in any particular order. However, the heap takes advantage of partial sorting found in the input: the closer the input sequence is to being sorted, the more efficient it is to convert the heap to a sorted sequence. This enables heap-sorting that is faster than O(n log n) when the input is almost sorted. In the best case, when only a constant number of elements are misplaced, then successive take run in O(1), and to_list_sorted runs in O(n). Complexity: O(n).

  • since 3.14
val to_list : t -> elt list

to_list h returns a list of the elements of the heap h, in no particular order. Complexity: O(n).

val to_iter : t -> elt iter

to_iter h is akin to to_list, but returning an iter of elements.

  • since 2.8
val to_seq : t -> elt Stdlib.Seq.t

to_seq h is akin to to_list, but returning a Seq.t of elements. Renamed from to_std_seq since 3.0.

  • since 3.0
val to_gen : t -> elt gen

to_gen h is akin to to_list, but returning a gen of elements.

val to_list_sorted : t -> elt list

to_list_sorted h returns the list of elements of the heap h in increasing order. Complexity: O(n log n).

  • since 1.1
val to_iter_sorted : t -> elt iter

to_iter_sorted h is akin to to_list_sorted, but returning an iter of elements.

  • since 2.8
val to_seq_sorted : t -> elt Stdlib.Seq.t

to_seq_sorted h is akin to to_list_sorted, but returning a Seq.t of elements. Renamed from to_std_seq_sorted since 3.0.

  • since 3.0
val to_tree : t -> elt ktree

to_tree h returns a ktree of the elements of the heap h. The layout is not specified. Complexity: O(n).

Pretty-printing

val to_string : ?sep:string -> (elt -> string) -> t -> string

to_string ?sep f h prints the heap h to a string, using f to convert elements to strings and sep (default: ",") as a separator between elements.

  • since 2.7
val pp : ?pp_start:unit printer -> ?pp_stop:unit printer -> ?pp_sep:unit printer -> elt printer -> t printer

pp ?pp_start ?pp_stop ?pp_sep ppf h prints h on ppf. Each element is formatted with ppf, pp_start is called at the beginning, pp_stop is called at the end, pp_sep is called between each element. By default, pp_start and pp_stop do nothing, and pp_sep is (fun out -> Format.fprintf out ",@ "). Renamed from print since 2.0

  • since 0.16
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