Module Fheap

Functional Heap implementation based on pairing-heap algorithm and immutable data structures. See more info at http://en.wikipedia.org/wiki/Pairing_heap.


type 'a t

t_of_sexp is not supported, because of the difficulty involved in recreating the comparison function.

val sexp_of_t : ('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t
include Container.S1 with type 'a t := 'a t
type 'a t
val mem : ?equal:('a -> 'a -> bool) -> 'a t -> 'a -> bool

Checks whether the provided element is there, using polymorphic compare if equal is not provided

val length : 'a t -> int
val is_empty : 'a t -> bool
val iter : 'a t -> f:('a -> unit) -> unit
val fold : 'a t -> init:'accum -> f:('accum -> 'a -> 'accum) -> 'accum

fold t ~init ~f returns f (... f (f (f init e1) e2) e3 ...) en, where e1..en are the elements of t

val exists : 'a t -> f:('a -> bool) -> bool

Returns true if and only if there exists an element for which the provided function evaluates to true. This is a short-circuiting operation.

val for_all : 'a t -> f:('a -> bool) -> bool

Returns true if and only if the provided function evaluates to true for all elements. This is a short-circuiting operation.

val count : 'a t -> f:('a -> bool) -> int

Returns the number of elements for which the provided function evaluates to true.

val sum : (module Commutative_group.S with type t = 'sum) -> 'a t -> f:('a -> 'sum) -> 'sum

Returns the sum of f i for i in the container

val find : 'a t -> f:('a -> bool) -> 'a option

Returns as an option the first element for which f evaluates to true.

val find_map : 'a t -> f:('a -> 'b option) -> 'b option

Returns the first evaluation of f that returns Some, and returns None if there is no such element.

val to_list : 'a t -> 'a list
val to_array : 'a t -> 'a array
val min_elt : 'a t -> cmp:('a -> 'a -> int) -> 'a option

Returns a minimum (resp maximum) element from the collection using the provided cmp function, or None if the collection is empty. In case of a tie, the first element encountered while traversing the collection is returned. The implementation uses fold so it has the same complexity as fold.

val max_elt : 'a t -> cmp:('a -> 'a -> int) -> 'a option
val min_elt : 'a t -> cmp:('a -> 'a -> int) -> 'a option

The comparison function in min_elt and max_elt are independent of that used to order the heap. Since the provided cmp may be different from the one used to create the heap, it is necessary for these functions to traverse the entire heap. If you want to access the smallest element of the heap according to the heap's comparison function, you should use top.

val max_elt : 'a t -> cmp:('a -> 'a -> int) -> 'a option
val to_list : 'a t -> 'a list

The elements of to_list t are not in any particular order. You need to sort the list afterwards if you want to get a sorted list.

val create : cmp:('a -> 'a -> int) -> 'a t

create ~cmp returns a new min-heap that uses ordering function cmp.

The top of the heap is the smallest element as determined by the provided comparison function.

val of_array : 'a array -> cmp:('a -> 'a -> int) -> 'a t
val of_list : 'a list -> cmp:('a -> 'a -> int) -> 'a t
val add : 'a t -> 'a -> 'a t

add t v returns the new heap after addition. Complexity O(1).

val top : 'a t -> 'a option

This returns the top (i.e. smallest) element of the heap. Complexity O(1).

val top_exn : 'a t -> 'a
val remove_top : 'a t -> 'a t option

remove_top t returns the new heap after a remove. It does nothing if t is empty.

The amortized time per remove_top t (or pop t, pop_exn t, pop_if t) is O(lg n). The complexity of the worst case is O(n).

val pop : 'a t -> ('a * 'a t) option

This removes and returns the top (i.e. least) element and the modified heap.

val pop_exn : 'a t -> 'a * 'a t
val pop_if : 'a t -> ('a -> bool) -> ('a * 'a t) option

pop_if t cond returns Some (top_element, rest_of_heap) if t is not empty and its top element satisfies condition cond, or None in any other case.

val to_sequence : 'a t -> 'a Sequence.t

to_sequence t is a sequence of the elements of t in ascending order.