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Module Removable

Removable augments a heap with the ability to remove elements from the heap in lg(n) (amortized) time at any point after they have been added. Elements within a Removable heap consume 4 words more memory and all heap operations will be somewhat slower.

Signature

include Core_kernel.Heap_intf.S
type 'a t

of_sexp and bin_io functions aren't supplied for heaps due to the difficulties in reconstructing the correct comparison function when de-serializing.

val sexp_of_t : ('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t
include Core_kernel.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

Even though these two functions are part of Container.S1, they are documented separately to make sure there is no confusion. They are independent of the comparison function used to order the heap. Instead, a traversal of the entire structure is done using the provided cmp function to find a min or max.

If you want to access the smallest element of the heap according to the heap's comparison function in constant time, you should use top.

val max_elt : 'a t -> cmp:('a -> 'a -> int) -> 'a option
val create : ?min_size:int -> cmp:('a -> 'a -> int) -> unit -> 'a t

create ?min_size ~cmp returns a new min-heap that can store min_size elements without reallocations, using ordering function cmp.

The top of the heap is the smallest element as determined by the provided comparison function. In particular, if cmp x y < 0 then x will be "on top of" y in the heap.

Memory use is surprising in two ways:

1. The underlying pool never shrinks, so current memory use will at least be proportional to the largest number of elements that the heap has ever held.

2. Not all the memory is freed upon remove, but rather after some number of subsequent pop operations. Alternating add and remove operations can therefore use unbounded memory.

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

min_size (see create) will be set to the size of the input array or list.

val of_list : 'a list -> cmp:('a -> 'a -> int) -> 'a t
val top : 'a t -> 'a option

returns the top (i.e., smallest) element of the heap

val top_exn : 'a t -> 'a
val add : 'a t -> 'a -> unit
val remove_top : _ t -> unit

remove_top t does nothing if t is empty

val pop : 'a t -> 'a option

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

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

pop_if t cond returns Some top_element of t if it satisfies condition cond, removing it, or None in any other case.

val copy : 'a t -> 'a t

copy t returns a shallow copy

module Elt : sig .. end
val add_removable : 'a t -> 'a -> 'a Elt.t

add_removable t v adds v to t, returning a token that can be used to delete v from t in lg(n) amortized time.

val remove : 'a t -> 'a Elt.t -> unit

If t and token are mismatched then behavior is undefined. remove may safely be called on a token more than once. This doesn't free all the memory associated with the Elt until some number of pop operations later -- see Heap_intf for details.

val update : 'a t -> 'a Elt.t -> 'a -> 'a Elt.t

update t token v is shorthand for remove t token; add_removable t v

val find_elt : 'a t -> f:('a -> bool) -> 'a Elt.t option

find_elt t ~f. If f is true for some element in t, return a Elt.t for that element. This operation is O(n).