# Module Fheap

    module Fheap: sig .. end

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.

    include Container.S1

Even though `min_elt`, `max_elt`, and `to_list` are in `Container.S1`, they are documented separately to make sure there is no confusion.

    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.

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

Even though `min_elt`, `max_elt`, and `to_list` are in `Container.S1`, they are documented separately to make sure there is no confusion.
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`.
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.
`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.
`add t v` returns the new heap after addition. Complexity O(1).
This returns the top (i.e. smallest) element of the heap. Complexity O(1).
`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).
This removes and returns the top (i.e. least) element and the modified heap.
`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.
`to_sequence t` is a sequence of the elements of `t` in ascending order.