├── .gitignore ├── CHANGES.md ├── COPYING ├── LICENSE ├── Makefile ├── README.md ├── bheap.opam ├── binary_heap.ml ├── binary_heap.mli ├── dune ├── dune-project └── test.ml /.gitignore: -------------------------------------------------------------------------------- 1 | .merlin 2 | _build/ 3 | -------------------------------------------------------------------------------- /CHANGES.md: -------------------------------------------------------------------------------- 1 | 2 | - added `remove_and_add` (more efficient than `remove` and `add` combined) 3 | 4 | # 2.0.0 5 | ## changes 6 | - change of API: switch to a *minimum* priority queue 7 | - improved memory footprint with internal shrinking 8 | ## fixes 9 | - switch from obuild to dune and to opam 2.0 10 | - fixed memory leaks 11 | ## added 12 | - add some quick tests 13 | 14 | # 1.0.0 15 | - first opam package 16 | 17 | -------------------------------------------------------------------------------- /COPYING: -------------------------------------------------------------------------------- 1 | bitv - Objective Caml bit vectors library 2 | Copyright (C) 1999 Jean-Christophe FILLIATRE 3 | 4 | This software is free software; you can redistribute it and/or 5 | modify it under the terms of the GNU Library General Public 6 | License version 2, with the special exception on linking 7 | described in file LICENSE. 8 | 9 | This software is distributed in the hope that it will be useful, 10 | but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 12 | 13 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | The Library is distributed under the terms of the GNU Library General 2 | Public License version 2.1 (included below). 3 | 4 | As a special exception to the GNU Library General Public License, you 5 | may link, statically or dynamically, a "work that uses the Library" 6 | with a publicly distributed version of the Library to produce an 7 | executable file containing portions of the Library, and distribute 8 | that executable file under terms of your choice, without any of the 9 | additional requirements listed in clause 6 of the GNU Library General 10 | Public License. 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Here is a sample; alter the names: 518 | 519 | Yoyodyne, Inc., hereby disclaims all copyright interest in the 520 | library `Frob' (a library for tweaking knobs) written by James 521 | Random Hacker. 522 | 523 | , 1 April 1990 524 | Ty Coon, President of Vice 525 | 526 | That's all there is to it! 527 | 528 | 529 | -------------------------------------------------------------------------------- /Makefile: -------------------------------------------------------------------------------- 1 | 2 | all: 3 | dune build 4 | 5 | test: 6 | dune runtest 7 | 8 | doc: 9 | dune build @doc 10 | 11 | clean: 12 | dune clean 13 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # bheap 2 | Traditional implementation of priority queues 3 | using a binary heap encoded in a resizable array. 4 | 5 | 6 | 7 | -------------------------------------------------------------------------------- /bheap.opam: -------------------------------------------------------------------------------- 1 | opam-version: "2.0" 2 | maintainer: "Jean-Christophe.Filliatre@lri.fr" 3 | authors: "Jean-Christophe Filliâtre" 4 | synopsis: "Priority queues" 5 | description: """ 6 | Traditional implementation using a binary heap encoded in a resizable array 7 | """ 8 | license: "LGPL-2.1" 9 | homepage: "https://github.com/backtracking/bheap" 10 | doc: "https://backtracking.github.io/bheap" 11 | bug-reports: "https://github.com/backtracking/bheap/issues" 12 | depends: [ 13 | "ocaml" 14 | "stdlib-shims" {with-test} 15 | "dune" {>= "2.0.0"} 16 | ] 17 | build: [ 18 | ["dune" "subst"] {pinned} 19 | ["dune" "build" "-p" name "-j" jobs] 20 | ["dune" "runtest" "-p" name] {with-test} 21 | ] 22 | dev-repo: "git+https://github.com/backtracking/bheap.git" 23 | -------------------------------------------------------------------------------- /binary_heap.ml: -------------------------------------------------------------------------------- 1 | (**************************************************************************) 2 | (* *) 3 | (* Copyright (C) Jean-Christophe Filliatre *) 4 | (* *) 5 | (* This software is free software; you can redistribute it and/or *) 6 | (* modify it under the terms of the GNU Library General Public *) 7 | (* License version 2.1, with the special exception on linking *) 8 | (* described in file LICENSE. *) 9 | (* *) 10 | (* This software is distributed in the hope that it will be useful, *) 11 | (* but WITHOUT ANY WARRANTY; without even the implied warranty of *) 12 | (* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *) 13 | (* *) 14 | (**************************************************************************) 15 | 16 | (*s Heaps *) 17 | 18 | module type Ordered = sig 19 | type t 20 | val compare : t -> t -> int 21 | end 22 | 23 | exception Empty 24 | 25 | module Make(X : Ordered) = struct 26 | 27 | (* The heap is encoded in the array [data], where elements are stored 28 | from [0] to [size - 1]. From an element stored at [i], the left 29 | (resp. right) subtree, if any, is rooted at [2*i+1] (resp. [2*i+2]). *) 30 | 31 | type t = { 32 | mutable size : int; 33 | mutable data : X.t array; 34 | dummy : X.t; 35 | min_cap : int; (* minimal capacity, as given initially *) 36 | } 37 | (* invariant 0 <= size <= length data *) 38 | (* invariant data[size..] only contains dummy *) 39 | 40 | let create ~dummy n = 41 | if n < 0 || n > Sys.max_array_length then invalid_arg "create"; 42 | let n = max 16 n in 43 | { size = 0; data = Array.make n dummy; dummy = dummy; min_cap = n } 44 | 45 | let length h = h.size 46 | 47 | let is_empty h = h.size = 0 48 | 49 | (* [enlarge] doubles the size of [data] *) 50 | let enlarge h = 51 | let n = h.size in 52 | assert (n > 0 && n = Array.length h.data); 53 | let n' = min (2 * n) Sys.max_array_length in 54 | if n' = n then failwith "maximum capacity reached"; 55 | let d = h.data in 56 | let d' = Array.make n' h.dummy in 57 | Array.blit d 0 d' 0 n; 58 | h.data <- d' 59 | 60 | let shrink h = 61 | let n = Array.length h.data in 62 | let n' = max h.min_cap (n / 2) in 63 | assert (h.size <= n' && n' <= n); 64 | if n' < n then begin 65 | let d = h.data in 66 | let d' = Array.make n' h.dummy in 67 | Array.blit d 0 d' 0 h.size; 68 | h.data <- d' 69 | end 70 | 71 | let add h x = 72 | let n = h.size in 73 | if n == Array.length h.data then enlarge h; 74 | let d = h.data in 75 | let rec moveup i = 76 | let fi = (i - 1) / 2 in 77 | if i > 0 && X.compare d.(fi) x > 0 then begin 78 | d.(i) <- d.(fi); 79 | moveup fi 80 | end else 81 | d.(i) <- x 82 | in 83 | moveup n; 84 | h.size <- n + 1 85 | 86 | let minimum h = 87 | if h.size <= 0 then raise Empty; 88 | h.data.(0) 89 | 90 | let rec movedown d n i x = 91 | let j = 2 * i + 1 in 92 | if j < n then 93 | let j = 94 | let j' = j + 1 in 95 | if j' < n && X.compare d.(j') d.(j) < 0 then j' else j 96 | in 97 | if X.compare d.(j) x < 0 then begin 98 | d.(i) <- d.(j); 99 | movedown d n j x 100 | end else 101 | d.(i) <- x 102 | else 103 | d.(i) <- x 104 | 105 | let remove h = 106 | if h.size <= 0 then raise Empty; 107 | let n = h.size - 1 in 108 | h.size <- n; 109 | let d = h.data in 110 | let x = d.(n) in 111 | d.(n) <- h.dummy; 112 | movedown d n 0 x; 113 | if 4 * h.size < Array.length h.data then shrink h 114 | 115 | let remove_and_add h x = 116 | if h.size = 0 then add h x else movedown h.data h.size 0 x 117 | 118 | let pop_minimum h = 119 | let m = minimum h in remove h; m 120 | 121 | let iter f h = 122 | let d = h.data in 123 | for i = 0 to h.size - 1 do f d.(i) done 124 | 125 | let fold f h x0 = 126 | let n = h.size in 127 | let d = h.data in 128 | let rec foldrec x i = if i >= n then x else foldrec (f d.(i) x) (succ i) in 129 | foldrec x0 0 130 | 131 | end 132 | -------------------------------------------------------------------------------- /binary_heap.mli: -------------------------------------------------------------------------------- 1 | (**************************************************************************) 2 | (* *) 3 | (* Copyright (C) Jean-Christophe Filliatre *) 4 | (* *) 5 | (* This software is free software; you can redistribute it and/or *) 6 | (* modify it under the terms of the GNU Library General Public *) 7 | (* License version 2.1, with the special exception on linking *) 8 | (* described in file LICENSE. *) 9 | (* *) 10 | (* This software is distributed in the hope that it will be useful, *) 11 | (* but WITHOUT ANY WARRANTY; without even the implied warranty of *) 12 | (* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *) 13 | (* *) 14 | (**************************************************************************) 15 | 16 | (** Traditional implementation of priority queues using a binary heap 17 | encoded in a resizable array. 18 | 19 | When documenting complexity below, `n` refers to the number of elements 20 | in the queue. 21 | 22 | The size of the internal array is doubled when insertion requires 23 | more space, and halved when less than 25% is used. As a 24 | consequence, the time spent in enlarging/shrinking the array in a 25 | sequence of `M` insertions (resp. deletions) is proportional to `M`, 26 | and thus be considered constant time for each operation. For this 27 | reason, we do not mention the possibility of a worst case complexity 28 | `O(n)` in operations add/remove/pop_minimum below. *) 29 | 30 | module type Ordered = sig 31 | type t 32 | val compare : t -> t -> int 33 | end 34 | 35 | exception Empty 36 | 37 | module Make(X: Ordered) : sig 38 | 39 | (** Type of priority queues. *) 40 | type t 41 | 42 | (** [create ~dummy c] creates a new heap, with initial capacity of [c]. 43 | The value [dummy] is used to fill unused cells of the internal array. 44 | Note: [dummy] can still be used as a regular value in the queue. *) 45 | val create : dummy:X.t -> int -> t 46 | 47 | (** [length h] returns the number of elements of [h] *) 48 | val length : t -> int 49 | 50 | (** [is_empty h] checks the emptiness of [h] *) 51 | val is_empty : t -> bool 52 | 53 | (** [add x h] adds a new element [x] in heap [h]; complexity O(log(n)). *) 54 | val add : t -> X.t -> unit 55 | 56 | (** [minimum h] returns the minimum element of [h]; raises [Empty] 57 | when [h] is empty; complexity O(1) *) 58 | val minimum : t -> X.t 59 | 60 | (** [remove h] removes the minimum element of [h]; raises [Empty] 61 | when [h] is empty; complexity O(log(n)). *) 62 | val remove : t -> unit 63 | 64 | (** [pop_minimum h] removes the minimum element of [h] and returns it; 65 | raises [Empty] when [h] is empty; complexity O(log(n)). *) 66 | val pop_minimum : t -> X.t 67 | 68 | (** [remove_and_add x h] removes the minimum element of [h] and adds [x]; 69 | complexity O(log(n)). More efficient than calling [remove] 70 | and [add]. *) 71 | val remove_and_add : t -> X.t -> unit 72 | 73 | (** usual iterators; elements are presented in arbitrary order *) 74 | val iter : (X.t -> unit) -> t -> unit 75 | 76 | val fold : (X.t -> 'a -> 'a) -> t -> 'a -> 'a 77 | 78 | end 79 | -------------------------------------------------------------------------------- /dune: -------------------------------------------------------------------------------- 1 | (library 2 | (public_name bheap) 3 | (name binary_heap) 4 | (modules binary_heap)) 5 | 6 | (test 7 | (name test) 8 | (modules test) 9 | (libraries stdlib-shims bheap)) 10 | -------------------------------------------------------------------------------- /dune-project: -------------------------------------------------------------------------------- 1 | (lang dune 2.0) 2 | (name bheap) 3 | (formatting (enabled_for dune)) 4 | -------------------------------------------------------------------------------- /test.ml: -------------------------------------------------------------------------------- 1 | 2 | (* quick test of Binary_heap *) 3 | 4 | module E = struct 5 | type t = int 6 | let compare = Stdlib.compare 7 | end 8 | module H = Binary_heap.Make(E) 9 | 10 | let dummy = 1729 11 | let h = H.create ~dummy 0 12 | let () = assert (H.is_empty h) 13 | let () = assert (H.length h = 0) 14 | let () = H.add h 42 15 | let () = assert (not (H.is_empty h)) 16 | let () = assert (H.length h = 1) 17 | let () = assert (H.minimum h = 42) 18 | let x = H.pop_minimum h 19 | let () = assert (x = 42) 20 | let () = assert (H.is_empty h) 21 | 22 | let () = for i = 200 downto -200 do H.add h i done 23 | let () = assert (H.minimum h = -200) 24 | let () = assert (H.length h = 401) 25 | let () = for i = -200 to 200 do 26 | assert (H.minimum h = i); 27 | let x = H.pop_minimum h in 28 | assert (x = i); 29 | assert (H.length h = 200 - i) 30 | done 31 | 32 | let () = 33 | let h = H.create ~dummy 10 in 34 | for x = 200 downto 1 do H.add h x done; 35 | assert (H.length h = 200); 36 | let v = 201 in 37 | for x = 1 to 200 do 38 | assert (H.minimum h = x); 39 | H.remove_and_add h v; assert (H.length h = 200); 40 | done; 41 | assert (H.fold (+) h 0 = 200 * v); 42 | for _ = 1 to 200 do assert (H.pop_minimum h = v) done 43 | 44 | let () = 45 | let h = H.create ~dummy 42 in 46 | for _ = 1 to 1000 do 47 | if Random.bool () then H.add h (Random.int 1000); 48 | if not (H.is_empty h) && Random.int 3 = 0 then H.remove h 49 | done; 50 | for _ = 1 to 1000 do 51 | if Random.bool () then H.add h (Random.int 1000); 52 | if not (H.is_empty h) && Random.int 3 < 2 then H.remove h 53 | done; 54 | Format.eprintf "%d@." (H.length h) 55 | --------------------------------------------------------------------------------