Source file setp.ml

(*

   Copyright (c) 2001-2002, 
    John Kodumal        <jkodumal@eecs.berkeley.edu>
   All rights reserved.
   
   Redistribution and use in source and binary forms, with or without
   modification, are permitted provided that the following conditions are
   met:

   1. Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

   2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.

   3. The names of the contributors may not be used to endorse or promote
   products derived from this software without specific prior written
   permission.

   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
   IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
   TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
   PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
   OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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 *)
(***********************************************************************)
(*                                                                     *)
(*                           Objective Caml                            *)
(*                                                                     *)
(*            Xavier Leroy, projet Cristal, INRIA Rocquencourt         *)
(*                                                                     *)
(*  Copyright 1996 Institut National de Recherche en Informatique et   *)
(*  en Automatique.  All rights reserved.  This file is distributed    *)
(*  under the terms of the GNU Library General Public License, with    *)
(*  the special exception on linking described in file ../LICENSE.     *)
(*                                                                     *)
(***********************************************************************)

(* $Id$ *)

(* Sets over ordered types *)

module type PolyOrderedType =
  sig
    type 'a t
    val compare: 'a t -> 'a t -> int
  end

module type S =
  sig
    type 'a elt
    type 'a t
    val empty: 'a t
    val is_empty: 'a t -> bool
    val mem: 'a elt -> 'a t -> bool
    val add: 'a elt -> 'a t -> 'a t
    val singleton: 'a elt -> 'a t
    val remove: 'a elt -> 'a t -> 'a t
    val union: 'a t -> 'a t -> 'a t
    val inter: 'a t -> 'a t -> 'a t
    val diff: 'a t -> 'a t -> 'a t
    val compare: 'a t -> 'a t -> int
    val equal: 'a t -> 'a t -> bool
    val subset: 'a t -> 'a t -> bool
    val iter: ('a elt -> unit) -> 'a t -> unit
    val fold: ('a elt -> 'b -> 'b) -> 'a t -> 'b -> 'b
    val for_all: ('a elt -> bool) -> 'a t -> bool
    val exists: ('a elt -> bool) -> 'a t -> bool
    val filter: ('a elt -> bool) -> 'a t -> 'a t
    val partition: ('a elt -> bool) -> 'a t -> 'a t * 'a t
    val cardinal: 'a t -> int
    val elements: 'a t -> 'a elt list
    val min_elt: 'a t -> 'a elt
    val max_elt: 'a t -> 'a elt
    val choose: 'a t -> 'a elt
  end

module Make(Ord: PolyOrderedType) =
  struct
    type 'a elt = 'a Ord.t
    type 'a t = Empty | Node of 'a t * 'a elt * 'a t * int

    (* Sets are represented by balanced binary trees (the heights of the
       children differ by at most 2 *)

    let height = function
        Empty -> 0
      | Node(_, _, _, h) -> h

    (* Creates a new node with left son l, value x and right son r.
       l and r must be balanced and | height l - height r | <= 2.
       Inline expansion of height for better speed. *)

    let create l x r =
      let hl = match l with Empty -> 0 | Node(_,_,_,h) -> h in
      let hr = match r with Empty -> 0 | Node(_,_,_,h) -> h in
      Node(l, x, r, (if hl >= hr then hl + 1 else hr + 1))

    (* Same as create, but performs one step of rebalancing if necessary.
       Assumes l and r balanced.
       Inline expansion of create for better speed in the most frequent case
       where no rebalancing is required. *)

    let bal l x r =
      let hl = match l with Empty -> 0 | Node(_,_,_,h) -> h in
      let hr = match r with Empty -> 0 | Node(_,_,_,h) -> h in
      if hl > hr + 2 then begin
        match l with
          Empty -> invalid_arg "Set.bal"
        | Node(ll, lv, lr, _) ->
            if height ll >= height lr then
              create ll lv (create lr x r)
            else begin
              match lr with
                Empty -> invalid_arg "Set.bal"
              | Node(lrl, lrv, lrr, _)->
                  create (create ll lv lrl) lrv (create lrr x r)
            end
      end else if hr > hl + 2 then begin
        match r with
          Empty -> invalid_arg "Set.bal"
        | Node(rl, rv, rr, _) ->
            if height rr >= height rl then
              create (create l x rl) rv rr
            else begin
              match rl with
                Empty -> invalid_arg "Set.bal"
              | Node(rll, rlv, rlr, _) ->
                  create (create l x rll) rlv (create rlr rv rr)
            end
      end else
        Node(l, x, r, (if hl >= hr then hl + 1 else hr + 1))

    (* Same as bal, but repeat rebalancing until the final result
       is balanced. *)

    let rec join l x r =
      match bal l x r with
        Empty -> invalid_arg "Set.join"
      | Node(l', x', r', _) as t' ->
          let d = height l' - height r' in
          if d < -2 || d > 2 then join l' x' r' else t'

    (* Merge two trees l and r into one.
       All elements of l must precede the elements of r.
       Assumes | height l - height r | <= 2. *)

    let rec merge t1 t2 =
      match (t1, t2) with
        (Empty, t) -> t
      | (t, Empty) -> t
      | (Node(l1, v1, r1, h1), Node(l2, v2, r2, h2)) ->
          bal l1 v1 (bal (merge r1 l2) v2 r2)

    (* Same as merge, but does not assume anything about l and r. *)

    let rec concat t1 t2 =
      match (t1, t2) with
        (Empty, t) -> t
      | (t, Empty) -> t
      | (Node(l1, v1, r1, h1), Node(l2, v2, r2, h2)) ->
          join l1 v1 (join (concat r1 l2) v2 r2)

    (* Splitting *)

    let rec split x = function
        Empty ->
          (Empty, None, Empty)
      | Node(l, v, r, _) ->
          let c = Ord.compare x v in
          if c = 0 then (l, Some v, r)
          else if c < 0 then
            let (ll, vl, rl) = split x l in (ll, vl, join rl v r)
          else
            let (lr, vr, rr) = split x r in (join l v lr, vr, rr)

    (* Implementation of the set operations *)

    let empty = Empty

    let is_empty = function Empty -> true | _ -> false

    let rec mem x = function
        Empty -> false
      | Node(l, v, r, _) ->
          let c = Ord.compare x v in
          c = 0 || mem x (if c < 0 then l else r)

    let rec add x = function
        Empty -> Node(Empty, x, Empty, 1)
      | Node(l, v, r, _) as t ->
          let c = Ord.compare x v in
          if c = 0 then t else
          if c < 0 then bal (add x l) v r else bal l v (add x r)

    let singleton x = Node(Empty, x, Empty, 1)

    let rec remove x = function
        Empty -> Empty
      | Node(l, v, r, _) ->
          let c = Ord.compare x v in
          if c = 0 then merge l r else
          if c < 0 then bal (remove x l) v r else bal l v (remove x r)

    let rec union s1 s2 =
      match (s1, s2) with
        (Empty, t2) -> t2
      | (t1, Empty) -> t1
      | (Node(l1, v1, r1, h1), Node(l2, v2, r2, h2)) ->
          if h1 >= h2 then
            if h2 = 1 then add v2 s1 else begin
              let (l2, _, r2) = split v1 s2 in
              join (union l1 l2) v1 (union r1 r2)
            end
          else
            if h1 = 1 then add v1 s2 else begin
              let (l1, _, r1) = split v2 s1 in
              join (union l1 l2) v2 (union r1 r2)
            end

    let rec inter s1 s2 =
      match (s1, s2) with
        (Empty, t2) -> Empty
      | (t1, Empty) -> Empty
      | (Node(l1, v1, r1, _), t2) ->
          match split v1 t2 with
            (l2, None, r2) ->
              concat (inter l1 l2) (inter r1 r2)
          | (l2, Some _, r2) ->
              join (inter l1 l2) v1 (inter r1 r2)

    let rec diff s1 s2 =
      match (s1, s2) with
        (Empty, t2) -> Empty
      | (t1, Empty) -> t1
      | (Node(l1, v1, r1, _), t2) ->
          match split v1 t2 with
            (l2, None, r2) ->
              join (diff l1 l2) v1 (diff r1 r2)
          | (l2, Some _, r2) ->
              concat (diff l1 l2) (diff r1 r2)

    let rec compare_aux l1 l2 =
        match (l1, l2) with
        ([], []) -> 0
      | ([], _)  -> -1
      | (_, []) -> 1
      | (Empty :: t1, Empty :: t2) ->
          compare_aux t1 t2
      | (Node(Empty, v1, r1, _) :: t1, Node(Empty, v2, r2, _) :: t2) ->
          let c = Ord.compare v1 v2 in
          if c <> 0 then c else compare_aux (r1::t1) (r2::t2)
      | (Node(l1, v1, r1, _) :: t1, t2) ->
          compare_aux (l1 :: Node(Empty, v1, r1, 0) :: t1) t2
      | (t1, Node(l2, v2, r2, _) :: t2) ->
          compare_aux t1 (l2 :: Node(Empty, v2, r2, 0) :: t2)

    let compare s1 s2 =
      compare_aux [s1] [s2]

    let equal s1 s2 =
      compare s1 s2 = 0

    let rec subset s1 s2 =
      match (s1, s2) with
        Empty, _ ->
          true
      | _, Empty ->
          false
      | Node (l1, v1, r1, _), (Node (l2, v2, r2, _) as t2) ->
          let c = Ord.compare v1 v2 in
          if c = 0 then
            subset l1 l2 && subset r1 r2
          else if c < 0 then
            subset (Node (l1, v1, Empty, 0)) l2 && subset r1 t2
          else
            subset (Node (Empty, v1, r1, 0)) r2 && subset l1 t2

    let rec iter f = function
        Empty -> ()
      | Node(l, v, r, _) -> iter f l; f v; iter f r

    let rec fold f s accu =
      match s with
        Empty -> accu
      | Node(l, v, r, _) -> fold f l (f v (fold f r accu))

    let rec for_all p = function
        Empty -> true
      | Node(l, v, r, _) -> p v && for_all p l && for_all p r

    let rec exists p = function
        Empty -> false
      | Node(l, v, r, _) -> p v || exists p l || exists p r

    let filter p s =
      let rec filt accu = function
        | Empty -> accu
        | Node(l, v, r, _) ->
            filt (filt (if p v then add v accu else accu) l) r in
      filt Empty s

    let partition p s =
      let rec part (t, f as accu) = function
        | Empty -> accu
        | Node(l, v, r, _) ->
            part (part (if p v then (add v t, f) else (t, add v f)) l) r in
      part (Empty, Empty) s

    let rec cardinal = function
        Empty -> 0
      | Node(l, v, r, _) -> cardinal l + 1 + cardinal r

    let rec elements_aux accu = function
        Empty -> accu
      | Node(l, v, r, _) -> elements_aux (v :: elements_aux accu r) l

    let elements s =
      elements_aux [] s

    let rec min_elt = function
        Empty -> raise Not_found
      | Node(Empty, v, r, _) -> v
      | Node(l, v, r, _) -> min_elt l

    let rec max_elt = function
        Empty -> raise Not_found
      | Node(l, v, Empty, _) -> v
      | Node(l, v, r, _) -> max_elt r

    let choose = min_elt

  end