(* intmapf.sml
 *
 * COPYRIGHT (c) 1996 Bell Laboratories.
 *
 *)

signature INTMAPF =
sig
  type 'a intmap
  val empty : 'a intmap
  val singleton : int * 'a  -> 'a intmap
  val overlay : 'a intmap * 'a intmap -> 'a intmap
  val add : 'a intmap * int * 'a  -> 'a intmap
  exception IntmapF
  val lookup : 'a intmap -> int -> 'a
  val members : 'a intmap -> (int * 'a) list
  val cardinality : 'a intmap -> int
  val difference : 'a intmap * 'b intmap -> 'a intmap
  val delete : int * 'a intmap -> 'a intmap
  val fold : (int * 'a * 'b -> 'b) -> 'b -> 'a intmap -> 'b
end

(*
    Copyright 1992 Stephen Adams.

    ALTERED FROM THE ORIGINAL by Andrew Appel

    This software may be used freely provided that:
      1. This copyright notice is attached to any copy, derived work,
         or work including all or part of this software.
      2. Any derived work must contain a prominent notice stating that
         it has been altered from the original.

*)

(* Name(s): Stephen Adams.
   Department, Institution: Electronics & Computer Science,
      University of Southampton
   Address:  Electronics & Computer Science
             University of Southampton
	     Southampton  SO9 5NH
	     Great Britian
   E-mail:   sra@ecs.soton.ac.uk

   Comments:

     1.  The implementation is based on Binary search trees of Bounded
         Balance, similar to Nievergelt & Reingold, SIAM J. Computing
         2(1), March 1973.  The main advantage of these trees is that
         they keep the size of the tree in the node, giving a constant
         time size operation.

     2.  The bounded balance criterion is simpler than N&R's alpha.
         Simply, one subtree must not have more than `weight' times as
         many elements as the opposite subtree.  Rebalancing is
         guaranteed to reinstate the criterion for weight>2.23, but
         the occasional incorrect behaviour for weight=2 is not
         detrimental to performance.

*)

structure IntmapF :> INTMAPF =
    struct

	local

	    val weight = 3

	    datatype 'a Map = E | T of int * 'a * int * 'a Map * 'a Map

	    fun size E = 0
	      | size (T(_,_,n,_,_)) = n
	    
	    (*fun N(v,a,l,r) = T(v,a,1+size(l)+size(r),l,r)*)
	    fun N(v,a,E,              E)               = T(v,a,1,E,E)
	      | N(v,a,E,              r as T(_,_,n,_,_)) = T(v,a,n+1,E,r)
	      | N(v,a,l as T(_,_,n,_,_),E)               = T(v,a,n+1,l,E)
	      | N(v,a,l as T(_,_,n,_,_),r as T(_,_,m,_,_)) = T(v,a,n+m+1,l,r)

	    fun single_L (a,a',x,T(b,b',_,y,z)) = N(b,b',N(a,a',x,y),z)
	      | single_L _ = raise Match
	    fun single_R (b,b',T(a,a',_,x,y),z) = N(a,a',x,N(b,b',y,z))
	      | single_R _ = raise Match
	    fun double_L (a,a',w,T(c,c',_,T(b,b',_,x,y),z)) = N(b,b',N(a,a',w,x),N(c,c',y,z))
	      | double_L _ = raise Match
	    fun double_R (c,c',T(a,a',_,w,T(b,b',_,x,y)),z) = N(b,b',N(a,a',w,x),N(c,c',y,z))
	      | double_R _ = raise Match

	    fun T' (v,v',E,E) = T(v,v',1,E,E)
	      | T' (v,v',E,r as T(_,_,_,E,E))     = T(v,v',2,E,r)
	      | T' (v,v',l as T(_,_,_,E,E),E)     = T(v,v',2,l,E)

	      | T' (p as (_,_,E,T(_,_,_,T(_,_,_,_,_),E))) = double_L p
	      | T' (p as (_,_,T(_,_,_,E,T(_,_,_,_,_)),E)) = double_R p

	      (* these cases almost never happen with small weight*)
	      | T' (p as (_,_,E,T(_,_,_,T(_,_,ln,_,_),T(_,_,rn,_,_)))) =
		if ln<rn then single_L p else double_L p
	      | T' (p as (_,_,T(_,_,_,T(_,_,ln,_,_),T(_,_,rn,_,_)),E)) =
		if ln>rn then single_R p else double_R p

	      | T' (p as (_,_,E,T(_,_,_,E,_)))  = single_L p
	      | T' (p as (_,_,T(_,_,_,_,E),E))  = single_R p

	      | T' (p as (v,v',l as T(lv,lv',ln,ll,lr),r as T(rv,rv',rn,rl,rr))) =
		if rn>=weight*ln then (*right is too big*)
		    let val rln = size rl
			val rrn = size rr
		    in
			if rln < rrn then  single_L p  else  double_L p
		    end
		    
		else if ln>=weight*rn then  (*left is too big*)
		    let val lln = size ll
			val lrn = size lr
		    in
			if lrn < lln then  single_R p  else  double_R p
		    end

		else
	             T(v,v',ln+rn+1,l,r)

	    fun add (E,x,x') = T(x,x',1,E,E)
	      | add (T(v,v',w,l,r),x,x') =
	        if x<v then T'(v,v',add(l,x,x'),r)
		else if x>v then T'(v,v',l,add(r,x,x'))
		     (* replace v,v' with x,x'! (blume/4/96) *)
		     else T(x,x',w,l,r)

	    fun concat3 (E,v,v',r) = add(r,v,v')
	      | concat3 (l,v,v',E) = add(l,v,v')
	      | concat3 (l as T(v1,v1',n1,l1,r1), v, v', r as T(v2,v2',n2,l2,r2)) =
		if weight*n1 < n2 then T'(v2,v2',concat3(l,v,v',l2),r2)
		else if weight*n2 < n1 then T'(v1,v1',l1,concat3(r1,v,v',r))
		     else N(v,v',l,r)

	    fun split_lt (E,x) = E
	      | split_lt (t as T(v,v',_,l,r),x) =
		if v>x then split_lt(l,x)
		else if v<x then concat3(l,v,v',split_lt(r,x))
		     else l

	    fun split_gt (E,x) = E
	      | split_gt (t as T(v,v',_,l,r),x) =
		if v<x then split_gt(r,x)
		else if v>x then concat3(split_gt(l,x),v,v',r)
		     else r

	    and delmin (T(v,v',_,E,r)) = (v,v',r)
	      | delmin (T(v,v',_,l,r)) = let val (x,x',l') = delmin l
		                          in (x,x',T'(v,v',l',r))
					 end
	      | delmin _ = raise Match

	    and cat2 (E,r) = r
	      | cat2 (l,E) = l
	      | cat2 (l,r) = let val (x,x',r') = delmin r
		                 in T'(x,x',l,r')
                                end

	    fun concat (E,  s2) = s2
	      | concat (s1, E)  = s1
	      | concat (t1 as T(v1,v1',n1,l1,r1), t2 as T(v2,v2',n2,l2,r2)) =
		if weight*n1 < n2 then T'(v2,v2',concat(t1,l2),r2)
		else if weight*n2 < n1 then T'(v1,v1',l1,concat(r1,t2))
		     else cat2(t1,t2)

	in

	    type  'a intmap = 'a Map

	    val empty = E
		
	    fun singleton (x,x') = T(x,x',1,E,E)

	    fun overlay (E,s2)  = s2
	      | overlay (s1,E)  = s1
	      | overlay (s1 as T(v,v',_,l,r),s2) = 
		let val l2 = split_lt(s2,v)
		    val r2 = split_gt(s2,v)
		in
		    concat3(overlay(l,l2),v,v',overlay(r,r2))
		end

	    val add = add

	    fun difference (E,s)  = E
	      | difference (s,E)  = s
	      | difference (s, T(v,_,_,l,r)) =
		let val l2 = split_lt(s,v)
		    val r2 = split_gt(s,v)
		in
		    concat(difference(l2,l),difference(r2,r))
		end

            exception IntmapF

	    fun lookup set x =
		let fun mem E = raise IntmapF
		      | mem (T(v,v',_,l,r)) = 
			if x<v then mem l else if x>v then mem r else v'
		in mem set end

	    fun fold f base map =
		let fun fold' (base,E) = base
		      | fold' (base,T(v,v',_,l,r)) =
			fold'(fold'(f(v, v', base), l), r)
		in
		    fold'(base, map)
		end

	    fun members m = fold (fn (i,v,res) => (i,v)::res) [] m

	    fun cardinality E = 0
	      | cardinality (T(_,_,n,_,_)) = n
	    
	    fun delete (x,E) = E
	      | delete (x,set as T(v,v',_,l,r)) =
		if x<v then T'(v,v',delete(x,l),r)
		else if x>v then T'(v,v',l,delete(x,r))
		     else cat2(l,r)

	end
    end

(*
 * $Log$
 *)