90356f9993
git-svn-id: https://yap.svn.sf.net/svnroot/yap/trunk@352 b08c6af1-5177-4d33-ba66-4b1c6b8b522a
353 lines
11 KiB
Prolog
353 lines
11 KiB
Prolog
% This file has been included as an YAP library by Vitor Santos Costa, 1999
|
|
|
|
% File : ORDSET.PL
|
|
% Author : R.A.O'Keefe
|
|
% Updated: 22 May 1983
|
|
% Purpose: Ordered set manipulation utilities
|
|
|
|
% In this module, sets are represented by ordered lists with no
|
|
% duplicates. Thus {c,r,a,f,t} would be [a,c,f,r,t]. The ordering
|
|
% is defined by the @< family of term comparison predicates, which
|
|
% is the ordering used by sort/2 and setof/3.
|
|
|
|
% The benefit of the ordered representation is that the elementary
|
|
% set operations can be done in time proportional to the Sum of the
|
|
% argument sizes rather than their Product. Some of the unordered
|
|
% set routines, such as member/2, length/2, select/3 can be used
|
|
% unchanged. The main difficulty with the ordered representation is
|
|
% remembering to use it!
|
|
|
|
:- module(ordsets, [
|
|
list_to_ord_set/2, % List -> Set
|
|
merge/3, % OrdList x OrdList -> OrdList
|
|
ord_add_element/3, % Set x Elem -> Set
|
|
ord_del_element/3, % Set x Elem -> Set
|
|
ord_disjoint/2, % Set x Set ->
|
|
ord_insert/3, % Set x Elem -> Set
|
|
ord_member/2, % Set -> Elem
|
|
ord_intersect/2, % Set x Set ->
|
|
ord_intersect/3, % Set x Set -> Set
|
|
ord_intersection/3, % Set x Set -> Set
|
|
ord_intersection/4, % Set x Set -> Set x Set
|
|
ord_seteq/2, % Set x Set ->
|
|
ord_setproduct/3, % Set x Set -> Set
|
|
ord_subset/2, % Set x Set ->
|
|
ord_subtract/3, % Set x Set -> Set
|
|
ord_symdiff/3, % Set x Set -> Set
|
|
ord_union/2, % Set^2 -> Set
|
|
ord_union/3, % Set x Set -> Set
|
|
ord_union/4 % Set x Set -> Set x Set
|
|
]).
|
|
|
|
/*
|
|
:- mode
|
|
list_to_ord_set(+, ?),
|
|
merge(+, +, -),
|
|
ord_disjoint(+, +),
|
|
ord_disjoint(+, +, +, +, +),
|
|
ord_insert(+, +, ?),
|
|
ord_insert(+, +, +, +, ?),
|
|
ord_intersect(+, +),
|
|
ord_intersect(+, +, +, +, +),
|
|
ord_intersect(+, +, ?),
|
|
ord_intersect(+, +, +, +, +, ?),
|
|
ord_seteq(+, +),
|
|
ord_subset(+, +),
|
|
ord_subset(+, +, +, +, +),
|
|
ord_subtract(+, +, ?),
|
|
ord_subtract(+, +, +, +, +, ?),
|
|
ord_symdiff(+, +, ?),
|
|
ord_symdiff(+, +, +, +, +, ?),
|
|
ord_union(+, +, ?),
|
|
ord_union(+, +, +, +, +, ?).
|
|
*/
|
|
|
|
|
|
% list_to_ord_set(+List, ?Set)
|
|
% is true when Set is the ordered representation of the set represented
|
|
% by the unordered representation List. The only reason for giving it
|
|
% a name at all is that you may not have realised that sort/2 could be
|
|
% used this way.
|
|
|
|
list_to_ord_set(List, Set) :-
|
|
sort(List, Set).
|
|
|
|
|
|
% merge(+List1, +List2, -Merged)
|
|
% is true when Merged is the stable merge of the two given lists.
|
|
% If the two lists are not ordered, the merge doesn't mean a great
|
|
% deal. Merging is perfectly well defined when the inputs contain
|
|
% duplicates, and all copies of an element are preserved in the
|
|
% output, e.g. merge("122357", "34568", "12233455678"). Study this
|
|
% routine carefully, as it is the basis for all the rest.
|
|
|
|
merge([Head1|Tail1], [Head2|Tail2], [Head2|Merged]) :-
|
|
Head1 @> Head2, !,
|
|
merge([Head1|Tail1], Tail2, Merged).
|
|
merge([Head1|Tail1], List2, [Head1|Merged]) :-
|
|
List2 \== [], !,
|
|
merge(Tail1, List2, Merged).
|
|
merge([], List2, List2) :- !.
|
|
merge(List1, [], List1).
|
|
|
|
|
|
|
|
% ord_disjoint(+Set1, +Set2)
|
|
% is true when the two ordered sets have no element in common. If the
|
|
% arguments are not ordered, I have no idea what happens.
|
|
|
|
ord_disjoint([], _) :- !.
|
|
ord_disjoint(_, []) :- !.
|
|
ord_disjoint([Head1|Tail1], [Head2|Tail2]) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_disjoint(Order, Head1, Tail1, Head2, Tail2).
|
|
|
|
ord_disjoint(<, _, Tail1, Head2, Tail2) :-
|
|
ord_disjoint(Tail1, [Head2|Tail2]).
|
|
ord_disjoint(>, Head1, Tail1, _, Tail2) :-
|
|
ord_disjoint([Head1|Tail1], Tail2).
|
|
|
|
|
|
|
|
% ord_insert(+Set1, +Element, ?Set2)
|
|
% ord_add_element(+Set1, +Element, ?Set2)
|
|
% is the equivalent of add_element for ordered sets. It should give
|
|
% exactly the same result as merge(Set1, [Element], Set2), but a bit
|
|
% faster, and certainly more clearly.
|
|
|
|
ord_add_element([], Element, [Element]).
|
|
ord_add_element([Head|Tail], Element, Set) :-
|
|
compare(Order, Head, Element),
|
|
ord_insert(Order, Head, Tail, Element, Set).
|
|
|
|
|
|
ord_insert([], Element, [Element]).
|
|
ord_insert([Head|Tail], Element, Set) :-
|
|
compare(Order, Head, Element),
|
|
ord_insert(Order, Head, Tail, Element, Set).
|
|
|
|
|
|
ord_insert(<, Head, Tail, Element, [Head|Set]) :-
|
|
ord_insert(Tail, Element, Set).
|
|
ord_insert(=, Head, Tail, _, [Head|Tail]).
|
|
ord_insert(>, Head, Tail, Element, [Element,Head|Tail]).
|
|
|
|
|
|
|
|
% ord_intersect(+Set1, +Set2)
|
|
% is true when the two ordered sets have at least one element in common.
|
|
% Note that the test is == rather than = .
|
|
|
|
ord_intersect([Head1|Tail1], [Head2|Tail2]) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_intersect(Order, Head1, Tail1, Head2, Tail2).
|
|
|
|
ord_intersect(=, _, _, _, _).
|
|
ord_intersect(<, _, Tail1, Head2, Tail2) :-
|
|
ord_intersect(Tail1, [Head2|Tail2]).
|
|
ord_intersect(>, Head1, Tail1, _, Tail2) :-
|
|
ord_intersect([Head1|Tail1], Tail2).
|
|
|
|
ord_intersect(L1, L2, L) :-
|
|
ord_intersection(L1, L2, L).
|
|
|
|
|
|
% ord_intersection(+Set1, +Set2, ?Intersection)
|
|
% is true when Intersection is the ordered representation of Set1
|
|
% and Set2, provided that Set1 and Set2 are ordered sets.
|
|
|
|
ord_intersection(_, [], []) :- !.
|
|
ord_intersection([], _, []) :- !.
|
|
ord_intersection([Head1|Tail1], [Head2|Tail2], Intersection) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_intersection(Order, Head1, Tail1, Head2, Tail2, Intersection).
|
|
|
|
ord_intersection(=, Head, Tail1, _, Tail2, [Head|Intersection]) :-
|
|
ord_intersection(Tail1, Tail2, Intersection).
|
|
ord_intersection(<, _, Tail1, Head2, Tail2, Intersection) :-
|
|
ord_intersection(Tail1, [Head2|Tail2], Intersection).
|
|
ord_intersection(>, Head1, Tail1, _, Tail2, Intersection) :-
|
|
ord_intersection([Head1|Tail1], Tail2, Intersection).
|
|
|
|
|
|
|
|
|
|
% ord_intersection(+Set1, +Set2, ?Intersection, ?Difference)
|
|
% is true when Intersection is the ordered representation of Set1
|
|
% and Set2, provided that Set1 and Set2 are ordered sets.
|
|
|
|
ord_intersection(L, [], [], L) :- !.
|
|
ord_intersection([], L, [], L) :- !.
|
|
ord_intersection([Head1|Tail1], [Head2|Tail2], Intersection, Difference) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_intersection(Order, Head1, Tail1, Head2, Tail2, Intersection, Difference).
|
|
|
|
ord_intersection(=, Head, Tail1, _, Tail2, [Head|Intersection], Difference) :-
|
|
ord_intersection(Tail1, Tail2, Intersection, Difference).
|
|
ord_intersection(<, Head1, Tail1, Head2, Tail2, Intersection, [Head1|Difference]) :-
|
|
ord_intersection(Tail1, [Head2|Tail2], Intersection, Difference).
|
|
ord_intersection(>, Head1, Tail1, Head2, Tail2, Intersection, [Head2|Difference]) :-
|
|
ord_intersection([Head1|Tail1], Tail2, Intersection, Difference).
|
|
|
|
|
|
|
|
% ord_seteq(+Set1, +Set2)
|
|
% is true when the two arguments represent the same set. Since they
|
|
% are assumed to be ordered representations, they must be identical.
|
|
|
|
|
|
ord_seteq(Set1, Set2) :-
|
|
Set1 == Set2.
|
|
|
|
|
|
|
|
% ord_subset(+Set1, +Set2)
|
|
% is true when every element of the ordered set Set1 appears in the
|
|
% ordered set Set2.
|
|
|
|
ord_subset([], _) :- !.
|
|
ord_subset([Head1|Tail1], [Head2|Tail2]) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_subset(Order, Head1, Tail1, Head2, Tail2).
|
|
|
|
ord_subset(=, _, Tail1, _, Tail2) :-
|
|
ord_subset(Tail1, Tail2).
|
|
ord_subset(>, Head1, Tail1, _, Tail2) :-
|
|
ord_subset([Head1|Tail1], Tail2).
|
|
|
|
|
|
|
|
% ord_subtract(+Set1, +Set2, ?Difference)
|
|
% is true when Difference contains all and only the elements of Set1
|
|
% which are not also in Set2.
|
|
|
|
|
|
ord_subtract(Set1, [], Set1) :- !.
|
|
ord_subtract([], _, []) :- !.
|
|
ord_subtract([Head1|Tail1], [Head2|Tail2], Difference) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_subtract(Order, Head1, Tail1, Head2, Tail2, Difference).
|
|
|
|
ord_subtract(=, _, Tail1, _, Tail2, Difference) :-
|
|
ord_subtract(Tail1, Tail2, Difference).
|
|
ord_subtract(<, Head1, Tail1, Head2, Tail2, [Head1|Difference]) :-
|
|
ord_subtract(Tail1, [Head2|Tail2], Difference).
|
|
ord_subtract(>, Head1, Tail1, _, Tail2, Difference) :-
|
|
ord_subtract([Head1|Tail1], Tail2, Difference).
|
|
|
|
|
|
% ord_del_element(+Set1, Element, ?Rest)
|
|
% is true when Rest contains the elements of Set1
|
|
% except for Set1
|
|
|
|
|
|
ord_del_element([], _, []).
|
|
ord_del_element([Head1|Tail1], Head2, Rest) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_del_element(Order, Head1, Tail1, Head2, Rest).
|
|
|
|
ord_del_element(=, _, Tail1, _, Tail1).
|
|
ord_del_element(<, Head1, Tail1, Head2, [Head1|Difference]) :-
|
|
ord_del_element(Tail1, Head2, Difference).
|
|
ord_del_element(>, Head1, Tail1, _, [Head1|Tail1]).
|
|
|
|
|
|
|
|
% ord_symdiff(+Set1, +Set2, ?Difference)
|
|
% is true when Difference is the symmetric difference of Set1 and Set2.
|
|
|
|
ord_symdiff(Set1, [], Set1) :- !.
|
|
ord_symdiff([], Set2, Set2) :- !.
|
|
ord_symdiff([Head1|Tail1], [Head2|Tail2], Difference) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_symdiff(Order, Head1, Tail1, Head2, Tail2, Difference).
|
|
|
|
ord_symdiff(=, _, Tail1, _, Tail2, Difference) :-
|
|
ord_symdiff(Tail1, Tail2, Difference).
|
|
ord_symdiff(<, Head1, Tail1, Head2, Tail2, [Head1|Difference]) :-
|
|
ord_symdiff(Tail1, [Head2|Tail2], Difference).
|
|
ord_symdiff(>, Head1, Tail1, Head2, Tail2, [Head2|Difference]) :-
|
|
ord_symdiff([Head1|Tail1], Tail2, Difference).
|
|
|
|
|
|
|
|
% ord_union(+Set1, +Set2, ?Union)
|
|
% is true when Union is the union of Set1 and Set2. Note that when
|
|
% something occurs in both sets, we want to retain only one copy.
|
|
|
|
ord_union(Set1, [], Set1) :- !.
|
|
ord_union([], Set2, Set2) :- !.
|
|
ord_union([Head1|Tail1], [Head2|Tail2], Union) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_union(Order, Head1, Tail1, Head2, Tail2, Union).
|
|
|
|
ord_union(=, Head, Tail1, _, Tail2, [Head|Union]) :-
|
|
ord_union(Tail1, Tail2, Union).
|
|
ord_union(<, Head1, Tail1, Head2, Tail2, [Head1|Union]) :-
|
|
ord_union(Tail1, [Head2|Tail2], Union).
|
|
ord_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union]) :-
|
|
ord_union([Head1|Tail1], Tail2, Union).
|
|
|
|
|
|
% ord_union(+Set1, +Set2, ?Union, ?Difference)
|
|
% is true when Union is the union of Set1 and Set2 and Difference is the
|
|
% difference between Set2 and Set1.
|
|
|
|
ord_union(Set1, [], Set1, []) :- !.
|
|
ord_union([], Set2, Set2, Set2) :- !.
|
|
ord_union([Head1|Tail1], [Head2|Tail2], Union, Diff) :-
|
|
compare(Order, Head1, Head2),
|
|
ord_union(Order, Head1, Tail1, Head2, Tail2, Union, Diff).
|
|
|
|
ord_union(=, Head, Tail1, _, Tail2, [Head|Union], Diff) :-
|
|
ord_union(Tail1, Tail2, Union, Diff).
|
|
ord_union(<, Head1, Tail1, Head2, Tail2, [Head1|Union], Diff) :-
|
|
ord_union(Tail1, [Head2|Tail2], Union, Diff).
|
|
ord_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union], [Head2|Diff]) :-
|
|
ord_union([Head1|Tail1], Tail2, Union, Diff).
|
|
|
|
|
|
|
|
% ord_setproduct(+Set1, +Set2, ?Product)
|
|
% is in fact identical to setproduct(Set1, Set2, Product).
|
|
% If Set1 and Set2 are ordered sets, Product will be an ordered
|
|
% set of x1-x2 pairs. Note that we cannot solve for Set1 and
|
|
% Set2, because there are infinitely many solutions when
|
|
% Product is empty, and may be a large number in other cases.
|
|
|
|
ord_setproduct([], _, []).
|
|
ord_setproduct([H|T], L, Product) :-
|
|
ord_setproduct(L, H, Product, Rest),
|
|
ord_setproduct(T, L, Rest).
|
|
|
|
ord_setproduct([], _, L, L).
|
|
ord_setproduct([H|T], X, [X-H|TX], TL) :-
|
|
ord_setproduct(T, X, TX, TL).
|
|
|
|
|
|
ord_member(El,[H|T]):-
|
|
compare(Op,El,H),
|
|
ord_member(Op,El,T).
|
|
|
|
ord_member(=,_,_).
|
|
ord_member(>,El,[H|T]) :-
|
|
compare(Op,El,H),
|
|
ord_member(Op,El,T).
|
|
|
|
ord_union([], []).
|
|
ord_union([Set|Sets], Union) :-
|
|
length([Set|Sets], NumberOfSets),
|
|
ord_union_all(NumberOfSets, [Set|Sets], Union, []).
|
|
|
|
ord_union_all(N,Sets0,Union,Sets) :-
|
|
( N=:=1 -> Sets0=[Union|Sets]
|
|
; N=:=2 -> Sets0=[Set1,Set2|Sets],
|
|
ord_union(Set1,Set2,Union)
|
|
; A is N>>1,
|
|
Z is N-A,
|
|
ord_union_all(A, Sets0, X, Sets1),
|
|
ord_union_all(Z, Sets1, Y, Sets),
|
|
ord_union(X, Y, Union)
|
|
).
|
|
|