108 lines
2.7 KiB
Perl
108 lines
2.7 KiB
Perl
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% clp(q,r) version 1.3.2 %
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% %
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% (c) Copyright 1992,1993,1994,1995 %
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% Austrian Research Institute for Artificial Intelligence (OFAI) %
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% Schottengasse 3 %
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% A-1010 Vienna, Austria %
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% %
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% File: squares.pl %
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% Author: Christian Holzbaur christian@ai.univie.ac.at %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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/*
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This beautiful example of disequations at work is due
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to [Colmerauer 90]. It addresses the task of tiling a rectangle
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with squares of all-different, a priori unknown sizes. Here is a
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translation of the original Prolog-III program to clp(q,r)
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[Colmerauer 90]
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Colmerauer A.: An Introduction to Prolog III,
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Communications of the ACM, 33(7), 69-90, 1990.
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| ?- length(L,9),filled_rectangle(A,L).
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A = 33/32,
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L = [15/32,9/16,1/4,7/32,1/8,7/16,1/32,5/16,9/32] ? ;
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A = 69/61,
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L = [33/61,36/61,28/61,5/61,2/61,9/61,25/61,7/61,16/61] ?
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*/
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rectangle( A, Rs) :-
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Rs = [X1,X2,X3,X4,X5,X6,X7,X8,X9],
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filled_rectangle( A, Rs).
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filled_rectangle( A, C) :-
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{ A >= 1 },
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distinct_squares( C), % also acts as generator [], [_], [_,_], ...
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filled_zone( [-1,A,1], _, C, []).
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distinct_squares( []).
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distinct_squares( [B|C]) :-
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{ B > 0 },
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outof( C, B),
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distinct_squares( C).
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outof( [], _).
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outof( [B1|C], B) :-
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{ B =\= B1 },
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outof( C, B).
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filled_zone( [V|L], [V|L], C0, C0) :-
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{ V >= 0 }.
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filled_zone( [V|L], L3, [B|C], C2) :-
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{ V < 0 },
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placed_square( B, L, L1),
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filled_zone( L1, L2, C, C1),
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{ Vb=V+B },
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filled_zone( [Vb,B|L2], L3, C1, C2).
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placed_square( B, [H,H0,H1|L], L1) :-
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{ B > H, H0=0, H2=H+H1 },
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placed_square( B, [H2|L], L1).
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placed_square( B, [B,V|L], [X|L]) :-
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{ X=V-B }.
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placed_square( B, [H|L], [X,Y|L]) :-
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{ B < H, X= -B, Y=H-B }.
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%
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% first nontrivial solution has 21 squares ...
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%
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perfect( S) :-
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{ A = 1 },
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distinct_squares( S),
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length( S, Len), Len > 1,
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print( try(Len)), nl,
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flush_output,
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time( filled_zone( [-1,A,1], _, S, [])).
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/*
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try(2)
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%%% Timing 00:00:00.030 0.030
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try(3)
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%%% Timing 00:00:00.070 0.070
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try(4)
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%%% Timing 00:00:00.270 0.270
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try(5)
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%%% Timing 00:00:01.060 1.060
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try(6)
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%%% Timing 00:00:04.470 4.470
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try(7)
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%%% Timing 00:00:19.960 19.960
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try(8)
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%%% Timing 00:01:33.380 93.380
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try(9)
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%%% Timing 00:07:27.380 447.380
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try(10)
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%%% Timing 00:37:03.770 2223.770
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try(11)
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%%% Timing 03:11:38.380 11498.380
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try(12)
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%%% Timing 16:18:43.110 58723.110
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*/
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